- Email: [email protected]
Inclusive π+ and π− distributions in electroproduction on protons
Nuclear Physics B54 (1973) 381-410. North-Holland Publishing Company
INCLUSIVE
7r+ A N D 7r- D | S T R I B U T 1 O N S
IN E L E C T R O P R O D U C T I O N
ON PROTONS
I. D A M M A N N , C. D R I V E R , K. HI~INLOTH, G. H O F M A N N , F. J A N A T A , P. KAROW, D. LUKE, D. SCHM1DT and G. SPECHT
Deutsches Elektronen-Synchrotron DESY. Hamburg Received 19 January 1973
Abstract : We investigate the inclusive pion spectra in the electroproduction reaction ep ~ e~r± + anything in a coincidence experiment at DESY. Data are presented from the kinematical region 0.1 < tq21 < 0.8 GeV 2 and 3.15 < W < 2.8 GeV as a function of the transverse momentum squared p}, the Feynman variable x, and the azinmth angle g,. The charge ratio 7r+/rr- is given in terms of the variables q2 and x. The inclusive spectra are compared with results from photoproduction.
1. I n t r o d u c t i o n Since in recent experiments on inelastic electron-nucleon scattering the electrop r o d u c t i o n o f various two-body hadronic final states (such as ~N, rrA, pN, KY), ref. [ 1 ], was investigated, there has been increasing interest in inclusive spectra of electrop r o d u c e d hadrons. Knowledge of the inclusive spectra should allow, together with inclusive spectra from p h o t o p r o d u c t i o n , a better understanding of some electromagnetic properties of hadrons. Results from several photoproduction experiments on inclusive pion distributions have been published [ 2 - 7 ] . F r o m electroproduction experiments one expects answers to the following questions: Does the transverse-momentum spectrum depend on q2, the square of the mass of the virtual photon'? How does the longitudinalm o m e n t u m distribution vary with q2? Do the 7r+ and rr spectra depend differently on q - ? Only few pubhshed data on inclusave spectra o f e l e c t r o p r o d u c e d ~pions are available up to n o w : 7r+ and rr- spectra were obtained at Iq21 = 0.7 G e V - and W = 1.93 GeV [8] and at Iq21 = 1.15 GeV 2 and W = 2.63 GeV [9], in b o t h cases for very s m a l l p 2 ~ 0.03 GeV 2 a n d x > 0.1. At Iq2l = 0.3, 0.6 and 1.2 GeV 2, W = 3 GeV, 7r+ p r o d u c t i o n has been measured at --O. 15 < x < - 0 . 0 5 [10]. In a recent streamer chamber e x p e r i m e n t at D E S Y rr data have been obtained for 0.3 < Iq2t < 1.5 GeV 2, W< 2.8 GeV [1 1]. At iq21 = 1.2 GeV 2, W = 2.2 GeV and tq2i = 2.0 GeV 2, W= 2.7 GeV lr -+ spectra have been measured ]12]. ")
.
.
382
L Dammann et al.. Inclusive 7r'- distributions
In this paper we present data on inclusive rr+ and rr duction on protons,
distributions in electropro-
ep -+ err+ + a n y t h i n g , ep -+ err- + anything. These data werc obtained in a coincidence experiment at DESY in the kinematic regions 0.1
2,
<0.3GeV 2
2.15
,
<1.0
,
0<~<360
°
o
In sect. 2 we shall discuss the kinematics. The apparatus and data analysis are described in sects. 3~ 4. The inclusive spectra of rr+ and lr are reported in sect. 5.
2. Kinematical
variables and their ranges
We use tile R)llowing notation :e, e', q, p, n are the four-momenta of the particles : the primary and tile scattered lepton, the virtual photon, the target and the detected pion: q2 = (e e') 2 is tile mass squared of the virtual l)hoton 3%; 1'92 = (q + p)2 is the ,nass squared of the outgoing hadron system; p2 is the transverse-momentum */ * squared of the rr (with respect to the direction o f q ) : x =pll Pmax is Feynman's longitudinal variable (p~ = hmgitudinal momentum of the rr with respect to the direction of q; P:i~mx = maximum possible momentum of the rr for fixed W; * denotes the c.m.s, of the qp system); and ~ is the azimuthal angle of the rr. q5 is the angle between the polarization plane, subtended by e and ¢', and the production plane, subtended by q and rr. Assuming one-photon exchange the virtual photoproduction cross section d3o/dx dp 2 d~ can be derived from the experimental cross section by the relation
ll31 d5o __ dq 2 dW 2 dx dp2T d~
-
r t 2r,
d3o .... dx dp 2 d~
.
The kinematical factor a
1
W2
M~
I~|
4(2~)2
E,'~"dMp"~ Iq2t
1 -
e
describes the virtual-photon flux (E 0 = lab energy of the primary lepton), and e= (l+.~q 2 ) - - - 7 tg2 {Oee' hq-I
l
is tile transverse-photon polarization.
I. D a m m a n n
383
e t al., I n c l u s i v e 7r± d i s t r i b u t i o n s
Iq21 Range of Acceptance
[G,v21
1.2 -~ 120°<$<2/,0° N 0<$<3600 ll;rlll ^
E0:5./,G~eV~
w [GeV]
~'ig:
Fig. 1. A c c e p t a n c e range Iq2l v e r s u s W o f the a p p a r a t u s for two d i f f e r e n t energies E 0 o f the p r i m a r y lepton. The areas labelled A or B were used in the analysis of this paper. ] ' h e d e n s i t y of the lines i n d i c a t e s the d e n s i t y of events.
Table 1 K i n e m a t i c regions region A Eli
(GeV)
4.9
W
(GeV)
2.15
Iq21
/ G e V 2)
0.45
x PT2
e
0.6
5.4 2.3
2.2
0.65 -- 1.0
(GeV 2 )
0
0.05
(deg)
0
- 360
0.77-
region 13
0.79
4.9
5.4
2.4
2.4
2.8
2.4
0.6
0.8
0.1
0.4
0.2
0.6
0.6
- 1.0
0.4
1.0
0.4
- 1.0
0
~ 0.05
0
0.3
0
0
- 360
60
+ 60
60
+ 60
0.78
0.51
0.58
0.59
O.65
0.77
2.8
0.3
l. Dammann et al., Inclusive 7r~ distributions
384
Tile virtual photoproduction cross section is expressed in terms of the two transverse and the longitudinal components of the virtual-photon polarization : d2OT d3o 1 t d2°u d2°L y ..... \-+e----+e - - - - cos 2~ dx dp~- d~ 2rr dx dp~ cLv dPT dx dPT
(I)
d2°l ) +x,/22e(e+ 1) . . . . . cos0 . dx dplIn the limit q - -+ 0, eq. (1) has to approach the differential cross section for unpol3' 3' . . . . . . arized real photons. The term d - o u / d x dp~ is the dHferentml cross secnon lor u n polarized transverse wrtual photons: e d-oT/dX dp~, cos 24~ is due to the photon transverse linear polarization: e d2oL/dX dp 2 accounts for longitudinal polarized photons, and X / 2 c ( e + 1) d2ol/dX dpq, cos ~ describes the interference between the transverse and longiludmal components. The differential cross section will be given in the Lorentz-invariant form •
k d2~° = ~ E* dp3
3'
")
.
d3o
P,~mx dx dp~ dq5
where p is the three-molnentum and E* the energy of the detected pion. We obtain
d2OL d2OT l:" d3° E* ( . d - °.u +,e . . . 3" + e cos 2g5 dp 3 rr P~nax I, dx dp~r ckv dp-~ dx dPT d2ol \ + ,,/2_ e(e + 1) . . . . cos •/ . ] dx dPT
(2)
Tire data which we will report were obtained at two different energies of tile primary lepton, E 0 = 4.9 and 5.4 GeV. We measured 22 000 and 35 700 events of the reacuon ep -~ err + anything, respecnvely, and 13 000 and 15 500 events of the reaction ep -+ err + anything. Fig. 1 and table 1 show the regions o f q 2 and W which were covered by our data. We distinguish between two kinematical ranges. In range A all azimuthal angles 0 < @< 360 ° are accepted. In this range we have investigated the qS-dependence according to eq. (1). In range B the acceptance of the apparatus is limited to - 6 0 ° < 4~< +60°; here we have investigated the cross sections averaged over the ¢)-interval. Tile bulk of events is lying in range B. •
-b
•
.
385
L Dammann et al., Inclusive ~¢+distributions
3. Apparatus
The apparatus is shown in fig. 2. The scattered lepton and the produced rr nreson are detected in coincidence in two spark-chamber spectrometers. After being deflected by a magnetic field both particles are detected in optical spark chambers and identified in ~erenkov and shower counters. More details of the apparatus are given elsewhere [14, 15]. To allow a comparison of ep -+ err+ + anything and ep -+ err + anything with the smallest possible systematic errors we measured both of these reactions with the same apparatus under identical magnetic-field configurations. We therefore used a primary electron beam for the rr+ data and a primary positron beam for the rr data. We only switched the polarities of the magnets in both spectrometers. The absolute field configuration remained unchanged. The spark chamber tracks and all counter infomration were photographed. The pictures were analyzed automatically [ 16].
\
BEAM T
~
\ \ItU-%'~\\k../----- /
~{
~
~ / I-- ~
~/~
i \ %O n i E%I-I~/I1~1%7\N N % \
/
/. ~/
~
/
FARADAY FAR CUP
/
r~ Fig. 2. Experimental layout. 4. Data analysis and corrections The calculation of the differential cross section d5o/dq 2 dW 2 dx dPT d~ and the corrections for the finite acceptance of the apparatus have been performed as described elsewhere [14, 171.
386
l. Dammann et al., Inclusive rr+-distributions
From the data we have included the 7vp -+ rr+n events because of the following reason. ") In the reactmn 7 vP -+ rr ,~n the -varmbles p.~ and x are not independent , + . . but are . related by the equation @ + (xp*) 2 = p* = m o m e n t u m ot rr wluch Is a function of W only. At fixed W and for very small PT' the measured cross section d2o/dx d p ; for the rr+n reaction shows a small peak n e a r x = I. With increasing p~- the position of this peak will shift to lower x-values. In consequence, when averaging over aP2T interval, the rr+n peak is smeared out to a broad bump in x which obscures events of reactions other than "Tvp -+ 7r+n, even though they are clearly separated in a missing-mass plot. In order to see more clearly the contributions from reactions other than + 7v p -~- 7r n, especially for a comparison with the reaction 7v p -+ rr + anything, where no two-particle final state is possible, we have excluded the rr+n events by a missing-mass cut. The cross sections have been corrected for efficiency losses in the trigger, ('erenkov and shower counters, for pion interaction and pion decay and for loss in the automatic data analysis procedure. The uncertainty of all these corrections including the uncertainty of the intensity of the primary beam add up to a systematic error of less than 4%. This systematic error is not included in the errors given in the figures and tables. The radiative corrections have n o t been taken into a c c o u n t for the experimental data as presented in this paper. They have been estimated in a crude approximation according to ref. [ 18]. They cause an increase of the cross sections of (10 + 6)% within the kinematic range of this experiment. In the ratio of rr+ and ~'- cross sections considered below, radiative corrections ahnost cancel. •
+
.
5. Results 5.1. Cross-section d e p e n d e n c e on the a z i m u t h a l angle
The 0-dependence was investigated in the kinematic regions A within the entire range 0
0.65
0.70-0.80
2.42 0 . 6 0 - 0 . 7 0
2.20-2.42
2.20
2.15 - 2.30 0.55
0.45-0.55
2.15-2.30
0 . 6 - 0.7 0.7 0.8 0.8 0.9
0.6-0.7 0.7 0.8 0.8 0.9
0.6 0.7 0.7 0.8 0.8-0.9
0.6-0.7 0.7 - 0.8 0.8 0.9
Iq21 (GeV 2) x
W(GeV)
_
30
19.2-+ 15.0+ 20.8+-
30.9+ 34.9+ 38.4+ 6.0 4.4 5.3
5.5 5.1 5.3
47.2+ 23.1 23.2+ 8.1 20.5± 7.6
16.3± 11.4 50.6 -+ 9.0 63.3+ 9.6
0
0 (deg)
n
25.1± 26.4+22.7±
41.1± 27.6± 42.7± 6.2 5~4 5.1
5.9 3.9 5.1
25.5+ 14.5 18.4± 6.4 30.7+ 8.2
55.1 ± 19.4 26.5 + 5.6 54.7± 7.9
30 -- 60
_
28.4+ 23.2± 25.0+
4.7 3.7 3.9
24.2+ 3.6 23.4± 3.1 33.t + 3.9
17.8± 17.5± 24.1±
29.3± 17.8± 31.5±
22.8± 20.9± 29.8±
3.l 2.6 3.3
3.7 2.5 3.8
9.2 4.0 5.1
45.6± 13.1 40.0± 5.0 47.2± 5.8
43.0+ 13.5 29.1± 4.8 47.1± 6.2 46.1± 14.3 31.7+ 6.1 41.2± 6.9
90
7r +
60 - 90
120
Table 2 Cross section E d3o/dp 3 (,ub/GeV 2) as a function o r e in the kinematic range p ~ < 0.05 GcV 7 for 3,vp ~
22.3-+ 20.0± 26.4±
26.3± 21.2+30.3+
24.4± 26.3± 35.0±
3.3 2.6 3.5
3.9 3.1 4.7
9.7 4.3 5.4
43.4± 17.5 43.4+ 5.9 27.2± 4.9
120 - 150
+ anything
180
19.9-+ 18.8-+ 15.8+
29.8± 19.5± 31.1±
3.9 3.0 3.1
6.1 3.9 6.0
22.0-+4.9 29.6±5.8
24.9± 5.9 50.0-+ 8.4
150
9.
388
1. D a m m a n n
e t al., I n c l u s i v e 7r± d i s t r i b u t i o n s
~'vP ~rc÷÷anything 2.15
,
r
i
I
PT2<0.05GeV 2
i
,
i
, -
r
,
i
r
r
i
,
,
0.45 < Iq 21< 0.55 GeV 2 O,6
I0(
~
II
0.7< X< 0.8
0.8
I00
>
4 ,-+-*-+
::::I.
I
I
f
i
f
I
I
I
I
I
I
I
i
I
i
0
0.55 < [q21 < 0.65 GeV2 I0 ~ I I
0.6
"7
Lid
t
0"8< X<0"g
100
+
o!J +:
0°
60°
Vv P ~
120°
0°
60 °
120°
180°
~÷÷anything p?< 0.05GeV 2
2.20
so :t.
+
~-
o
~
%j,_
b
so
o
J
°7
i00 •
0.~<~<0.7
LU
0.7<~<0.8
~
0.8<×
±
so
0°
~
50°
120°
0°
- 100 i 5o
60 °
Fig. 3a.
120°
0°
60°
120°
180°
L Dammann
389
e t al., I n c l u s i v e rr+- d i s t r i b u t i o n s
3%P~ - * o n y t h i n g 2.15 < W < 2.30GeV f
f
f
;
,
,
4 < 0.05 GeV 2 ,
i
,
~
i
r
i
J
f
I
i
i
0.45 < Iq21< 0.55GeV 2 0.6< x<0.7
10(
>e
0.7
0.8
0 . 8 < x < 0.9
0 . 9 < x < 1.0
100
50
so
Jo
.=. o
I
I
I
I
I
I
I
I
I
I
I
I
J
i
I
I
I
I
t
0
I
0.554 h21<0.65GeV 2 iii
0.6< x<0.7
100
__
0.7-,= x < 0 . 8
-
C)o
60°
120°
__
0.8< x< 0.9
0.9
-
0o
60°
120°
100
50
-
0o '
6'0° '
120o'
0o
60o
120°
180°
qb
Yv P ~ - +
anything
2.20
p2 <0.05GeV 2 0.6<1q21 < 0.TGeV 2
10C
>
5c
0 ,.-t
I
i
I
I
I
I
I
I
I I I I I ; 0.7
I
:
1
1
~
:
:
',
,-41
o
"~1-~ 10, iii
, ~.-,+,-.-,+t+~, , + ~ + S r ~ F , 60 °
120 °
0°
60 °
120 °
0°
,+,+,+,~:~-,+,+,+,60 °
120 °
0°
60 °
120 °
180 °
Fig. 3b. Fig. 3. lnvariant cross section E d 3 a / d p 3 as a function of the azimuthal angle ~ for different W, 2 q and x intervals. Kinematic range : 0 < p~, < 0.05 GeV ~.
2.42
2.42
2.20
2.20
0.6 0.7 0.7 0.8 0.8-0.9 0.9 1.0
0.7 0.8 0.9 1.0
10.7± 15.8+ 4.1+
18.5± 16.4+ 23.9+ 25.2±
5.3 6.4 2.9
6.2 4.9 5.6 5.5
30.9+21.8 10.3± 7.2 40.1+12.6 12.4± 6.1
0.6 0.7 0.7 0.8 0 . 8 - 0.9 0.9-1.0
30
29.1~ 14.5 28.3+11.3 46.1+ 9.6 24.9± 6.4
0
0.6 0.7 0.7 0.8 0.8-0.9 0.9 1.0
0.7/t 0.6 0.7 0.8 0.9
0.70-0.80
0.60
2.30 0.55
2.15
0.65
2.30 0 . 4 5 - 0 . 5 5
Iq21(GeV 2) x
2.15
W(GeV)
(deg)
ll.l± 15.4± 8.1±
16.6~ 15.4~ 27.7+ 18.6+
4.9 5.7 3.6
5.2 4.0 5.5 4.2
11.8±11.8 24.0± 9.6 37.8±10.8 7.3+ 4.1
20.7+10.2 27.5± 7.3 41.3+ 8.1 24.9+ 5.8
3 0 - 60
90
120
21.2+4.0 17.9~3.4 27.4±4.5 14.2~3.4 10.6±3.1 5.0±1.9 13.7±3.3 10.8±2.9
5.4±3.0 9.2±3.2 6.8+2.7 13.4+3.7
21.3±6.1 22.7±5.0 34.6±6.3 19.8±4.7
26.2±5.7 21.9±4.3 31.8±5.4 16.3±3.8
90
18.6±4.4 17.0±3.7 25.2±4.5 23.2±4.3
9.1±6.5 15.5±5.5 27.5±6.6 27.0±6.2
34.1±9.1 24.6±5.5 54.3±7.7 13.4±3.7
60
18.9±5.6 15.5±4.6 12.1+4.5 11.0+4.9 13.0±3.6 8.6+2.7 14.0~3.7 10.8+3.4
7.4±2.2 14.8±3.1 8.3±2.5 7.7±2.5
27.0+7.2 13.4±4.4 24.6±5.9 10.2±3.8
7.9 6.7 7.5 6.3
25.2 23.3 32.0 20.0
+ + ± ±
180
150
16.0±3.7 18.2±3.9 15.0~4.0 22.6±5.4
15.2+4.1 19.2±4.3 22.2±4.7 24.1±5.1
23.2±5.4 17.7±4.3 20.7a4.7 9.7±3.2
1 2 0 - 150
Table 3 Cross section E d3o/dp 3 (,ub/GeV 2 ) as a function o14~ in the kinematic range p~, < 0.005 GeV 2 for 7vp ~ 7r- + anything
NI+
+
1. Dammann et al., Inclusive ~- distribunons
391
This can be partly due to 7rA(1236) p r o d u c t i o n ( c o n t r i b u t i o n to the region 0.8 < x < 0.9) for which a non-vanishing interference term has already been measured 119]. On the other hand, the transverse c o n t r i b u t i o n d2OT/dX dp2r_ is always found to be compatible with zero.
5.2. Cross-section dependence on the transverse m o m e n t u m squared p 2 We now turn to the study o f the p2, x and q2 dependences. This was done in the range 60 ° < q~ < + 60 °, where most of our events are lying (see fig. 1). The average of eq. (2) over this ~b-range is
f [I-tb/GeV2]j ~'v p--rt'+anythingj ~'v P--rc-.anythin, I 1001 o.t,.x-0.7 / 0.7.x-0.9 /o.t,.x-0.7 ' 0.7-x-0.9 Iq21[GeM2] STREAMEIq CHAMBER
',X--~ :
÷
:
i
"~..~;~= : "
10-
.
soL._
:
?
20
'
10
"
2
,
l
-
-
,
,
] o,
o.~ o.~I
0A
- 0.5
a=5
°ol
o
o.l-o,2
\..
-
,
,
r,
o. -oo
a:8 ,
o,
. . . . . .
o.~ o.~,
o.~ o.~ o.~i
PT2[GeV2]
. . . . .
o, o.~ o.~
t:ig. 4. lnvariant cross section f, as defined in subsect. 5.1, as function of the transverse momentum squared p~ for different x and q2 intervals. For comparison data at q2 = 0 [6] are shown. Kinematic range : 2.5 < W< 2.8GeV, 60 ° < ~ < + 6 0 ° ; f o r d a t a a t q 2 = 0 : 2.4< W< 2.SGeV. 0 < ~, < 360 °.
L Dammann et al., Inclusive n± distributions
392 +60 ° f 27r
E*
d3o w
dO
_60o rrp,~mx dx dp2T dq5
E*
d2°l
( d2°u --
d2°T
+e--~"
rcp*nax \ d x dPT
+0.826x/22e(e+l)
+ 0.413e----
dx dp 2 d2°l
dx dp2T
1
dx dp~T / "
ASSUlning for region B a similar ~b-dependence as was found in region A, we estimate that f is well approximated by the ~-independent cross section : E*
f
7rpt~mx
t
t
d2°u
-5
ely dp~
d2°L dx dPT
The dependence of the invariant cross section on the transverse m o m e n t u m I + squared p~- for the rr and rr data is shown in figs. 4a, b and tables 4a, b for different x and q2 intervals. One sees a rapid decrease of the cross section with increasingp 2. for both the rr+ and rr " data. Within statistics the spectra show in general an exponential behaviour except at small values of p~- where they become more flat. This deviation from an exponential is not due to the finite resolution in p~- of our apparatus, because the corrections due to this effect are rather small on the orderof+5%forPT<0.025GeV2andabout l % f o r O . O 2 5 < p 2
"Fable 4 C r o s s sectionf(#b/GeV2) as a l u n c t l o n ol - 6 0 ° <~< + 6 0 ° for + (a) 3,vp ~ rr + a n y t h i n g •
2
PT (GeV2) 0.0 -0.025 0.025 -0.050 0.050 0.075 0.075 0.100 0.100 0.125 0.125 - 0.150 0.150 0.175 0.175 0.200 0.200-0.225 0.225 0.250 0.2511 0.275 0.275 0.300 0.0 - 0.025 0.025 - 0.050 0.050- 0.075 0 . 0 7 5 -- 0 . 1 0 0 0.100-0.125 0.125 0.150 0.150--0.175 0.175 0.200 0.200 0.225 0.225 -0.2511 0.250 - 0.275 1t.275 0.300 (b) 7v p ~ 0.0 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275 0.0 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 11.225 0.250 0.275
-
PT in 2
the k i n e m a t i c r a n g e 2.5 < I¥ < 2.8 G e V ,
Iq21 ( G e V z)
_ •
•
-
-
-
--
rr
0.1
O.4 - 0.7
7 9 . 3 + 17.7 77.0-+ 4 . 4 71.2± 3.2 53.2-+ 2.5 54.0± 2.9 47.7± 3.1 40.1 + 3.4 36.6± 4.0 35.6± 4.9 21.2+ 4.8 1 5 . 3 + 5.1 20.5 ± 9 . 0
0.7
0.9
0.2
43.0± 36. l + 24.2_+ 21.4 ± 19.4± 16.6± 13.5± 13.3+ 8.8± 6.5 +
9.2 4.8 2.9 2.3 2.0 1.9 1.6 1.7 1.5 1.3
69.6± 52.1± 45.6± 43.0± 41.6± 30.6± 23.1± 26.2+ 14.0± 22.2 ± 7.9 ±
6.8 2.6 2.3 2.4 2.9 2.9 3.1 4.4 4.0 7.5 5.7
. 0.2
0.3
0.3
. 0.4
.
. 0.4
. 0.5
0.5
- 0.6
5 8 . 5 ± 3.4 56.8-+ 1.7 48.1 ± 1.4 44.4± 1.5 44.0-+ 1.8 3 8 . 7 + 2.2 34.8+ 2.7 3 3 . 6 ± 3.6 18.6 ± 3.7 15.5-+ 5.0 16.9 + 10.4
43.9± i.9 4 4 . 0 ± 1.3 4 1 . 3 ± 1.3 3 5 . 9 + 1.5 35.3±2.1 32.1 -+ 2.8 22.8-+ 3.3 21.5+ 4.9 1 1 . 7 ± 5.4
35.5 + 1.6 3 4 . 0 ± 1.4 3 2 . 7 + 1.7 27.8-+ 2.1 22.3+2.8 30.0-+ 5.4 2 1 . 9 ± 7.0 1 4 . 8 ± 8.9
30.5-+ 1.9 3 2 . 3 + 2.1 27.3-+ 2.9 18. l ± 4 . 0 3.3±3.3
2 3 . 4 ± 10.6 37.2± 3.6 31.6 ± 2.1 2 9 . 3 ± 1.6 24.2± 1.3 19.4± 1.2 16.0± 1.1 13.9-+ 1.1 10.8± 1.0 8.5 ± 1.0 8.5 ± 1.2 6.4+ 1.3
40.4 ± 29.7+ 26.2 ± 23.5 + 18.6+ 15.7 + 14.7-+ 12.9-+ 9.7± 7.3± 10.9± 7.3+
6.2 1.9 1.4 1.2 1.1 1.1 1.2 1.3 1.4 1.5 2.5 2.6
2 6 . 7 + 3.1 2 4 . 5 ± 1.7 21.1 ± 1.4 20.1 ± 1.4 17.0-+ 1.5 15.1 ± 1.7 10.7_+ 1.7 10.2_+2.1 6 . 3 + 2.1 6 . 0 ± 2.7 2 . 3 + 2.3
2 0 . 8 ± 2.6 211.9± 1.8 19.3 + 1.9 18.8-+ 2.1 11.9-+ 2.2 7.5_+ 2.7 111.5±4.8 5.0+5.0
46.3 ± 40.7 ± 36.5± 34.1± 32.6± 25.8± 22.6± 19.7± 16.0±
1.9 1.3 1.3 1.6 2.0 2.4 3.1 4.3 6.3
3 5 . 3 + 1.3 3 4 . 4 + 1.2 3 0 . 2 ± 1.4 27.1 ± 1.8 26.6-+ 2.7 2 1 . 2 ± 3.4 18.0+5.0 12.1+-7.1 9 . 4 ± 9.4
2 5 . 4 -+ i . 3 2 5 . 4 ± 1.5 19.3 ± 1.8 1 7 . 8 ± 2.5 1 4 . 4 ~ 3.5 12.6 ± 5.8 6.1±6.1
1610± i-.4
4 3 . 7 ± 10.6 28.2± 2.8 2 4 . 5 ± 1.8 23.4± 1.6 19.3+ 1.3 1 7 . 9 + 1.3 14.0± 1.2 9.5 ± 1.1 8.2 + 1.2 6.5 ± 1.2 6.4± 1.4 4.3± 1.5
30.7+4.5 29.7±2.0 2 2 . 2 ± 1.4 21.1 ± 1.4 1 6 . 5 ± 1.3 1 5 . 1 ± 1.4 1 0 . 8 ± 1.4 9 . 6 + 1.5 7 . 9 + 1.7 3 . 3 ± 1.5 4 . 2 + 2.1 2 . 0 ± 2.0
2 2 . 5 ± 2.9 1 7 . 8 ± 1.7 1 6 . 6 ± 1.5 1 5 . 1 + 1.6 1 3 . 0 -+ 1.7 8.2 + 1.6 6 . 7 + 1.9 5.9 * 2.2 8.5 -+ 3.5 2.3 + 2.3
14.1 ± 9.6± 14.9+ 6.9-+ 4.7±
+ anything
0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.25O 0.275 0.300 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275 0.300
x
0.4
0.7
0.7
0.9
53.5± 20.0 40.8± 7.7 3 3 . 2 ± 4.5 28.6+ 3.3 17.3 + 2.2 18.9-+ 2.2 16.6 + 2.1 12.7+ 1.9 10.5 ± 1.8 1 0 . 2 ± 2.0 7 . 9 ± 2.0
1 4 . 9 ± 1.9 11.7-+ 2.9 5 . 0 + 3.5
2.3 1.5 2.1 1.7 1.9
394
I. Dammann et al., Inclusive rr± distributions
5,3. Dependence o] the p ~ slope on x and q2 In order to compare the forms of the different p~. spectra given in figs. 4a, b we have drawn some arbitrary exponentials with wlrious slopes a. One sees that all given values of q2 the rr+ e l e c t r o p r o d u c t i o n data roughly follow an exponential exp( a p ~ , ) w i t h a ~ - 3 . 5 G e V 2in0.4
5.4. x-dependence We study the x - d e p e n d e n c e of the invariant cross section for both the rr+ and rr data in two regions o f P T : (a) at p~, -~ 0 where we compare with,) c o u n t e r experiments on photo- and e l e c t r o p r o d u c t i o n which were p e r f o r m e d near p~, = 0, (b) in the re. ,) gmn P'i < 0.2 ( ; e V 2, where we c o m p a r e the average of the cross section with photop r o d u c t i o n results from a steamer c h a m b e r experiment. Figs. 7a, b and tables 7a, b show ** the " n e a r l y - f o r w a r d " cross section, normalized to Oto f as a function o f x for two ranges o f q 2. The total virtual p h o t o n cross section Otot(q- , W) = ou, m t + e OL,to t has been calculated by interpolation [21 ] of the existing data on the total inelastic cross section oL,tot/Ou,to t = 0.1 8. * e.g. for W = 2.65 (;eV, x = 0.9, Mt = missing inass of tile unobserved hadrnn systenl) > 1.15GeV, only transverse momenta squared in tire regton PT .< ~ 0.07 GeV 2 are kinematically allowed. ** "File cross sections shown in figs. 7a, b have been taken from l:ehrenbach [9 I. This work contains a refined analysis of the data. *** t:orE 0 = 4.9 GeV, W= 2.65 GeV we obtain O t o t (q2, W) = 95.9, 82.8, 73.1, 66.5, 6{).4 ,ub for iq21 = 0.15, 0.25, 0.35, 0.45, 0.55 GeV 2, respectively• .
2
0
'
I
J
+
i
I
0.6
i
[
0.8
-4'-
+
0.~
I
,
aPT),
' max
t ++++++
( Eo= 5.4GeV)
o.2<1021<0.6GeV2
T
+
~._ +__~__#_~_-e --4-
0.1 < Iq21<0.L,GeV 2
(Eo =4"9GeV)
'
Yv P ~ l I + * a n y t h i n g f~e-a-~ 2
q2:0 AHHM Streamerchamber
I
+
1.0
Cl
Ig
2
5
I0
2
S
I0
20
5O
[G~V ~]
I
-
,~
i
I
0.4
t
I
,
I
0,8
+, +++
0.6 X = p,*//£. ''max
i
+
-*-
,
-4--
+
+++++++ +
0.2< Jq2J
IEo:S~OeVl
0.1< Jq2J< O.Z,GeV 2 (Eo =L,.9GeV)
#
'
Yv P --~-+ anything f ~e-a.PT2 q2=O AHHM Streamerchamber
I
1.0
2 • . " 2 o" Fig. 5. Slope a of the form exp( fitted to each PT2 d i. s t r i b. u t i o. n ot. the . m v a. r l a n .t cross s e c n o n f t o t PT2 < 0._3 GeV . The slope a I"S ~wen as a f u n c t i o n o f x for two d i f f e r e n t qZ intervals c o r r e s p o n d i n g to two d i f f e r e n t energies/:'o o f the p r i m a r y lepton. The d a t a at q--= 0 m a r k e d AHHM are t a k e n from ref. [6]. K i n e n l a t i c range: 2.5 < W < 2.8 GeV, 6 0 ° < 0 < + 6 0 ° ; for data at q2 = 0 : 2 . 4 < W < 2.8 GeV, 0<0<+360 °.
sc
be~Z
~1+
4.3±
4.2±
5.3+
5.7±
6,2±
7.3*
15.8±
26.3±10.0
0.55-0.60
0.60-0.65
0.65-0.70
0.70-0.75
0.75-0.80
0.80-0.85
0.85-0.90
0.90-0.95
1.1
0.7
0.6
0.5
0.5
0.5
0.6
28.1*3.8
13.3±0.8
7.0±0.6
3.8±0.5
4.8t0.5
4.6±0.5
3.7±0.5
2.8±0.6
2.7±0.7
4.4±
0.50-0.55
0.8
2.3±2.4 5.4± 1.1
1.2
3.4±
(E o = 5.4 GeV)
(E o = 4.9 GeV)
0.45
0.2 < Iq2[ < 0.6 GeV 2
0.1 < Iq21 < 0.4 GeV 2
+ anything
16.7±2.8
9.9±0.9
7.3±0.8
5.9±0.8
6.0±0.7
5.3±0.7
6.8±0.8
4.7±0.9
4.0±1.0
3.1± 1.2
3.2±1.8
(E o = 4.9 GeV)
0.1 < Iq21 < 0.4 GeV 2
(b) yvp ~ n - + anything
0.2GeV 2
18.2±2.0
10.1±0.8
5.8±0.7
4.6±0.8
5.5±0.8
3.6±0.8
5.1±0.8
3.1±0.9
6.2±1.1
1.8±1.3
(E o = 5.4 GeV)
0.2 < iq21 < 0.6 (;eV 2
ap~-) as a function of x in the kinematic range 2.5 < W < 2 . 8 G c V , - 60 ° < q ~ < + 6 0 ° , p ~ <
0 . 4 5 - 0.50
0.40
x
(a) 7vp ~
Table 5 Slopea(GeV 2 ) o f f ~ e x p (
~.
5.
~t+
2
L D a m m a n n et al., I n c l u s i v e 7r+ d i s t r i b u t i o n s
I
I
I
I
I
I
I
397
I
5'v p ~ g % a n y t h i n g
Q
[GeV-2]
f~e-aP2
10 O.&
'AHHM
+++++++_+_ I I I I f
5
0
I
I
I
0.7
AHHM
Cor
nell
W=2.2Ge o
5
I
I
I
L
0.2
|
I
J
ox
I
I
Q
I
I
0.6 Iq21 [G~v z]
I
I
r
I
0.8
I
I
1.0
1.2
I
i
I
yv p ~ r C * a n y t h i n g
[GeV~]
f -e-Opt2
IC
AHHM
J
0.,'-< x< 0.7
I
I
I
f
I
I
I
t
I
I (28
I
t
0.7 < x-,:O.9 10
~.HHM
+ ++++-+-@
5
00
[
I (22
I
I 0./.
I
I 0.6
1
1,0
I
1.2
Iq~/ [Gev ~] 2
2
Fig. 6. S l o p e a o f t h e f o r m e x p ( - a P T ) f i t t e d to the P T d i s t r i b u t i o n o f the i n v a r i a n t c r o s s secas a f u n c t i"o n 2o f q 2 f o r t w o2 d l"f t"e r e n t x intervals. U•o n f f O r z p T2 < 0 . 2 G e V 2 . T h e slope a 2is given . " Dataatq =0markedAHHMaretakenfromref. [6];atlq I = 1.2GeV a result of the Cornell e x p e r i m e n t [ 1 2 ] is s h o w n . K i n e m a t i c r a n g e : 2.5 < W < 2.8 G e V , - 6 0 ° < O < + 6 0 °; f o r d a t a at q2=0: 2.4< W< 2.8GeV, 0<(9<+ 360 °;fordataatlq21 = 1.2GeV 2:W=2.2 GeV, 0 < <9 < + 3 6 0 ° .
5.7±0.5
4.1±0.4
3.9±0.5
4.5±0.6
2.7±0.7
4.3±0.9
3.0±1.3
0.15-0.20
0.20-0.25
0.25-0.30
0.30-0.35
0.35-0.40
0.40-0.45
0.45-0.50
0.55 - 0.60
0.50-0.55
5.0±0.8
0.4 < x < 0.7
5.9 ± 1.3
6.2±0.6
5.8±0.7
6.5±0.6
7.1±0.6
7.4±0.6
7.5±0.8
7.4±2.1
0.7 < x < 0.9
5.5±1.2
3.9+0.6
4.5±0.7
4.0±0.6
5.3±0.7
6.8±1.1
0.4 < x < 0.7
(b) "~vp ~ rr- + anything
6.3 + 2.6
6.9±0.9
7.0±0.9
8.2±0.8
7.8±0.7
7.6~0.7
7.1±0.8
0.7
/
aP 2T ) as a function' of q2 in the kinematic range 2.5 < W < 2.8 GeV, - 60 ° < ¢ < + 6 0 ° , p 2, < 0.2 GeV 2
(a) -rvp --, ~-+ + anything
exp(-
0.10-0.15
Lq21 (GeV 2)
Table 6 Slope a(GeV - 2 ) o f f ~
3.
4.
.2
oo
I
~,
r
'
I OJ,
J.C.Al=ld'1er]q2] 5GeV 2etCll.
(Eo: 5.4GeV)
• • •
l
I
..._,~_ _q~_
+~r-
I
~
•
I
x=p:/p~,
I
I
I
*
0.8 "FigTe 1.0
(
~ ' - + _~__~__4t- .l~,l~-4t.,
_4._-+-
-+---+--4'-0.2<]q2]<0.6GeV2 .-+.-
IE°= ~'gGeV)
o,. i~ I-o~oov~
J
,
I
++-.--.-÷_,_++~L~
H.Burfeindt et QL
q2=0
~'I' 'i' +
I
YvP --n;*+onything (pT2:0)
.
2
0.2
o
0.5
05
tO
os
1.C
051
10i
÷ +
I
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I
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|
,
I
L~T
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,, • •
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O.Z,
I
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.,
2
x=p{'~/p~na '
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J.C. Aider eta[.
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°2"lq2n~°6 G~v;*-+~-*-++/ T (Eo=5.4GeV)
~- ~ - * -
01<]q2l(0J'GeV (Eo =¢.9GeV)
I
~' ÷ + +
-.--.-_._
H,Burfeindt et al
q2 =0
1
f/O,o,Oev-2] YvP--n:-+°nything (~?=oI
1.0
Fig. 7. Invariant cross section f, as defined in subsect. 5.1, norrnaltzed to Otot(q , W), as a function o f x for t w o dstferent q intervals corresponding to two different energies E 0 of the primary lepton. F o r c o m p a r i s o n data at q2 = 0 [71 and at t q2t = 1.15 GeV z [9] are shown. Kinematic < + 6 0 ° 0 < p 2 < 0 0 2 5 G e V 2" for data at q2 = 0 : I¢ = 2 . 6 3 G e V 0 < ~ < 3 6 0 ° ,0
0.2
o,
o.s
0.5
L(
osl
1.(
0.51
u:)
~Oto,3eV-2]
,g
::11+
e.a
e-,o
0.51 + 0.05
0.52 + 0.06
(t.55 + 0.09
0.56 + 0.12
0.63 ~ 0.20
0.55
0.60
(I.65
0.70
0.60
0.65
0.75 - 0.80
0.80 -- 0.85
0.95
0.55
0.7(t - 0.75
0.90
0.50
0.85
0.90
0.22 ~ 0.15
0.63 ± 0.05
(I.67 + 0.05
0.84 ± 0.08
0.50
(t.45
0.81 + 0.16
0.45
0.1 < fq21 < 0.4 G e V 2
0.40
x
+
(t.22 , 0.13
0.25 ± 0.10
0.46 :- 0.09
0.42 ± 0.06
0.40 ± (I.05
0.47 + 0.04
0.52 ± 0.04
0.57 -+ 0.03
0.62 + 0.03
0.85 ~ 0.06
0.72 +- 0.18
0.2 < Iq21 < 0.6 G e V 2
+ anything
0.52 ± 0.15
0.48 + 0.29
0.40 ± (I.14
0.46 .+- 0.09
0.40 ± 0.06
0.46 + 0.05
0.49 ~ 0.05
0.56 + 0.05
0.67 ÷ 0.05
0.63 -+ 0.04
2
0.22 + 0.08
0.27 ± 0.07
0.38 ± 0.06
0.27 + 0.04
0.3(I -* 0.04
0.37 + 0.04
0.41 ± 0.03
0.50 +- 0.03
(I.52 ± 0.03
0.58 ± 0.04
0.2 < Iq21 < 0.6 G e V 2
60°<~<+60",p~<0.025GeV
0.1 < Iq2i < 0.4 G e V 2
(b) y v p - - rr
2) as a f u n c t i o n o f x in the k i n e m a t i c range 2.5 < W < 2 . 8 G e V ,
(a) yv p - rr + a n y t h i n g
Cross section ratio j[O tot {GeV
Table 7
2
4a.
+
L Darnmann et al., Inclusive n- distributions
401
As we saw in subsect. 5. l that it is uncertain how to extrapolate the p~. distribu2 = 0, we prefer to show the cross section in our lowest p i~ bin, - 1.e. • tion to PT p~- < 0.025 GeV 2. We compare our data with photoproduction values [7] (W = 2.63 GeV p2 ~ 0.01 GeV 2) and with electroproduction values [9] at 2 iq-I = 1.15GeV' 2 j(W= 2.63 GeV, 'P T < ~ 0 . 0 3 G e V 2 ). In general the n ± cross sections decrease when x rises from 0.4 to 0.8. This decrease becomes stronger for larger values of bq2 h. The dependence of the rr+/n -ratio on x is discussed in more detail in subsect. 5.6. In the region 0.8 < x < 0.9 the rr+ and rr-- data indicate a broad bump at all values o f q 2 (except m " n + -photoproducnon), which is due to nA(1236) production. As is known from photo- and electroproduction of nA(1236) [19, 22] the ratio o ( n - A + + ( 1 2 3 6 ) ) / o ( n + A 0 ( 1 2 3 6 ) ) changes from 3 (in photoproduction) to about ") . ") . 1.5 (at iq2i ~ 0.6 GeV-) for fixed transverse m o m e n t u m p~- -~ 0 and fixed W. The rrA(1236) contributions indicated in the inclusive data are in agreement with those expected ratios. In the region x ~> 0.9 it is difficult to compare the n + data obtained in the three different experiments. In the photoproduction experiment [7] no 7r+n peak near x = 1 can be seen because of the finite resolution in x. Front our data the events ep -+ en+n have intentionally been excluded by a missing mass cut (see sect. 4). In the experiment done at Iq21 = 1.15 GeV 2 the n+n events which had not been excluded show a peak near x = 1. Figs. 8a, b and tables 8a, b show the invariant cross sections f/Oto t ofrt + and rrdata, averaged over the range PT < 0.2 GeV 2, as a function o f x for different q2 bins. The photoproduction values from the AHHM-streamer chamber group [6], which are shown for comparison, have been averaged over the same p2T region. For the averaged cross sections, we find in general the same trend as for the forward cross sections. They show a significant decrease with increasing x from 0.4 to 0.8. Within this x-range, the form of the x-distribution seems to be independent of q2; the variation of the absolute height with q2 will be discussed in more detail in the next section. In photoproduction the n + and rr- spectra in the range 0.4 < x < 0.7 are equal in height, whereas in electroproduction the ratio n+/rr increases with increasing Iq21 up to a value of about 2 (a more detailed discussion is given in subsect. + 5.6. The rr photoproductlon data fall more rapidly with x > 0.7 than the n+-electroproduction data. We mention that events of the reaction 7v p -+ n+n(n 0 . .. ) ( 1prong events) were not detected in the n + photoproduction experiment [6]. The authors [6] apply a correction of ~ 10% in the entire x-range due to the Joss of these events. For the ~r+ and rr photo- and electroproduction cross sections a shoulder or a broad bump from rr`5(1236) production is seen in the region 0.8 < x < 0.9 (figs. 8a, b). In the n + photoproduction data this shoulder is smaller because, due to the loss of l-prong events, only ½ oflthe rr+`5°cross section can be seen according to the ratio (,50-+ n - p ) / ( , 5 0 - + nOn)= ~.
402
l. D a m m a n n
e t al., I n c l u s i v e rr+- d i s t r i b u t i o n s
%p--,~%anything 'Io,o,[~v -~] (~,~o~v~) •
I
I
I
I
q2=0
[
~
I
I
-*- 4k-
AHHM
I
I
I
I
q2=0
~
0.1<'q2'< 0.2GeV
0.5
%p--P~-.anything (&~v~)
Z
"~\
"~ + 4,--~_ 0.2<,q 21<0.3GeV2 ~-~
~-
/ / ~
i
i
-~
•÷-
AHHM
*
01< q21<0'2GeV2
~
~'-~
+~~ 0.2
++--~-~=~ \
", ',
o.sl L
i +
= °-'-+
o.~":lq21
4~_
++-.~
"~ ;
0.4
~
\/,
'1 /II
+++4-++ 0.5
0.5
0"11
OD1 0.2
i
I
0.4
]
I 1 0.8I /
0.6 x =p~l/p, I mox
1.0
I
J
0.4
J
I
I
0.6 x=p* , IVPmax
I
0.8
I
1.0
Fig. 8. lnvariant cross section f, as defined in subsect. 5.1, averaged over p ~ < 0.2 GeV 2 and normalized to atot(q z, W), as a function o f x for different q2 intervals. The data points at q2 =0 marked AttHM are taken from ref. [6]. Kinematic range: 2.5 < W < 2.8 GeV, - 60 ° < 0 < +60 ° 0
+
.
.
.
L Dammann et al., Inclusive 7r- dlstrtbuttons
403
Table 8 Cross section ratio f / O t o t (GeV --2) as a f u n c t i o n o f x in the k i n e m a t i c range 2.5 < W < 2.8 GeV, -60 °
.
0.1 (a)
-
.
.
0.2
.
.
.
0.3
.
.
.
.
.
.
.
.
.
.
0.3 - 0.4
0.4
0 . 7 7 8 +- 0 . 0 7 0 0.601 -+ 0 . 0 2 3 0 . 5 0 8 -+ 0 . 0 1 6 0.456 +- /t.013 0.454 + 0.014 0.435 +- 0 . 0 1 4 0 . 3 4 7 +_ 0.014 0 . 3 0 9 +_ I).014 0.325 +_ 0 . 0 1 8 0.2//3+0.016 0.014 +~ 0.005
0 . 6 5 2 +- 0 . 0 7 0 0 . 5 9 0 +_ 0.027 0 . 4 4 6 -+ 0.016 0 . 3 9 8 -+ 0.013 0 . 4 1 7 +_ 0 . 0 1 4 0 . 3 4 2 +_ 0.013 0.321 +- 0.013 0.275 + 0.013 0.277 +- 0 . 0 1 4 0.159-+0.011 0 . 0 3 0 -+ 0.005
0 . 3 9 8 -+ 0.076 0 . 4 2 6 -+ 0 . 0 3 2 0.403 -+ 0 . 0 2 0 0.345 -+ 0 . 0 1 7 0.346 +- 0 . 0 1 7 0.305 +_ 0 . 0 1 6 0.286 +_ 0.015 0 . 2 3 2 +_ 0 . 0 1 4 0 . 2 3 9 +_ 0.015 //.145÷0.012 0 . 0 2 2 +- 0.005
0 . 5 1 3 -+ 0.025 0.445-+0.018 0 . 3 8 4 +_ 0.015 0 . 3 1 4 + 0.013 0 . 3 1 3 + 0.013 0.268+-0.1113 0.245+-0.013 0.235+0.014 0.255±0.016 0 . 2 5 9 +_ 0 . 0 1 8 0.101+0.014 0.020 + 0,020
0.436 + 0 . 0 2 6 0.398+_0.019 0.344 +_ 0 . 0 1 6 0.321 +- 0.015 0.247 -+ 0 . 0 1 3 /I.226+-0.012 0.249+-0.013 0.214+_0.013 0.263+-0.016 0.261 +_ 0 . 0 1 7 0.143+_0.014 0 . 0 4 2 +_ 0 . 0 2 4
0.314 +- 0 . 0 3 3 0.302-+0.025 0.269 +_ 0.1120 0 . 2 2 0 -+ 0 . 0 1 7 0.210 ± 0.017 0.186+0.016 0.168+_0.015 0.167 +- 0.015 0.178"-0.017 0.221 -+ 0 . 0 2 0 0.109-'0.-14
.
0.5
0.5 -- 0.6
3,vp -, n+ + a n y t h i n g
0.40 -0.45 0.50 0.550.60 O.65 0.700.75 O.80 0.85 0.90
0.45 0.50 0.55 0.60 0.65 O.70 0.75 0.80 0.85 0.90 0.95
0.792 + 0.094 0 . 6 9 0 -+ 0.036 0 . 6 0 4 + //.027 0.551 +_ 0.025 0 . 4 9 7 -+ 0.025 0.503 + 0 . 0 2 9 0 . 3 7 4 -+ 0 . 0 2 8 0 . 3 3 9 + 0.031 0.335 -+ 0 . 0 4 2 0.213+_0.042
(b) 7v p ~ 7r
+ anything
0 . 4 0 -- 0.45
0 . 5 3 8 -+ 0.034 0.563-+0.031 0.397 +_ 0 . 0 2 3 0.401 +- 0 . 0 2 3 0.371 ± 0.023 0.287+-0.022 0.328+-0.027 0.272-+0.028 0.309-+0.036 0.265 -+ 0 . 0 4 3 0.094-+0.038
0.45
.
0.2
-- 0.50
0.50 0.55 0.55 0.60 0 . 6 0 - 0.65 0.65 - 0.70 0.70 0.75 0.75 - 0.80 0.80 0.85 0.85 0.90 0.90 0.95 O.95 1.00
0.389 ± 0.068 0.346 +- 0 . 0 3 0 0.386 +_ 0.029 0 . 3 2 6 + 0.025 0 . 2 4 0 -+ 0 . 0 2 2 0.225 +_ 0 . 0 2 0 0.192 +_ 0 . 0 1 8 0.201 -+ 0 . 0 1 9 0.161±0.017 0 . 0 3 2 +_ 0.01/7
0 . 2 2 2 +- 0.049 0.186+_0.033 0.161 + 0 . 0 2 6 0 . 1 4 6 -+ 0.023 0 . 1 4 4 -+ 0.021 0.127+-0.0211 0.092÷0.017 0.119+0.019 0.130+-0.021 0 . 1 5 9 -+ 0.023 0.080-+0.016 0 . 0 1 3 +_ 0 . 0 0 9
5.5. q2-dependence We show the q2-dependence 7r
production
of the invariant cross section for both
data in two ranges of the transverse momentum .
9
t h e 7r+ a n d
squared"
(a) at
p 2T ~ 0 , ( b ) i n t h e r e g i o n P'i" < 0 . 2 G e V 2. F i g . 9 a n d t a b l e 9 s h o w t h e n e a r l y f o r ward cross section
]" =__Ed3O °tot
1
dp 3 °tot
'
a v e r a g e d o v e r a s m a l l b i n p 2 < 0 . 0 2 5 G e V 2.
+
404
I. D a m m a n n et al., Inclusive ~r d i s t r i b u t i o n s
E .dd~. a_~.,[GeV-Z] ,, i, ~ot '
.g, p ~t+ anything (w=2.65 6ey, pl2 =0
'
,
,
,
,-
,
t
i
C
,
,
,
,
i
1.0 oQ,~
t'
{'
" =" [O.t,-x-0.7
l
1.0
q el zl.
HBurfeindt
~ n-
A1 thi' 'xperim'nt
0.7
]OESV
O.l
C) J C.Alder el zl. i
.
.
.
.
o2
.
i
o'.~ 3
i
16 ' o'.o
Iq21 [GeV 2 ]
3
i
J
to
i
iz
I
~
li
l~
+
t~lg. 9 . 1 n v a r l a n t c r o s s s e c t l o n k d o / d p , f o r r r andrr data, normalized to otot(q 2, W ) , a s a function of [q21 for two different x intervals. For comparison data at q2 = 0 [ 7 ] and at Iq21 = 1.15 GeV 2 [9] are shown. The lines are just for eye guidance. Kinematic range: same as in fig. 7.
Table 9 Cross section r a t i o f / o t o t (GeV 2) as a function o f q 2 in the kinematic range 2.5 < W < 2.8 GeV, 60 ° < q ~ < + 6 0 °, p } < 0.025 GeV 2
Iq21(GeV 2) 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55
0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60
(a) 7vp ~ ~z+ + anything
(b) 'yv p ~ ~- + anything
0.4
0.7
0.4
0.83 + 0.08
0.55 ± 0.18
0.61 ± 0.06
0.67 0.69 0.59 0.58 0.56 0.51 0.56 0.42
+ (t.06 ± 0.05 ± 0.04 ± 0.03 ± 0.03 -+ 0.04 ± 0.04 + 0.05
0.50 ± 0.06 0.54 0.51 0.40 0.40
± 0.08 +- 0.09 +- 0.06 -+ 0.07
0.34 +- 0.04
0.53 0.56 0.51 0.43 0.39 0.38 0.28 0.26
± 0.03 ± 0.03 -+ 0.03 ± 0.02 ± 0.02 ± 0.03 ± 0.03 ± 0.04
0.7
0.56 0.49 0.50 0.55 0,34 0,36 0,28 0.21 0,25
+ ± + + + * ± ± ±
0.08 0.05 0.05 0.05 0.06 0.06 0.06 0.05 0.06
T h e c r o s s s e c t i o n s g i v e n f o r c o m p a r i s o n at q 2 = 0 [7] a n d iq2t = 1.15 G e V 2 [9] w e r e m e a s u r e d at a b o u t t h e s a m e W ~ 2 . 6 5 G e V , b u t in s l i g h t l y s m a l l e r p 2 r a n g e s (see s u b s e c t . 5.4. All c r o s s s e c t i o n s h a v e b e e n a v e r a g e d o v e r t h e x - i n t e r v a l s 0.4
I
I
7L
I
I
_<,_-~"+ 0.4
I
I
.
.
0.7
4,-
i
0.2
I
I
0.4
J
Iq21[G~v2]
I
0.6
I
I
++-'--'- ._-.- ,__.__._t
+
+ + + + +
I
-~--~--'~--~-o--*--°--e---°--+ -0"6"= x<0"7 I
-*--*---*-~--*-__._~_ _+ +0"5
I
(P2< 0.2GeV2}
YvP ~Tt++anything
2
",I,
0.
0
°I
02.
0.5
0.2
Ib
0.5
0.2
0.5'
i
-
I
0.2
I
0.4
0.5
I
+
TI
0.6
0.8
4-
0.7
1
0.6
++
++
I
0.4
++
Iq21[GeV2]
I
-+-_1_-,--*--,- -¢I
'
-I-_¢_
-'~--4,-_,_
+ + ~4__--4~
~--+_e__e
-4'--e--l- -,~--"-- -e-
-~--¢__4F
'
(p2<0.2OeV2)
YvP~ n;-+onything ~+-+'._
,o-.-.AHHM
0.~'
f/O,o, [GeV-2]
I
Fig. 10. Invariant cross section f, as defined in subsect. 5.1, averaged over p T < 0.2 GeV 2 and normalized to Otot(q 2, W), as a function o f q 2 for different x intervals. The data points at q2 = 0 marked AHHM are taken from ref. [6 ]. Kinematic range : same as in fig. 8.
0.2
0.
O.2
0.2 0.5 =
0.5
I
\AHHM
o.?.
0.5
Ii I
f/otot [GeV-2]
4~
=11+
,7
e~
rb
+
406
1. D a m m a n n
et al., I n c l u s i v e rr d i s t r i b u t i o n s
"Fable 10 Cross section r a t i o f / O t o t (GeV 2 ) a s a f u n c t i o n o f q 2 in ttle kinematic range : 2 . 5 < W < 2 . 8 G e V , 60 ° < ~ < + 6 0 ° , p 2 < 0.2 (]eV 2 Iq21 IGeV 2 )
x 0.4 - 0.5
(a) yvp -
rr +
0.6 - 0.7
0.7
0.8
0.8 - 0.9
0.603 0.558 0.511 0.445 0.454 (I.385 (I.392 0.336 (I.397 tl.325
0.496 ± 0.046 0.494± 0.020 0.463 ± 0.015 0.434 ~ 0.014 0.381 -+ 0.013 0.391 -+ 0.014 0.337± 0.014 0.314+ 0.018 0.310± (I.022 0.253 ± 0.026
0.435 ± 0.068 0.328 + 0.020 0.352 ± 0.015 0.290-+ 0.l)12 0.314 + 0.013 0.269 + 0.012 (t.252 ± 0.013 1t.251 -+ 0.015 0.226 ± 0.018 (I. 169± 0.019
0.409+ (I.289+_ 0.301 ± 0.287 ± 0.235 ± 0.252± 0.220± 0.198 + 0.220+ 0.184 +
(I.382± 0.041 0.318-+ 0.017 0.305 ± 0.013 /I.285-+0.013 (I.248 ~- 0.012 0.233-± 0.013 0.218 + 0.014 0.182+0.017 0.141 ±0.019 0.132± 0.024
0.344+ 0.056 0.285 ± 0.019 0.236 + (/.013 0.234±0.013 0.252-+ 0.014 0.201 + 0.012 0.168-+ 0.013 0.165±0.017 0.116-+0.017 0.(t84+ 0.018
0.398+ 0.140 0.294 ± 0.029 0.266+- 0.019 0.277±0.018 0.283 + 0.018 0.273 + 0.017 0.229 ± 0.018 0.179±0.019 0.168+0.022 0.132+ 0.025
+ anyHling
0.10 0.15 0.15 - 0 . 2 0 0.2(I 0.25 0.25 0.30 0.30 0.35 (/.35 0.40 0,411 0.45 0.45 0.50 0.50 0.55 0.55 0.60
0.725 ± (/.062 0.711 + 0.042 0.638 ± 0.032 0.649± 0.033 0.634± (I.036 t1.572 + 0.038 0.407-+ 0.036 0.489-+ (I.055 0.469-+ 0.088 0.195 + (I.099
(b) yvp ~n-
+anything
0.10 0.15 0.20 0.25 0.30 (I.35 0.40 0.45 0.50 0.55
0.526 + 0.044 0.553 ± 0.026 0.460± 0.020 0.493-+0.022 0.448 ± 0.(122 0.386 ± 0.023 0.324± 0.025 0.285±0.031 0.218±(I.035 0.168 + 0.047
0.15 0.20 0.25 0.3(/ 0.35 0.40 0.45 (/.50 0.55 0.60
0.5 - 0.6
± 0.042 + 0.020 + 0.015 ± 0.014 + 0.015 ± 0.014 ± 0.017 +- (I.019 ± (I.027 +_ 0.{133
0.396 + 0.033 0.384± 0.017 0.352+ 0.014 0.331+0.014 0.335 + 0.015 0.316 ± 0.0t5 0.254± 0.016 0.221±0.019 0.162+0.022 0.133 +- 0.027
C o m p a r i n g t h e rr + w i t h rr
0.191 0.031 0.020 0.017 0.(t14 (I.(t14 0.014 0.016 0.019 0.022
c r o s s s e c t i o n s , o n e sees t h a t in g e n e r a l the n o r m a l i z e d
rr+ c r o s s s e c t i o n s are larger. T h e rr- d a t a s h o w a s t e e p e r d e s c e n t w i t h rising iq2k t h a n tile rr + d a t a ( f o r t h e r a l i o rr+/rr In tile r e g i o n 0.7 < x < 0.9 tire rr
see s u b s e c t . 5.6. photoproduction
c r o s s s e c t i o n is larger t h a n
the rr+ c r o s s s e c t i o n . T h i s is m a i n l y d u e to rrA(1 2 3 6 ) p r o d u c t i o n : at q 2 = 0 m o r e rr A ++ t h a n rr+A 0 are p r o d u c e d (see figs. 7a, b) [22]. N e x t w e s h o w in figs. 10a, b a n d t a b l e s 10a, b tire n o r m a l i z e d i n v a r i a n t c r o s s sect i o n ) ' / o m t a v e r a g e d o v e r p 2 < 0.2 G e V 2, as a f u n c t i o n o f q2 in small x - i n t e r v a l s . T h e 7r+ a n d rr
d a t a i n c r e a s e w i t h i n c r e a s i n g Iq2i f r o m [q2i = 0.2 G e V 2 t o
Iq 2 I =
0.6 G e V -~. F o r c o m p a r i"s o n r e s u l t s f"r o m 7r-+ p h o t o p r o d u c t l o' n are given f o r 2 ~ + • 2.4 < W < 2.8 G e V , also a v e r a g e d o v e r P'F < 0.2 G e V - . T h e 7r p h o t o p r o d u c t l o n v a l u e s lie s i g n i f i c a n t l y b e l o w t h e e l e c t r o p r o d u c t i o n v a l u e s at lq2t ~ 0.2 G e V 2. T h e c o r r e c t i o n s d u e to t h e l o s s e s o f l - p r o n g e v e n t s are i n c l u d e d in the rr+ p h o t o p r o d u c t i o n d a t a [6] (see s u b s e c t . 5.4). F o r the 7r- d a t a (fig. 10b) t h e d i f f e r e n c e b e t w e e n t h e c r o s s s e c t i o n s at q 2 = 0 a n d [q21 ~ 0.2 G e V 2 is s m a l l e r .
+ . . L D a m m a n n et al., Inclusive ~ d i s t r t b u t t o n s
407
In figs. 10a, b one sees a similar tendency with respect to q2 as in fig. 9: )'/o.. 2 /" 2 tot increases (or is nearly constant) for Iq 1~ 0.3 GeV and then decreases with rising Iq2j. Within the statistical significance of our data, this q2dependence off/Oto t is the same for all given x-intervals. We mention that such a decrease ofj'/Oto t with increasing ]q2i as seen in figs. 9 and 10a, b f o r x > 0.4 has not been found in the a+ electroproduction experiment of Lazarus et al. [10] in the range 0.15 < x < 0.05, performed at a somewhat higher energy W = 3 GeV. There,JTOtotWas found to be rather constant at Iq21 = 0.3, 0.6 and 1.2 GeV 2.
5.6. Charge ratio n+/n In the previous subsections we pointed to the differences in t h e x and q2 dependence of the rr+ compared with the ~ cross sections. To see this different behaviour .
R- do(~ )
-do--~
Zi--"
r
~f,p ~ t
÷
.
+onythmg
" (~2~o.2o~v 2) I~
I
u
I
I
--I---~ q2=0 AHHM I I
~ I
t
_,~_1
I
__~ ,
+-~--*--'-+ -~-+4,-q,_ 0,1
I
]
I
I +
0.2
+ 21
0,3<1q21< 0.Z,GeV 2 I I I
+
I
I_~_
I
i~ -
~ -+-+++q'- + +
1 0,4
-t~
0
+ O.S
t
O~
_~_ I
.0.6 x= Pll/pmNax
I
i 0.8
i --r~igtt '
1.0
Fig. 11. R a t i o R = da(n+)/do(~-) o f the cross sections d 2 o / d x d p } for n + and rr- data, aver2 aged over P T < 0 . 2 G e V 2, as a f u n c t i o n o f x, for different q2 intervals. T h e data points at q 2 = 0 marked AHHM are taken from ref. {6]. Kinematic range: same as in fig. 8.
L Dammann et al., Inclusive ~r-+distributions
408
R= do(~') doltC) I
%'vp ~ n : = + a n y t h i n g ( p2 < 0,2 GeV2) I
I
I
I I
I
AHH-~t- _4_+__,__ --iF-- 4 , - + + T
I
0.4
t
/
-+--4-'--*---
I
I
_4,_-~ :
-*-~-
I
!
0.5
II
~-
I
++
++ -*-~__~_ -*--~--q-
+
I
,-,--*--*--~F~-+O.6
,
0 0
-
+-*-+ o[2
0.7
__,_÷-*-+J'-0.8 <,.~ 0.g '
I
o'.~
I
o.~ lq~l [OeV2]
l:ig. 12. RatioR=do(n+)/do(Tr )ofthecrosssectionsd2o/dxdp}forn+andTr d a t a , avera g e d o v e r p 3f < 0 . 2 G e V 2 , as a f u n c t i o n o f q 2 f o r d i f f e r e n t x intervals. T h e d a t a p o i n t s a t q 2 = 0 m a r k e d A H H M are t a k e n f r o m ref. [6]. K i n e m a t i c r a n g e : s a m e as in fig. 8.
T a b l e 11 C r o s s s e c t i o n r a t i o R = d u ( r r + ) / d o ( r r - ) as a f u n c t i o n o f x in the k i n e m a t i c r a n g e : 2.5 < W < 2 . 8 G e V , o 2 60 ° <0<+60 ,pT < 0.2GeV 2 x
Iq21 ( G e V 2 ) 0. l
0.40 - 0.45 0.45 - 0.50 0.50-0.55 0.55 0.60 0.6(/ 0.65 0.65 - 0.70 0.70 - 0.75 0.75- 0.80 0.80 0.85 0.85-0.90 0.90 0.95
0.2
1.47 -+ 0.2(i 1.23 .+ 0 . 0 9 1.52+-0.11 1.37 -+ 0 . 1 0 1.34±0.11 1.75 -+ 0 . 1 7 1.14 +- 0 . 1 3 1.25+-0.17 1.08+-0.19 0.80+-0.21
0.2
--0.3
1.52 +. 0 . 1 6 1.35 .+ 0 . 0 8 1.32_+0.07 1.45 ± 0 . 0 7 1.45.+0.08 1.62 -+ 0 . 0 9 1.42 -+ 0 . 0 9 1.31-+0.10 1.28-+0.11 0.78+0.08 0 . 1 4 +. 0 . 0 6
0.3
0.4
1 . 5 0 +- 0 . 1 8 1.48 -+ 0 . 1 0 1.30_+0.08 1.24 +- 0 . 0 7 1.69-+0.10 1.51 +- 0 . 1 0 1.29 -+ 0 . 0 9 1.29+-0.10 1.06-+0.08 0.61-+0.06 0 . 2 1 -+ 0 . 0 4
0.4
0.5
1,27 + (t.28 1,41 -+ 0 . 1 6 1,50+-0.14 1,57 +- 0 . 1 4 1.65-+0.15 1,64 -+ 0 . 1 6 1 . 7 0 -+ 0 . 1 8 1.39+-0.16 1.34-+0.16 0.66_+0.08 0 . 2 0 +- 0 . 0 5
0.5
-0.6
2.09 ± 0.52 2.15-+0.39 2 . 6 5 -+- 0 . 4 6 2.27+-0.38 1.89 -+ 0 . 3 5 2 . 4 4 +- 0 . 5 0 1.61-+0.30 1.55-+0.29 1.01+0.18 0 . 3 9 -+ 0 . 1 2
+
.
.
.
1. Darnrnann et al., Inclusive rr- dtstrtbuttons
409
Table 12 Cross section ratioR = dc~lrr )/do(~r ) as a lunctlon ofq in the kinematic range: 2.5 < W< 2.8GeV, 60 ° < ~ < +60 ° ,p-~-< O.2 GeV2 +
•
Iq21 (GeV 2 )
2
x 0.4
0.10 0.15 0.15 0.20 0.20 0.25 0.25 - 0.30 0.30-0.35 0.35 - 0.40 0.40 - 0.45 0.45 0.50 0.50 0.55 1/.55 - 0.60
,
0.5
1.38-+0.16 1.28-+0.10 1.39+--0.09 1.32 -+ 0.09 1.41-+0.11 1.48 -+ 0.13 1.26 -+ 0.15 1.72-+0.27 2.15 -+ 0.53
0.5
0.6
1.52±0,17 1.45+0.08 1.45-+0.07 1.35 -+ 0.07 1.35-+0.07 1.22 ± 0.07 1.54 -+ 0.12 1.52 ± 0.16 2.44 -+ 0.37 2.45 + 0.55
0.6 - 0.7
0.7
0.8
1.30-+0.19 1.55-+0.10 1.52-+0.08 1.53 -+ 0.09 1.54-+0.09 1.68 -+ 0.11 1.55 -+ 0.12 1.73-+0.19 2.20 -+ 0.34 1.91 -+ 0.40
1.27+-0.29 1.15-+0.11 1.49-+0.10 1.24 + 0.09 1.25+0.09 1.34 + 0.10 1.50 + 0.14 1.52-+0.18 1.95 -+ 0.32 2.00-+ 0.49
0.8 - 0.9 1.03-+0.60 0.98-+0.14 1.13-+0.11 1.04 -+ 0.09 0.83-+0.07 0.93 -+ I).08 0.96 -+ 0.10 1.11+-0.15 1.31 + 0.21 1.39-+ 11.31
o f the 7r+ and lr cross sections more clearly, we show the r a t i o R = do0r+)/doOr - ) of the cross sections d 2 o / d x dp2T as a function o f x in fig. 1 1 and table 1 1, and as a function o f q 2 in fig. 12 and table 12. The cross sections d 2 o ( ~ + ) / d x dp 2 and d 2 o ( r r - ) / d x dPT have been averaged over p ~ < 0.2 GeV 2. Radiative corrections do not significantly influence the values of R as m e n t i o n e d above. For comparison the ratio obtained in p h o t o p r o d u c t i o n [6] is given, also as an average over p . ~ < 0.2 GeV 2. F r o m fig. 11 we see that in all bins o f q 2, R is i n d e p e n d e n t o f x up t o x ~ 0.7. Above x ~ 0.8, R falls to nauch smaller values. We m e n t i o n again the exclusion of ep ~eTr+n events which would mainly contribute to the region 0,9 < x < 1 (see subsect. 5.4.). While at q2 = 0 the n u m b e r of p r o d u c e d lr + equals the n u m b e r o f ~ r - (at 0.4 < x < 0.7), the ratio R increases with increasing Iq2i up to R ~ 2 at iq21 ~ 0.6 GeV 2 (see fig. 12). We m e n t i o n that in the e x p e r i m e n t [9] p e r f o r m e d at iq2[ 1.15GeV 2andp{,~0aratioof2<~R<~3hasbeenfoundintheregion 0.4 < x < 0.7 (see figs. 7a, b).
6, S u m m a r y 1. The invariant n + and n cross sections dn not significantly depend on the azinmthal angle qS, i.e. d2aT/'Ckr dPT and d2Ol/dX dp 2 are small c o m p a r e d with d2Ou/dX dp 2 + e d2OL/dX dp 2. (see fig. 3). 2. For b o t h the lr + and ~ data the p 2 distributions show an a p p r o x i m a t e ex2 The slope depends ponential behaviour apart from the region o f very small PT" strongly on x (in the region 0.4 < x < 1) but varies very little with q2 t h r o u g h o u t the region 0.3 < Iq21 < 0.6 GeV2; however, it is smaller than in p h o t o p r o d u c t i o n (see fig. 6).
+
410
L D a m m a n n et al., Inclusive n distributions
3. T h e i n v a r i a n t n+ and 7r cross s e c t i o n s f decrease w i t h rising x ( w i t h i n 0.4 < x < 0.7). This d e s c e n t is r a t h e r flat at q2 = 0 b u t b e c o m e s m o r e p r o n o u n c e d w i t h increasing Iq2i (see figs. 7 a n d 8). 4. T h e i n v a r i a n t n+ a n d n cross sections)'~ divided by the total inelastic cross section Oto t ( q " W), are larger at Iq21 ~ 0.2 G e V 2 t h a n for p h o t o p r o d u c t i o n ; for [q21 ~ 0.2 G e V 2 .['/Otot(q" "), W) decreases again (see fig. 9). •
5. In the interval 0.4 < x < 0.8 the ratio R = do(rr+)/do(Tr -) increases w i t h increasing tq2l f r o m R ~ I (at q2 = 0) to R ~ 2 (at Iq2l ~ 0.6 G e V 2) (see fig. 12). We like to t h a n k all o t h e r m e m b e r s of o u r g r o u p for t h e i r e x c e l l e n t technical assistance. T h e s u p e r i o r p e r f o r m a n c e o f the S y n c h r o t r o n crew in p r o v i d i n g the intense p o s i t r o n b e a m is gratefully a c k n o w l e d g e d . We also t h a n k the H a l l e n d i e n s t , the K~iltetechnik a n d the R e c h e n z e n t r u m for their valuable c o o p e r a t i o n . M a n y discussions w i t h Drs. H. Meyer a n d B.H. Wiik have b e e n very valuable.
References [1] 11. Kendall, K. Berkelman and .I. Bjorken in Int. Symposium on electron and photon interactions at high energies, Cornell University, 1971, ed. N.B. Mistry. [2] K.C. Moffeit et al., Phys. Rev. D5 (1972) 1603. [3] W.P. Swanson et al., Phys. Rev. Letters 27 (1971) 1472. [4] A.M. Boyarski et al., as quoted by 13. Wiik, talk at the Cornell Conference (1971). [5] Aachen-Hamburg-Heidelberg-M~inchen Collaboration, as quoted by 13. Wiik, talk at the Cornell Conference ( 1971 ). 16] Aachen-ltamburg-Heidelberg-Miinchen Collaboration, Inclusive photoproduction of rr+ and p at energies up lo 6.3 (;eV, and comparison to electroproduction, Contribution no. 668 to the 16th int. Conf. on high energy physics, Chicago, 1972, and private communications• [7] H. Burfcindt et al., DESY 72/75 (1972); B.H. Wiik, private communication. [8] A. Sot'air et al., Nucl. Phys. B42 (1972) 369. [9] J.C. Adler et al., Nucl. Phys. B46 (19721 415; W. Fehrenbach Hamburg, thesis. [ 10] E. Lazarus et al., Phys. Rev. Letters 29 (1972) 743. [11] V. Eckhardt et al., DESY 72•67 (19621. [12] C.J. Bebek et al., contribution no. 952 to Chicago Conference (1972). [131 See e.g.S.M. Berman, Phys. Rev. 135 (1964) 1249. [141 C. Driver et al., Nucl. Phys. B30 (19711 245. [15] J. Ralhje, ttamburg thesis (1971), DESY F32-71/3 (19711. [16] G. llofmann, Hamburg thesis (1971), DESY t"32-71/2 (1971). [17] P. Karow, ltamburg thesis (19711, DESY F32-71/1 (1971). [18] LW. Mo and YS. Tsai, Rev. Mod. Phys. 41 (19691 205. [ 19] 1. Dammann el al., DESY 72]70 (1972). [2(1] H. Cheng and T.T. Wu, Phys. Rev. 183 (19691 1324; J.D. Bjorken, J. Kogut and D. Soper, Phys. Rev. D3 (1971) 1382; It.T. Nieh, Phys. Letters B38 (1972) 100. [21] F.W. Brasse et al., Nucl. Phys. B39 (19721421. [22] A.M. Boyarski et al., Phys. Rev. Letters 25 (1970) 695.
INCLUSIVE
7r+ A N D 7r- D | S T R I B U T 1 O N S
IN E L E C T R O P R O D U C T I O N
ON PROTONS
I. D A M M A N N , C. D R I V E R , K. HI~INLOTH, G. H O F M A N N , F. J A N A T A , P. KAROW, D. LUKE, D. SCHM1DT and G. SPECHT
Deutsches Elektronen-Synchrotron DESY. Hamburg Received 19 January 1973
Abstract : We investigate the inclusive pion spectra in the electroproduction reaction ep ~ e~r± + anything in a coincidence experiment at DESY. Data are presented from the kinematical region 0.1 < tq21 < 0.8 GeV 2 and 3.15 < W < 2.8 GeV as a function of the transverse momentum squared p}, the Feynman variable x, and the azinmth angle g,. The charge ratio 7r+/rr- is given in terms of the variables q2 and x. The inclusive spectra are compared with results from photoproduction.
1. I n t r o d u c t i o n Since in recent experiments on inelastic electron-nucleon scattering the electrop r o d u c t i o n o f various two-body hadronic final states (such as ~N, rrA, pN, KY), ref. [ 1 ], was investigated, there has been increasing interest in inclusive spectra of electrop r o d u c e d hadrons. Knowledge of the inclusive spectra should allow, together with inclusive spectra from p h o t o p r o d u c t i o n , a better understanding of some electromagnetic properties of hadrons. Results from several photoproduction experiments on inclusive pion distributions have been published [ 2 - 7 ] . F r o m electroproduction experiments one expects answers to the following questions: Does the transverse-momentum spectrum depend on q2, the square of the mass of the virtual photon'? How does the longitudinalm o m e n t u m distribution vary with q2? Do the 7r+ and rr spectra depend differently on q - ? Only few pubhshed data on inclusave spectra o f e l e c t r o p r o d u c e d ~pions are available up to n o w : 7r+ and rr- spectra were obtained at Iq21 = 0.7 G e V - and W = 1.93 GeV [8] and at Iq21 = 1.15 GeV 2 and W = 2.63 GeV [9], in b o t h cases for very s m a l l p 2 ~ 0.03 GeV 2 a n d x > 0.1. At Iq2l = 0.3, 0.6 and 1.2 GeV 2, W = 3 GeV, 7r+ p r o d u c t i o n has been measured at --O. 15 < x < - 0 . 0 5 [10]. In a recent streamer chamber e x p e r i m e n t at D E S Y rr data have been obtained for 0.3 < Iq2t < 1.5 GeV 2, W< 2.8 GeV [1 1]. At iq21 = 1.2 GeV 2, W = 2.2 GeV and tq2i = 2.0 GeV 2, W= 2.7 GeV lr -+ spectra have been measured ]12]. ")
.
.
382
L Dammann et al.. Inclusive 7r'- distributions
In this paper we present data on inclusive rr+ and rr duction on protons,
distributions in electropro-
ep -+ err+ + a n y t h i n g , ep -+ err- + anything. These data werc obtained in a coincidence experiment at DESY in the kinematic regions 0.1
2,
<0.3GeV 2
2.15
,
<1.0
,
0<~<360
°
o
In sect. 2 we shall discuss the kinematics. The apparatus and data analysis are described in sects. 3~ 4. The inclusive spectra of rr+ and lr are reported in sect. 5.
2. Kinematical
variables and their ranges
We use tile R)llowing notation :e, e', q, p, n are the four-momenta of the particles : the primary and tile scattered lepton, the virtual photon, the target and the detected pion: q2 = (e e') 2 is tile mass squared of the virtual l)hoton 3%; 1'92 = (q + p)2 is the ,nass squared of the outgoing hadron system; p2 is the transverse-momentum */ * squared of the rr (with respect to the direction o f q ) : x =pll Pmax is Feynman's longitudinal variable (p~ = hmgitudinal momentum of the rr with respect to the direction of q; P:i~mx = maximum possible momentum of the rr for fixed W; * denotes the c.m.s, of the qp system); and ~ is the azimuthal angle of the rr. q5 is the angle between the polarization plane, subtended by e and ¢', and the production plane, subtended by q and rr. Assuming one-photon exchange the virtual photoproduction cross section d3o/dx dp 2 d~ can be derived from the experimental cross section by the relation
ll31 d5o __ dq 2 dW 2 dx dp2T d~
-
r t 2r,
d3o .... dx dp 2 d~
.
The kinematical factor a
1
W2
M~
I~|
4(2~)2
E,'~"dMp"~ Iq2t
1 -
e
describes the virtual-photon flux (E 0 = lab energy of the primary lepton), and e= (l+.~q 2 ) - - - 7 tg2 {Oee' hq-I
l
is tile transverse-photon polarization.
I. D a m m a n n
383
e t al., I n c l u s i v e 7r± d i s t r i b u t i o n s
Iq21 Range of Acceptance
[G,v21
1.2 -~ 120°<$<2/,0° N 0<$<3600 ll;rlll ^
E0:5./,G~eV~
w [GeV]
~'ig:
Fig. 1. A c c e p t a n c e range Iq2l v e r s u s W o f the a p p a r a t u s for two d i f f e r e n t energies E 0 o f the p r i m a r y lepton. The areas labelled A or B were used in the analysis of this paper. ] ' h e d e n s i t y of the lines i n d i c a t e s the d e n s i t y of events.
Table 1 K i n e m a t i c regions region A Eli
(GeV)
4.9
W
(GeV)
2.15
Iq21
/ G e V 2)
0.45
x PT2
e
0.6
5.4 2.3
2.2
0.65 -- 1.0
(GeV 2 )
0
0.05
(deg)
0
- 360
0.77-
region 13
0.79
4.9
5.4
2.4
2.4
2.8
2.4
0.6
0.8
0.1
0.4
0.2
0.6
0.6
- 1.0
0.4
1.0
0.4
- 1.0
0
~ 0.05
0
0.3
0
0
- 360
60
+ 60
60
+ 60
0.78
0.51
0.58
0.59
O.65
0.77
2.8
0.3
l. Dammann et al., Inclusive 7r~ distributions
384
Tile virtual photoproduction cross section is expressed in terms of the two transverse and the longitudinal components of the virtual-photon polarization : d2OT d3o 1 t d2°u d2°L y ..... \-+e----+e - - - - cos 2~ dx dp~- d~ 2rr dx dp~ cLv dPT dx dPT
(I)
d2°l ) +x,/22e(e+ 1) . . . . . cos0 . dx dplIn the limit q - -+ 0, eq. (1) has to approach the differential cross section for unpol3' 3' . . . . . . arized real photons. The term d - o u / d x dp~ is the dHferentml cross secnon lor u n polarized transverse wrtual photons: e d-oT/dX dp~, cos 24~ is due to the photon transverse linear polarization: e d2oL/dX dp 2 accounts for longitudinal polarized photons, and X / 2 c ( e + 1) d2ol/dX dpq, cos ~ describes the interference between the transverse and longiludmal components. The differential cross section will be given in the Lorentz-invariant form •
k d2~° = ~ E* dp3
3'
")
.
d3o
P,~mx dx dp~ dq5
where p is the three-molnentum and E* the energy of the detected pion. We obtain
d2OL d2OT l:" d3° E* ( . d - °.u +,e . . . 3" + e cos 2g5 dp 3 rr P~nax I, dx dp~r ckv dp-~ dx dPT d2ol \ + ,,/2_ e(e + 1) . . . . cos •/ . ] dx dPT
(2)
Tire data which we will report were obtained at two different energies of tile primary lepton, E 0 = 4.9 and 5.4 GeV. We measured 22 000 and 35 700 events of the reacuon ep -~ err + anything, respecnvely, and 13 000 and 15 500 events of the reaction ep -+ err + anything. Fig. 1 and table 1 show the regions o f q 2 and W which were covered by our data. We distinguish between two kinematical ranges. In range A all azimuthal angles 0 < @< 360 ° are accepted. In this range we have investigated the qS-dependence according to eq. (1). In range B the acceptance of the apparatus is limited to - 6 0 ° < 4~< +60°; here we have investigated the cross sections averaged over the ¢)-interval. Tile bulk of events is lying in range B. •
-b
•
.
385
L Dammann et al., Inclusive ~¢+distributions
3. Apparatus
The apparatus is shown in fig. 2. The scattered lepton and the produced rr nreson are detected in coincidence in two spark-chamber spectrometers. After being deflected by a magnetic field both particles are detected in optical spark chambers and identified in ~erenkov and shower counters. More details of the apparatus are given elsewhere [14, 15]. To allow a comparison of ep -+ err+ + anything and ep -+ err + anything with the smallest possible systematic errors we measured both of these reactions with the same apparatus under identical magnetic-field configurations. We therefore used a primary electron beam for the rr+ data and a primary positron beam for the rr data. We only switched the polarities of the magnets in both spectrometers. The absolute field configuration remained unchanged. The spark chamber tracks and all counter infomration were photographed. The pictures were analyzed automatically [ 16].
\
BEAM T
~
\ \ItU-%'~\\k../----- /
~{
~
~ / I-- ~
~/~
i \ %O n i E%I-I~/I1~1%7\N N % \
/
/. ~/
~
/
FARADAY FAR CUP
/
r~ Fig. 2. Experimental layout. 4. Data analysis and corrections The calculation of the differential cross section d5o/dq 2 dW 2 dx dPT d~ and the corrections for the finite acceptance of the apparatus have been performed as described elsewhere [14, 171.
386
l. Dammann et al., Inclusive rr+-distributions
From the data we have included the 7vp -+ rr+n events because of the following reason. ") In the reactmn 7 vP -+ rr ,~n the -varmbles p.~ and x are not independent , + . . but are . related by the equation @ + (xp*) 2 = p* = m o m e n t u m ot rr wluch Is a function of W only. At fixed W and for very small PT' the measured cross section d2o/dx d p ; for the rr+n reaction shows a small peak n e a r x = I. With increasing p~- the position of this peak will shift to lower x-values. In consequence, when averaging over aP2T interval, the rr+n peak is smeared out to a broad bump in x which obscures events of reactions other than "Tvp -+ 7r+n, even though they are clearly separated in a missing-mass plot. In order to see more clearly the contributions from reactions other than + 7v p -~- 7r n, especially for a comparison with the reaction 7v p -+ rr + anything, where no two-particle final state is possible, we have excluded the rr+n events by a missing-mass cut. The cross sections have been corrected for efficiency losses in the trigger, ('erenkov and shower counters, for pion interaction and pion decay and for loss in the automatic data analysis procedure. The uncertainty of all these corrections including the uncertainty of the intensity of the primary beam add up to a systematic error of less than 4%. This systematic error is not included in the errors given in the figures and tables. The radiative corrections have n o t been taken into a c c o u n t for the experimental data as presented in this paper. They have been estimated in a crude approximation according to ref. [ 18]. They cause an increase of the cross sections of (10 + 6)% within the kinematic range of this experiment. In the ratio of rr+ and ~'- cross sections considered below, radiative corrections ahnost cancel. •
+
.
5. Results 5.1. Cross-section d e p e n d e n c e on the a z i m u t h a l angle
The 0-dependence was investigated in the kinematic regions A within the entire range 0
0.65
0.70-0.80
2.42 0 . 6 0 - 0 . 7 0
2.20-2.42
2.20
2.15 - 2.30 0.55
0.45-0.55
2.15-2.30
0 . 6 - 0.7 0.7 0.8 0.8 0.9
0.6-0.7 0.7 0.8 0.8 0.9
0.6 0.7 0.7 0.8 0.8-0.9
0.6-0.7 0.7 - 0.8 0.8 0.9
Iq21 (GeV 2) x
W(GeV)
_
30
19.2-+ 15.0+ 20.8+-
30.9+ 34.9+ 38.4+ 6.0 4.4 5.3
5.5 5.1 5.3
47.2+ 23.1 23.2+ 8.1 20.5± 7.6
16.3± 11.4 50.6 -+ 9.0 63.3+ 9.6
0
0 (deg)
n
25.1± 26.4+22.7±
41.1± 27.6± 42.7± 6.2 5~4 5.1
5.9 3.9 5.1
25.5+ 14.5 18.4± 6.4 30.7+ 8.2
55.1 ± 19.4 26.5 + 5.6 54.7± 7.9
30 -- 60
_
28.4+ 23.2± 25.0+
4.7 3.7 3.9
24.2+ 3.6 23.4± 3.1 33.t + 3.9
17.8± 17.5± 24.1±
29.3± 17.8± 31.5±
22.8± 20.9± 29.8±
3.l 2.6 3.3
3.7 2.5 3.8
9.2 4.0 5.1
45.6± 13.1 40.0± 5.0 47.2± 5.8
43.0+ 13.5 29.1± 4.8 47.1± 6.2 46.1± 14.3 31.7+ 6.1 41.2± 6.9
90
7r +
60 - 90
120
Table 2 Cross section E d3o/dp 3 (,ub/GeV 2) as a function o r e in the kinematic range p ~ < 0.05 GcV 7 for 3,vp ~
22.3-+ 20.0± 26.4±
26.3± 21.2+30.3+
24.4± 26.3± 35.0±
3.3 2.6 3.5
3.9 3.1 4.7
9.7 4.3 5.4
43.4± 17.5 43.4+ 5.9 27.2± 4.9
120 - 150
+ anything
180
19.9-+ 18.8-+ 15.8+
29.8± 19.5± 31.1±
3.9 3.0 3.1
6.1 3.9 6.0
22.0-+4.9 29.6±5.8
24.9± 5.9 50.0-+ 8.4
150
9.
388
1. D a m m a n n
e t al., I n c l u s i v e 7r± d i s t r i b u t i o n s
~'vP ~rc÷÷anything 2.15
,
r
i
I
PT2<0.05GeV 2
i
,
i
, -
r
,
i
r
r
i
,
,
0.45 < Iq 21< 0.55 GeV 2 O,6
I0(
~
II
0.7< X< 0.8
0.8
I00
>
4 ,-+-*-+
::::I.
I
I
f
i
f
I
I
I
I
I
I
I
i
I
i
0
0.55 < [q21 < 0.65 GeV2 I0 ~ I I
0.6
"7
Lid
t
0"8< X<0"g
100
+
o!J +:
0°
60°
Vv P ~
120°
0°
60 °
120°
180°
~÷÷anything p?< 0.05GeV 2
2.20
so :t.
+
~-
o
~
%j,_
b
so
o
J
°7
i00 •
0.~<~<0.7
LU
0.7<~<0.8
~
0.8<×
±
so
0°
~
50°
120°
0°
- 100 i 5o
60 °
Fig. 3a.
120°
0°
60°
120°
180°
L Dammann
389
e t al., I n c l u s i v e rr+- d i s t r i b u t i o n s
3%P~ - * o n y t h i n g 2.15 < W < 2.30GeV f
f
f
;
,
,
4 < 0.05 GeV 2 ,
i
,
~
i
r
i
J
f
I
i
i
0.45 < Iq21< 0.55GeV 2 0.6< x<0.7
10(
>e
0.7
0.8
0 . 8 < x < 0.9
0 . 9 < x < 1.0
100
50
so
Jo
.=. o
I
I
I
I
I
I
I
I
I
I
I
I
J
i
I
I
I
I
t
0
I
0.554 h21<0.65GeV 2 iii
0.6< x<0.7
100
__
0.7-,= x < 0 . 8
-
C)o
60°
120°
__
0.8< x< 0.9
0.9
-
0o
60°
120°
100
50
-
0o '
6'0° '
120o'
0o
60o
120°
180°
qb
Yv P ~ - +
anything
2.20
p2 <0.05GeV 2 0.6<1q21 < 0.TGeV 2
10C
>
5c
0 ,.-t
I
i
I
I
I
I
I
I
I I I I I ; 0.7
I
:
1
1
~
:
:
',
,-41
o
"~1-~ 10, iii
, ~.-,+,-.-,+t+~, , + ~ + S r ~ F , 60 °
120 °
0°
60 °
120 °
0°
,+,+,+,~:~-,+,+,+,60 °
120 °
0°
60 °
120 °
180 °
Fig. 3b. Fig. 3. lnvariant cross section E d 3 a / d p 3 as a function of the azimuthal angle ~ for different W, 2 q and x intervals. Kinematic range : 0 < p~, < 0.05 GeV ~.
2.42
2.42
2.20
2.20
0.6 0.7 0.7 0.8 0.8-0.9 0.9 1.0
0.7 0.8 0.9 1.0
10.7± 15.8+ 4.1+
18.5± 16.4+ 23.9+ 25.2±
5.3 6.4 2.9
6.2 4.9 5.6 5.5
30.9+21.8 10.3± 7.2 40.1+12.6 12.4± 6.1
0.6 0.7 0.7 0.8 0 . 8 - 0.9 0.9-1.0
30
29.1~ 14.5 28.3+11.3 46.1+ 9.6 24.9± 6.4
0
0.6 0.7 0.7 0.8 0.8-0.9 0.9 1.0
0.7/t 0.6 0.7 0.8 0.9
0.70-0.80
0.60
2.30 0.55
2.15
0.65
2.30 0 . 4 5 - 0 . 5 5
Iq21(GeV 2) x
2.15
W(GeV)
(deg)
ll.l± 15.4± 8.1±
16.6~ 15.4~ 27.7+ 18.6+
4.9 5.7 3.6
5.2 4.0 5.5 4.2
11.8±11.8 24.0± 9.6 37.8±10.8 7.3+ 4.1
20.7+10.2 27.5± 7.3 41.3+ 8.1 24.9+ 5.8
3 0 - 60
90
120
21.2+4.0 17.9~3.4 27.4±4.5 14.2~3.4 10.6±3.1 5.0±1.9 13.7±3.3 10.8±2.9
5.4±3.0 9.2±3.2 6.8+2.7 13.4+3.7
21.3±6.1 22.7±5.0 34.6±6.3 19.8±4.7
26.2±5.7 21.9±4.3 31.8±5.4 16.3±3.8
90
18.6±4.4 17.0±3.7 25.2±4.5 23.2±4.3
9.1±6.5 15.5±5.5 27.5±6.6 27.0±6.2
34.1±9.1 24.6±5.5 54.3±7.7 13.4±3.7
60
18.9±5.6 15.5±4.6 12.1+4.5 11.0+4.9 13.0±3.6 8.6+2.7 14.0~3.7 10.8+3.4
7.4±2.2 14.8±3.1 8.3±2.5 7.7±2.5
27.0+7.2 13.4±4.4 24.6±5.9 10.2±3.8
7.9 6.7 7.5 6.3
25.2 23.3 32.0 20.0
+ + ± ±
180
150
16.0±3.7 18.2±3.9 15.0~4.0 22.6±5.4
15.2+4.1 19.2±4.3 22.2±4.7 24.1±5.1
23.2±5.4 17.7±4.3 20.7a4.7 9.7±3.2
1 2 0 - 150
Table 3 Cross section E d3o/dp 3 (,ub/GeV 2 ) as a function o14~ in the kinematic range p~, < 0.005 GeV 2 for 7vp ~ 7r- + anything
NI+
+
1. Dammann et al., Inclusive ~- distribunons
391
This can be partly due to 7rA(1236) p r o d u c t i o n ( c o n t r i b u t i o n to the region 0.8 < x < 0.9) for which a non-vanishing interference term has already been measured 119]. On the other hand, the transverse c o n t r i b u t i o n d2OT/dX dp2r_ is always found to be compatible with zero.
5.2. Cross-section dependence on the transverse m o m e n t u m squared p 2 We now turn to the study o f the p2, x and q2 dependences. This was done in the range 60 ° < q~ < + 60 °, where most of our events are lying (see fig. 1). The average of eq. (2) over this ~b-range is
f [I-tb/GeV2]j ~'v p--rt'+anythingj ~'v P--rc-.anythin, I 1001 o.t,.x-0.7 / 0.7.x-0.9 /o.t,.x-0.7 ' 0.7-x-0.9 Iq21[GeM2] STREAMEIq CHAMBER
',X--~ :
÷
:
i
"~..~;~= : "
10-
.
soL._
:
?
20
'
10
"
2
,
l
-
-
,
,
] o,
o.~ o.~I
0A
- 0.5
a=5
°ol
o
o.l-o,2
\..
-
,
,
r,
o. -oo
a:8 ,
o,
. . . . . .
o.~ o.~,
o.~ o.~ o.~i
PT2[GeV2]
. . . . .
o, o.~ o.~
t:ig. 4. lnvariant cross section f, as defined in subsect. 5.1, as function of the transverse momentum squared p~ for different x and q2 intervals. For comparison data at q2 = 0 [6] are shown. Kinematic range : 2.5 < W< 2.8GeV, 60 ° < ~ < + 6 0 ° ; f o r d a t a a t q 2 = 0 : 2.4< W< 2.SGeV. 0 < ~, < 360 °.
L Dammann et al., Inclusive n± distributions
392 +60 ° f 27r
E*
d3o w
dO
_60o rrp,~mx dx dp2T dq5
E*
d2°l
( d2°u --
d2°T
+e--~"
rcp*nax \ d x dPT
+0.826x/22e(e+l)
+ 0.413e----
dx dp 2 d2°l
dx dp2T
1
dx dp~T / "
ASSUlning for region B a similar ~b-dependence as was found in region A, we estimate that f is well approximated by the ~-independent cross section : E*
f
7rpt~mx
t
t
d2°u
-5
ely dp~
d2°L dx dPT
The dependence of the invariant cross section on the transverse m o m e n t u m I + squared p~- for the rr and rr data is shown in figs. 4a, b and tables 4a, b for different x and q2 intervals. One sees a rapid decrease of the cross section with increasingp 2. for both the rr+ and rr " data. Within statistics the spectra show in general an exponential behaviour except at small values of p~- where they become more flat. This deviation from an exponential is not due to the finite resolution in p~- of our apparatus, because the corrections due to this effect are rather small on the orderof+5%forPT<0.025GeV2andabout l % f o r O . O 2 5 < p 2
"Fable 4 C r o s s sectionf(#b/GeV2) as a l u n c t l o n ol - 6 0 ° <~< + 6 0 ° for + (a) 3,vp ~ rr + a n y t h i n g •
2
PT (GeV2) 0.0 -0.025 0.025 -0.050 0.050 0.075 0.075 0.100 0.100 0.125 0.125 - 0.150 0.150 0.175 0.175 0.200 0.200-0.225 0.225 0.250 0.2511 0.275 0.275 0.300 0.0 - 0.025 0.025 - 0.050 0.050- 0.075 0 . 0 7 5 -- 0 . 1 0 0 0.100-0.125 0.125 0.150 0.150--0.175 0.175 0.200 0.200 0.225 0.225 -0.2511 0.250 - 0.275 1t.275 0.300 (b) 7v p ~ 0.0 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275 0.0 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 11.225 0.250 0.275
-
PT in 2
the k i n e m a t i c r a n g e 2.5 < I¥ < 2.8 G e V ,
Iq21 ( G e V z)
_ •
•
-
-
-
--
rr
0.1
O.4 - 0.7
7 9 . 3 + 17.7 77.0-+ 4 . 4 71.2± 3.2 53.2-+ 2.5 54.0± 2.9 47.7± 3.1 40.1 + 3.4 36.6± 4.0 35.6± 4.9 21.2+ 4.8 1 5 . 3 + 5.1 20.5 ± 9 . 0
0.7
0.9
0.2
43.0± 36. l + 24.2_+ 21.4 ± 19.4± 16.6± 13.5± 13.3+ 8.8± 6.5 +
9.2 4.8 2.9 2.3 2.0 1.9 1.6 1.7 1.5 1.3
69.6± 52.1± 45.6± 43.0± 41.6± 30.6± 23.1± 26.2+ 14.0± 22.2 ± 7.9 ±
6.8 2.6 2.3 2.4 2.9 2.9 3.1 4.4 4.0 7.5 5.7
. 0.2
0.3
0.3
. 0.4
.
. 0.4
. 0.5
0.5
- 0.6
5 8 . 5 ± 3.4 56.8-+ 1.7 48.1 ± 1.4 44.4± 1.5 44.0-+ 1.8 3 8 . 7 + 2.2 34.8+ 2.7 3 3 . 6 ± 3.6 18.6 ± 3.7 15.5-+ 5.0 16.9 + 10.4
43.9± i.9 4 4 . 0 ± 1.3 4 1 . 3 ± 1.3 3 5 . 9 + 1.5 35.3±2.1 32.1 -+ 2.8 22.8-+ 3.3 21.5+ 4.9 1 1 . 7 ± 5.4
35.5 + 1.6 3 4 . 0 ± 1.4 3 2 . 7 + 1.7 27.8-+ 2.1 22.3+2.8 30.0-+ 5.4 2 1 . 9 ± 7.0 1 4 . 8 ± 8.9
30.5-+ 1.9 3 2 . 3 + 2.1 27.3-+ 2.9 18. l ± 4 . 0 3.3±3.3
2 3 . 4 ± 10.6 37.2± 3.6 31.6 ± 2.1 2 9 . 3 ± 1.6 24.2± 1.3 19.4± 1.2 16.0± 1.1 13.9-+ 1.1 10.8± 1.0 8.5 ± 1.0 8.5 ± 1.2 6.4+ 1.3
40.4 ± 29.7+ 26.2 ± 23.5 + 18.6+ 15.7 + 14.7-+ 12.9-+ 9.7± 7.3± 10.9± 7.3+
6.2 1.9 1.4 1.2 1.1 1.1 1.2 1.3 1.4 1.5 2.5 2.6
2 6 . 7 + 3.1 2 4 . 5 ± 1.7 21.1 ± 1.4 20.1 ± 1.4 17.0-+ 1.5 15.1 ± 1.7 10.7_+ 1.7 10.2_+2.1 6 . 3 + 2.1 6 . 0 ± 2.7 2 . 3 + 2.3
2 0 . 8 ± 2.6 211.9± 1.8 19.3 + 1.9 18.8-+ 2.1 11.9-+ 2.2 7.5_+ 2.7 111.5±4.8 5.0+5.0
46.3 ± 40.7 ± 36.5± 34.1± 32.6± 25.8± 22.6± 19.7± 16.0±
1.9 1.3 1.3 1.6 2.0 2.4 3.1 4.3 6.3
3 5 . 3 + 1.3 3 4 . 4 + 1.2 3 0 . 2 ± 1.4 27.1 ± 1.8 26.6-+ 2.7 2 1 . 2 ± 3.4 18.0+5.0 12.1+-7.1 9 . 4 ± 9.4
2 5 . 4 -+ i . 3 2 5 . 4 ± 1.5 19.3 ± 1.8 1 7 . 8 ± 2.5 1 4 . 4 ~ 3.5 12.6 ± 5.8 6.1±6.1
1610± i-.4
4 3 . 7 ± 10.6 28.2± 2.8 2 4 . 5 ± 1.8 23.4± 1.6 19.3+ 1.3 1 7 . 9 + 1.3 14.0± 1.2 9.5 ± 1.1 8.2 + 1.2 6.5 ± 1.2 6.4± 1.4 4.3± 1.5
30.7+4.5 29.7±2.0 2 2 . 2 ± 1.4 21.1 ± 1.4 1 6 . 5 ± 1.3 1 5 . 1 ± 1.4 1 0 . 8 ± 1.4 9 . 6 + 1.5 7 . 9 + 1.7 3 . 3 ± 1.5 4 . 2 + 2.1 2 . 0 ± 2.0
2 2 . 5 ± 2.9 1 7 . 8 ± 1.7 1 6 . 6 ± 1.5 1 5 . 1 + 1.6 1 3 . 0 -+ 1.7 8.2 + 1.6 6 . 7 + 1.9 5.9 * 2.2 8.5 -+ 3.5 2.3 + 2.3
14.1 ± 9.6± 14.9+ 6.9-+ 4.7±
+ anything
0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.25O 0.275 0.300 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275 0.300
x
0.4
0.7
0.7
0.9
53.5± 20.0 40.8± 7.7 3 3 . 2 ± 4.5 28.6+ 3.3 17.3 + 2.2 18.9-+ 2.2 16.6 + 2.1 12.7+ 1.9 10.5 ± 1.8 1 0 . 2 ± 2.0 7 . 9 ± 2.0
1 4 . 9 ± 1.9 11.7-+ 2.9 5 . 0 + 3.5
2.3 1.5 2.1 1.7 1.9
394
I. Dammann et al., Inclusive rr± distributions
5,3. Dependence o] the p ~ slope on x and q2 In order to compare the forms of the different p~. spectra given in figs. 4a, b we have drawn some arbitrary exponentials with wlrious slopes a. One sees that all given values of q2 the rr+ e l e c t r o p r o d u c t i o n data roughly follow an exponential exp( a p ~ , ) w i t h a ~ - 3 . 5 G e V 2in0.4
5.4. x-dependence We study the x - d e p e n d e n c e of the invariant cross section for both the rr+ and rr data in two regions o f P T : (a) at p~, -~ 0 where we compare with,) c o u n t e r experiments on photo- and e l e c t r o p r o d u c t i o n which were p e r f o r m e d near p~, = 0, (b) in the re. ,) gmn P'i < 0.2 ( ; e V 2, where we c o m p a r e the average of the cross section with photop r o d u c t i o n results from a steamer c h a m b e r experiment. Figs. 7a, b and tables 7a, b show ** the " n e a r l y - f o r w a r d " cross section, normalized to Oto f as a function o f x for two ranges o f q 2. The total virtual p h o t o n cross section Otot(q- , W) = ou, m t + e OL,to t has been calculated by interpolation [21 ] of the existing data on the total inelastic cross section oL,tot/Ou,to t = 0.1 8. * e.g. for W = 2.65 (;eV, x = 0.9, Mt = missing inass of tile unobserved hadrnn systenl) > 1.15GeV, only transverse momenta squared in tire regton PT .< ~ 0.07 GeV 2 are kinematically allowed. ** "File cross sections shown in figs. 7a, b have been taken from l:ehrenbach [9 I. This work contains a refined analysis of the data. *** t:orE 0 = 4.9 GeV, W= 2.65 GeV we obtain O t o t (q2, W) = 95.9, 82.8, 73.1, 66.5, 6{).4 ,ub for iq21 = 0.15, 0.25, 0.35, 0.45, 0.55 GeV 2, respectively• .
2
0
'
I
J
+
i
I
0.6
i
[
0.8
-4'-
+
0.~
I
,
aPT),
' max
t ++++++
( Eo= 5.4GeV)
o.2<1021<0.6GeV2
T
+
~._ +__~__#_~_-e --4-
0.1 < Iq21<0.L,GeV 2
(Eo =4"9GeV)
'
Yv P ~ l I + * a n y t h i n g f~e-a-~ 2
q2:0 AHHM Streamerchamber
I
+
1.0
Cl
Ig
2
5
I0
2
S
I0
20
5O
[G~V ~]
I
-
,~
i
I
0.4
t
I
,
I
0,8
+, +++
0.6 X = p,*//£. ''max
i
+
-*-
,
-4--
+
+++++++ +
0.2< Jq2J
IEo:S~OeVl
0.1< Jq2J< O.Z,GeV 2 (Eo =L,.9GeV)
#
'
Yv P --~-+ anything f ~e-a.PT2 q2=O AHHM Streamerchamber
I
1.0
2 • . " 2 o" Fig. 5. Slope a of the form exp( fitted to each PT2 d i. s t r i b. u t i o. n ot. the . m v a. r l a n .t cross s e c n o n f t o t PT2 < 0._3 GeV . The slope a I"S ~wen as a f u n c t i o n o f x for two d i f f e r e n t qZ intervals c o r r e s p o n d i n g to two d i f f e r e n t energies/:'o o f the p r i m a r y lepton. The d a t a at q--= 0 m a r k e d AHHM are t a k e n from ref. [6]. K i n e n l a t i c range: 2.5 < W < 2.8 GeV, 6 0 ° < 0 < + 6 0 ° ; for data at q2 = 0 : 2 . 4 < W < 2.8 GeV, 0<0<+360 °.
sc
be~Z
~1+
4.3±
4.2±
5.3+
5.7±
6,2±
7.3*
15.8±
26.3±10.0
0.55-0.60
0.60-0.65
0.65-0.70
0.70-0.75
0.75-0.80
0.80-0.85
0.85-0.90
0.90-0.95
1.1
0.7
0.6
0.5
0.5
0.5
0.6
28.1*3.8
13.3±0.8
7.0±0.6
3.8±0.5
4.8t0.5
4.6±0.5
3.7±0.5
2.8±0.6
2.7±0.7
4.4±
0.50-0.55
0.8
2.3±2.4 5.4± 1.1
1.2
3.4±
(E o = 5.4 GeV)
(E o = 4.9 GeV)
0.45
0.2 < Iq2[ < 0.6 GeV 2
0.1 < Iq21 < 0.4 GeV 2
+ anything
16.7±2.8
9.9±0.9
7.3±0.8
5.9±0.8
6.0±0.7
5.3±0.7
6.8±0.8
4.7±0.9
4.0±1.0
3.1± 1.2
3.2±1.8
(E o = 4.9 GeV)
0.1 < Iq21 < 0.4 GeV 2
(b) yvp ~ n - + anything
0.2GeV 2
18.2±2.0
10.1±0.8
5.8±0.7
4.6±0.8
5.5±0.8
3.6±0.8
5.1±0.8
3.1±0.9
6.2±1.1
1.8±1.3
(E o = 5.4 GeV)
0.2 < iq21 < 0.6 (;eV 2
ap~-) as a function of x in the kinematic range 2.5 < W < 2 . 8 G c V , - 60 ° < q ~ < + 6 0 ° , p ~ <
0 . 4 5 - 0.50
0.40
x
(a) 7vp ~
Table 5 Slopea(GeV 2 ) o f f ~ e x p (
~.
5.
~t+
2
L D a m m a n n et al., I n c l u s i v e 7r+ d i s t r i b u t i o n s
I
I
I
I
I
I
I
397
I
5'v p ~ g % a n y t h i n g
Q
[GeV-2]
f~e-aP2
10 O.&
'AHHM
+++++++_+_ I I I I f
5
0
I
I
I
0.7
AHHM
Cor
nell
W=2.2Ge o
5
I
I
I
L
0.2
|
I
J
ox
I
I
Q
I
I
0.6 Iq21 [G~v z]
I
I
r
I
0.8
I
I
1.0
1.2
I
i
I
yv p ~ r C * a n y t h i n g
[GeV~]
f -e-Opt2
IC
AHHM
J
0.,'-< x< 0.7
I
I
I
f
I
I
I
t
I
I (28
I
t
0.7 < x-,:O.9 10
~.HHM
+ ++++-+-@
5
00
[
I (22
I
I 0./.
I
I 0.6
1
1,0
I
1.2
Iq~/ [Gev ~] 2
2
Fig. 6. S l o p e a o f t h e f o r m e x p ( - a P T ) f i t t e d to the P T d i s t r i b u t i o n o f the i n v a r i a n t c r o s s secas a f u n c t i"o n 2o f q 2 f o r t w o2 d l"f t"e r e n t x intervals. U•o n f f O r z p T2 < 0 . 2 G e V 2 . T h e slope a 2is given . " Dataatq =0markedAHHMaretakenfromref. [6];atlq I = 1.2GeV a result of the Cornell e x p e r i m e n t [ 1 2 ] is s h o w n . K i n e m a t i c r a n g e : 2.5 < W < 2.8 G e V , - 6 0 ° < O < + 6 0 °; f o r d a t a at q2=0: 2.4< W< 2.8GeV, 0<(9<+ 360 °;fordataatlq21 = 1.2GeV 2:W=2.2 GeV, 0 < <9 < + 3 6 0 ° .
5.7±0.5
4.1±0.4
3.9±0.5
4.5±0.6
2.7±0.7
4.3±0.9
3.0±1.3
0.15-0.20
0.20-0.25
0.25-0.30
0.30-0.35
0.35-0.40
0.40-0.45
0.45-0.50
0.55 - 0.60
0.50-0.55
5.0±0.8
0.4 < x < 0.7
5.9 ± 1.3
6.2±0.6
5.8±0.7
6.5±0.6
7.1±0.6
7.4±0.6
7.5±0.8
7.4±2.1
0.7 < x < 0.9
5.5±1.2
3.9+0.6
4.5±0.7
4.0±0.6
5.3±0.7
6.8±1.1
0.4 < x < 0.7
(b) "~vp ~ rr- + anything
6.3 + 2.6
6.9±0.9
7.0±0.9
8.2±0.8
7.8±0.7
7.6~0.7
7.1±0.8
0.7
/
aP 2T ) as a function' of q2 in the kinematic range 2.5 < W < 2.8 GeV, - 60 ° < ¢ < + 6 0 ° , p 2, < 0.2 GeV 2
(a) -rvp --, ~-+ + anything
exp(-
0.10-0.15
Lq21 (GeV 2)
Table 6 Slope a(GeV - 2 ) o f f ~
3.
4.
.2
oo
I
~,
r
'
I OJ,
J.C.Al=ld'1er]q2] 5GeV 2etCll.
(Eo: 5.4GeV)
• • •
l
I
..._,~_ _q~_
+~r-
I
~
•
I
x=p:/p~,
I
I
I
*
0.8 "FigTe 1.0
(
~ ' - + _~__~__4t- .l~,l~-4t.,
_4._-+-
-+---+--4'-0.2<]q2]<0.6GeV2 .-+.-
IE°= ~'gGeV)
o,. i~ I-o~oov~
J
,
I
++-.--.-÷_,_++~L~
H.Burfeindt et QL
q2=0
~'I' 'i' +
I
YvP --n;*+onything (pT2:0)
.
2
0.2
o
0.5
05
tO
os
1.C
051
10i
÷ +
I
~'
L
'('
I
I
|
,
I
L~T
~
,, • •
I
I
J~-
__t
O.Z,
I
jr_+ +
.,
2
x=p{'~/p~na '
0,8
•
÷+++++++++ i ] _~
J.C. Aider eta[.
Iq2] =UsO'v2
°2"lq2n~°6 G~v;*-+~-*-++/ T (Eo=5.4GeV)
~- ~ - * -
01<]q2l(0J'GeV (Eo =¢.9GeV)
I
~' ÷ + +
-.--.-_._
H,Burfeindt et al
q2 =0
1
f/O,o,Oev-2] YvP--n:-+°nything (~?=oI
1.0
Fig. 7. Invariant cross section f, as defined in subsect. 5.1, norrnaltzed to Otot(q , W), as a function o f x for t w o dstferent q intervals corresponding to two different energies E 0 of the primary lepton. F o r c o m p a r i s o n data at q2 = 0 [71 and at t q2t = 1.15 GeV z [9] are shown. Kinematic < + 6 0 ° 0 < p 2 < 0 0 2 5 G e V 2" for data at q2 = 0 : I¢ = 2 . 6 3 G e V 0 < ~ < 3 6 0 ° ,0
0.2
o,
o.s
0.5
L(
osl
1.(
0.51
u:)
~Oto,3eV-2]
,g
::11+
e.a
e-,o
0.51 + 0.05
0.52 + 0.06
(t.55 + 0.09
0.56 + 0.12
0.63 ~ 0.20
0.55
0.60
(I.65
0.70
0.60
0.65
0.75 - 0.80
0.80 -- 0.85
0.95
0.55
0.7(t - 0.75
0.90
0.50
0.85
0.90
0.22 ~ 0.15
0.63 ± 0.05
(I.67 + 0.05
0.84 ± 0.08
0.50
(t.45
0.81 + 0.16
0.45
0.1 < fq21 < 0.4 G e V 2
0.40
x
+
(t.22 , 0.13
0.25 ± 0.10
0.46 :- 0.09
0.42 ± 0.06
0.40 ± (I.05
0.47 + 0.04
0.52 ± 0.04
0.57 -+ 0.03
0.62 + 0.03
0.85 ~ 0.06
0.72 +- 0.18
0.2 < Iq21 < 0.6 G e V 2
+ anything
0.52 ± 0.15
0.48 + 0.29
0.40 ± (I.14
0.46 .+- 0.09
0.40 ± 0.06
0.46 + 0.05
0.49 ~ 0.05
0.56 + 0.05
0.67 ÷ 0.05
0.63 -+ 0.04
2
0.22 + 0.08
0.27 ± 0.07
0.38 ± 0.06
0.27 + 0.04
0.3(I -* 0.04
0.37 + 0.04
0.41 ± 0.03
0.50 +- 0.03
(I.52 ± 0.03
0.58 ± 0.04
0.2 < Iq21 < 0.6 G e V 2
60°<~<+60",p~<0.025GeV
0.1 < Iq2i < 0.4 G e V 2
(b) y v p - - rr
2) as a f u n c t i o n o f x in the k i n e m a t i c range 2.5 < W < 2 . 8 G e V ,
(a) yv p - rr + a n y t h i n g
Cross section ratio j[O tot {GeV
Table 7
2
4a.
+
L Darnmann et al., Inclusive n- distributions
401
As we saw in subsect. 5. l that it is uncertain how to extrapolate the p~. distribu2 = 0, we prefer to show the cross section in our lowest p i~ bin, - 1.e. • tion to PT p~- < 0.025 GeV 2. We compare our data with photoproduction values [7] (W = 2.63 GeV p2 ~ 0.01 GeV 2) and with electroproduction values [9] at 2 iq-I = 1.15GeV' 2 j(W= 2.63 GeV, 'P T < ~ 0 . 0 3 G e V 2 ). In general the n ± cross sections decrease when x rises from 0.4 to 0.8. This decrease becomes stronger for larger values of bq2 h. The dependence of the rr+/n -ratio on x is discussed in more detail in subsect. 5.6. In the region 0.8 < x < 0.9 the rr+ and rr-- data indicate a broad bump at all values o f q 2 (except m " n + -photoproducnon), which is due to nA(1236) production. As is known from photo- and electroproduction of nA(1236) [19, 22] the ratio o ( n - A + + ( 1 2 3 6 ) ) / o ( n + A 0 ( 1 2 3 6 ) ) changes from 3 (in photoproduction) to about ") . ") . 1.5 (at iq2i ~ 0.6 GeV-) for fixed transverse m o m e n t u m p~- -~ 0 and fixed W. The rrA(1236) contributions indicated in the inclusive data are in agreement with those expected ratios. In the region x ~> 0.9 it is difficult to compare the n + data obtained in the three different experiments. In the photoproduction experiment [7] no 7r+n peak near x = 1 can be seen because of the finite resolution in x. Front our data the events ep -+ en+n have intentionally been excluded by a missing mass cut (see sect. 4). In the experiment done at Iq21 = 1.15 GeV 2 the n+n events which had not been excluded show a peak near x = 1. Figs. 8a, b and tables 8a, b show the invariant cross sections f/Oto t ofrt + and rrdata, averaged over the range PT < 0.2 GeV 2, as a function o f x for different q2 bins. The photoproduction values from the AHHM-streamer chamber group [6], which are shown for comparison, have been averaged over the same p2T region. For the averaged cross sections, we find in general the same trend as for the forward cross sections. They show a significant decrease with increasing x from 0.4 to 0.8. Within this x-range, the form of the x-distribution seems to be independent of q2; the variation of the absolute height with q2 will be discussed in more detail in the next section. In photoproduction the n + and rr- spectra in the range 0.4 < x < 0.7 are equal in height, whereas in electroproduction the ratio n+/rr increases with increasing Iq21 up to a value of about 2 (a more detailed discussion is given in subsect. + 5.6. The rr photoproductlon data fall more rapidly with x > 0.7 than the n+-electroproduction data. We mention that events of the reaction 7v p -+ n+n(n 0 . .. ) ( 1prong events) were not detected in the n + photoproduction experiment [6]. The authors [6] apply a correction of ~ 10% in the entire x-range due to the Joss of these events. For the ~r+ and rr photo- and electroproduction cross sections a shoulder or a broad bump from rr`5(1236) production is seen in the region 0.8 < x < 0.9 (figs. 8a, b). In the n + photoproduction data this shoulder is smaller because, due to the loss of l-prong events, only ½ oflthe rr+`5°cross section can be seen according to the ratio (,50-+ n - p ) / ( , 5 0 - + nOn)= ~.
402
l. D a m m a n n
e t al., I n c l u s i v e rr+- d i s t r i b u t i o n s
%p--,~%anything 'Io,o,[~v -~] (~,~o~v~) •
I
I
I
I
q2=0
[
~
I
I
-*- 4k-
AHHM
I
I
I
I
q2=0
~
0.1<'q2'< 0.2GeV
0.5
%p--P~-.anything (&~v~)
Z
"~\
"~ + 4,--~_ 0.2<,q 21<0.3GeV2 ~-~
~-
/ / ~
i
i
-~
•÷-
AHHM
*
01< q21<0'2GeV2
~
~'-~
+~~ 0.2
++--~-~=~ \
", ',
o.sl L
i +
= °-'-+
o.~":lq21
4~_
++-.~
"~ ;
0.4
~
\/,
'1 /II
+++4-++ 0.5
0.5
0"11
OD1 0.2
i
I
0.4
]
I 1 0.8I /
0.6 x =p~l/p, I mox
1.0
I
J
0.4
J
I
I
0.6 x=p* , IVPmax
I
0.8
I
1.0
Fig. 8. lnvariant cross section f, as defined in subsect. 5.1, averaged over p ~ < 0.2 GeV 2 and normalized to atot(q z, W), as a function o f x for different q2 intervals. The data points at q2 =0 marked AttHM are taken from ref. [6]. Kinematic range: 2.5 < W < 2.8 GeV, - 60 ° < 0 < +60 ° 0
+
.
.
.
L Dammann et al., Inclusive 7r- dlstrtbuttons
403
Table 8 Cross section ratio f / O t o t (GeV --2) as a f u n c t i o n o f x in the k i n e m a t i c range 2.5 < W < 2.8 GeV, -60 °
.
0.1 (a)
-
.
.
0.2
.
.
.
0.3
.
.
.
.
.
.
.
.
.
.
0.3 - 0.4
0.4
0 . 7 7 8 +- 0 . 0 7 0 0.601 -+ 0 . 0 2 3 0 . 5 0 8 -+ 0 . 0 1 6 0.456 +- /t.013 0.454 + 0.014 0.435 +- 0 . 0 1 4 0 . 3 4 7 +_ 0.014 0 . 3 0 9 +_ I).014 0.325 +_ 0 . 0 1 8 0.2//3+0.016 0.014 +~ 0.005
0 . 6 5 2 +- 0 . 0 7 0 0 . 5 9 0 +_ 0.027 0 . 4 4 6 -+ 0.016 0 . 3 9 8 -+ 0.013 0 . 4 1 7 +_ 0 . 0 1 4 0 . 3 4 2 +_ 0.013 0.321 +- 0.013 0.275 + 0.013 0.277 +- 0 . 0 1 4 0.159-+0.011 0 . 0 3 0 -+ 0.005
0 . 3 9 8 -+ 0.076 0 . 4 2 6 -+ 0 . 0 3 2 0.403 -+ 0 . 0 2 0 0.345 -+ 0 . 0 1 7 0.346 +- 0 . 0 1 7 0.305 +_ 0 . 0 1 6 0.286 +_ 0.015 0 . 2 3 2 +_ 0 . 0 1 4 0 . 2 3 9 +_ 0.015 //.145÷0.012 0 . 0 2 2 +- 0.005
0 . 5 1 3 -+ 0.025 0.445-+0.018 0 . 3 8 4 +_ 0.015 0 . 3 1 4 + 0.013 0 . 3 1 3 + 0.013 0.268+-0.1113 0.245+-0.013 0.235+0.014 0.255±0.016 0 . 2 5 9 +_ 0 . 0 1 8 0.101+0.014 0.020 + 0,020
0.436 + 0 . 0 2 6 0.398+_0.019 0.344 +_ 0 . 0 1 6 0.321 +- 0.015 0.247 -+ 0 . 0 1 3 /I.226+-0.012 0.249+-0.013 0.214+_0.013 0.263+-0.016 0.261 +_ 0 . 0 1 7 0.143+_0.014 0 . 0 4 2 +_ 0 . 0 2 4
0.314 +- 0 . 0 3 3 0.302-+0.025 0.269 +_ 0.1120 0 . 2 2 0 -+ 0 . 0 1 7 0.210 ± 0.017 0.186+0.016 0.168+_0.015 0.167 +- 0.015 0.178"-0.017 0.221 -+ 0 . 0 2 0 0.109-'0.-14
.
0.5
0.5 -- 0.6
3,vp -, n+ + a n y t h i n g
0.40 -0.45 0.50 0.550.60 O.65 0.700.75 O.80 0.85 0.90
0.45 0.50 0.55 0.60 0.65 O.70 0.75 0.80 0.85 0.90 0.95
0.792 + 0.094 0 . 6 9 0 -+ 0.036 0 . 6 0 4 + //.027 0.551 +_ 0.025 0 . 4 9 7 -+ 0.025 0.503 + 0 . 0 2 9 0 . 3 7 4 -+ 0 . 0 2 8 0 . 3 3 9 + 0.031 0.335 -+ 0 . 0 4 2 0.213+_0.042
(b) 7v p ~ 7r
+ anything
0 . 4 0 -- 0.45
0 . 5 3 8 -+ 0.034 0.563-+0.031 0.397 +_ 0 . 0 2 3 0.401 +- 0 . 0 2 3 0.371 ± 0.023 0.287+-0.022 0.328+-0.027 0.272-+0.028 0.309-+0.036 0.265 -+ 0 . 0 4 3 0.094-+0.038
0.45
.
0.2
-- 0.50
0.50 0.55 0.55 0.60 0 . 6 0 - 0.65 0.65 - 0.70 0.70 0.75 0.75 - 0.80 0.80 0.85 0.85 0.90 0.90 0.95 O.95 1.00
0.389 ± 0.068 0.346 +- 0 . 0 3 0 0.386 +_ 0.029 0 . 3 2 6 + 0.025 0 . 2 4 0 -+ 0 . 0 2 2 0.225 +_ 0 . 0 2 0 0.192 +_ 0 . 0 1 8 0.201 -+ 0 . 0 1 9 0.161±0.017 0 . 0 3 2 +_ 0.01/7
0 . 2 2 2 +- 0.049 0.186+_0.033 0.161 + 0 . 0 2 6 0 . 1 4 6 -+ 0.023 0 . 1 4 4 -+ 0.021 0.127+-0.0211 0.092÷0.017 0.119+0.019 0.130+-0.021 0 . 1 5 9 -+ 0.023 0.080-+0.016 0 . 0 1 3 +_ 0 . 0 0 9
5.5. q2-dependence We show the q2-dependence 7r
production
of the invariant cross section for both
data in two ranges of the transverse momentum .
9
t h e 7r+ a n d
squared"
(a) at
p 2T ~ 0 , ( b ) i n t h e r e g i o n P'i" < 0 . 2 G e V 2. F i g . 9 a n d t a b l e 9 s h o w t h e n e a r l y f o r ward cross section
]" =__Ed3O °tot
1
dp 3 °tot
'
a v e r a g e d o v e r a s m a l l b i n p 2 < 0 . 0 2 5 G e V 2.
+
404
I. D a m m a n n et al., Inclusive ~r d i s t r i b u t i o n s
E .dd~. a_~.,[GeV-Z] ,, i, ~ot '
.g, p ~t+ anything (w=2.65 6ey, pl2 =0
'
,
,
,
,-
,
t
i
C
,
,
,
,
i
1.0 oQ,~
t'
{'
" =" [O.t,-x-0.7
l
1.0
q el zl.
HBurfeindt
~ n-
A1 thi' 'xperim'nt
0.7
]OESV
O.l
C) J C.Alder el zl. i
.
.
.
.
o2
.
i
o'.~ 3
i
16 ' o'.o
Iq21 [GeV 2 ]
3
i
J
to
i
iz
I
~
li
l~
+
t~lg. 9 . 1 n v a r l a n t c r o s s s e c t l o n k d o / d p , f o r r r andrr data, normalized to otot(q 2, W ) , a s a function of [q21 for two different x intervals. For comparison data at q2 = 0 [ 7 ] and at Iq21 = 1.15 GeV 2 [9] are shown. The lines are just for eye guidance. Kinematic range: same as in fig. 7.
Table 9 Cross section r a t i o f / o t o t (GeV 2) as a function o f q 2 in the kinematic range 2.5 < W < 2.8 GeV, 60 ° < q ~ < + 6 0 °, p } < 0.025 GeV 2
Iq21(GeV 2) 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55
0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60
(a) 7vp ~ ~z+ + anything
(b) 'yv p ~ ~- + anything
0.4
0.7
0.4
0.83 + 0.08
0.55 ± 0.18
0.61 ± 0.06
0.67 0.69 0.59 0.58 0.56 0.51 0.56 0.42
+ (t.06 ± 0.05 ± 0.04 ± 0.03 ± 0.03 -+ 0.04 ± 0.04 + 0.05
0.50 ± 0.06 0.54 0.51 0.40 0.40
± 0.08 +- 0.09 +- 0.06 -+ 0.07
0.34 +- 0.04
0.53 0.56 0.51 0.43 0.39 0.38 0.28 0.26
± 0.03 ± 0.03 -+ 0.03 ± 0.02 ± 0.02 ± 0.03 ± 0.03 ± 0.04
0.7
0.56 0.49 0.50 0.55 0,34 0,36 0,28 0.21 0,25
+ ± + + + * ± ± ±
0.08 0.05 0.05 0.05 0.06 0.06 0.06 0.05 0.06
T h e c r o s s s e c t i o n s g i v e n f o r c o m p a r i s o n at q 2 = 0 [7] a n d iq2t = 1.15 G e V 2 [9] w e r e m e a s u r e d at a b o u t t h e s a m e W ~ 2 . 6 5 G e V , b u t in s l i g h t l y s m a l l e r p 2 r a n g e s (see s u b s e c t . 5.4. All c r o s s s e c t i o n s h a v e b e e n a v e r a g e d o v e r t h e x - i n t e r v a l s 0.4
I
I
7L
I
I
_<,_-~"+ 0.4
I
I
.
.
0.7
4,-
i
0.2
I
I
0.4
J
Iq21[G~v2]
I
0.6
I
I
++-'--'- ._-.- ,__.__._t
+
+ + + + +
I
-~--~--'~--~-o--*--°--e---°--+ -0"6"= x<0"7 I
-*--*---*-~--*-__._~_ _+ +0"5
I
(P2< 0.2GeV2}
YvP ~Tt++anything
2
",I,
0.
0
°I
02.
0.5
0.2
Ib
0.5
0.2
0.5'
i
-
I
0.2
I
0.4
0.5
I
+
TI
0.6
0.8
4-
0.7
1
0.6
++
++
I
0.4
++
Iq21[GeV2]
I
-+-_1_-,--*--,- -¢I
'
-I-_¢_
-'~--4,-_,_
+ + ~4__--4~
~--+_e__e
-4'--e--l- -,~--"-- -e-
-~--¢__4F
'
(p2<0.2OeV2)
YvP~ n;-+onything ~+-+'._
,o-.-.AHHM
0.~'
f/O,o, [GeV-2]
I
Fig. 10. Invariant cross section f, as defined in subsect. 5.1, averaged over p T < 0.2 GeV 2 and normalized to Otot(q 2, W), as a function o f q 2 for different x intervals. The data points at q2 = 0 marked AHHM are taken from ref. [6 ]. Kinematic range : same as in fig. 8.
0.2
0.
O.2
0.2 0.5 =
0.5
I
\AHHM
o.?.
0.5
Ii I
f/otot [GeV-2]
4~
=11+
,7
e~
rb
+
406
1. D a m m a n n
et al., I n c l u s i v e rr d i s t r i b u t i o n s
"Fable 10 Cross section r a t i o f / O t o t (GeV 2 ) a s a f u n c t i o n o f q 2 in ttle kinematic range : 2 . 5 < W < 2 . 8 G e V , 60 ° < ~ < + 6 0 ° , p 2 < 0.2 (]eV 2 Iq21 IGeV 2 )
x 0.4 - 0.5
(a) yvp -
rr +
0.6 - 0.7
0.7
0.8
0.8 - 0.9
0.603 0.558 0.511 0.445 0.454 (I.385 (I.392 0.336 (I.397 tl.325
0.496 ± 0.046 0.494± 0.020 0.463 ± 0.015 0.434 ~ 0.014 0.381 -+ 0.013 0.391 -+ 0.014 0.337± 0.014 0.314+ 0.018 0.310± (I.022 0.253 ± 0.026
0.435 ± 0.068 0.328 + 0.020 0.352 ± 0.015 0.290-+ 0.l)12 0.314 + 0.013 0.269 + 0.012 (t.252 ± 0.013 1t.251 -+ 0.015 0.226 ± 0.018 (I. 169± 0.019
0.409+ (I.289+_ 0.301 ± 0.287 ± 0.235 ± 0.252± 0.220± 0.198 + 0.220+ 0.184 +
(I.382± 0.041 0.318-+ 0.017 0.305 ± 0.013 /I.285-+0.013 (I.248 ~- 0.012 0.233-± 0.013 0.218 + 0.014 0.182+0.017 0.141 ±0.019 0.132± 0.024
0.344+ 0.056 0.285 ± 0.019 0.236 + (/.013 0.234±0.013 0.252-+ 0.014 0.201 + 0.012 0.168-+ 0.013 0.165±0.017 0.116-+0.017 0.(t84+ 0.018
0.398+ 0.140 0.294 ± 0.029 0.266+- 0.019 0.277±0.018 0.283 + 0.018 0.273 + 0.017 0.229 ± 0.018 0.179±0.019 0.168+0.022 0.132+ 0.025
+ anyHling
0.10 0.15 0.15 - 0 . 2 0 0.2(I 0.25 0.25 0.30 0.30 0.35 (/.35 0.40 0,411 0.45 0.45 0.50 0.50 0.55 0.55 0.60
0.725 ± (/.062 0.711 + 0.042 0.638 ± 0.032 0.649± 0.033 0.634± (I.036 t1.572 + 0.038 0.407-+ 0.036 0.489-+ (I.055 0.469-+ 0.088 0.195 + (I.099
(b) yvp ~n-
+anything
0.10 0.15 0.20 0.25 0.30 (I.35 0.40 0.45 0.50 0.55
0.526 + 0.044 0.553 ± 0.026 0.460± 0.020 0.493-+0.022 0.448 ± 0.(122 0.386 ± 0.023 0.324± 0.025 0.285±0.031 0.218±(I.035 0.168 + 0.047
0.15 0.20 0.25 0.3(/ 0.35 0.40 0.45 (/.50 0.55 0.60
0.5 - 0.6
± 0.042 + 0.020 + 0.015 ± 0.014 + 0.015 ± 0.014 ± 0.017 +- (I.019 ± (I.027 +_ 0.{133
0.396 + 0.033 0.384± 0.017 0.352+ 0.014 0.331+0.014 0.335 + 0.015 0.316 ± 0.0t5 0.254± 0.016 0.221±0.019 0.162+0.022 0.133 +- 0.027
C o m p a r i n g t h e rr + w i t h rr
0.191 0.031 0.020 0.017 0.(t14 (I.(t14 0.014 0.016 0.019 0.022
c r o s s s e c t i o n s , o n e sees t h a t in g e n e r a l the n o r m a l i z e d
rr+ c r o s s s e c t i o n s are larger. T h e rr- d a t a s h o w a s t e e p e r d e s c e n t w i t h rising iq2k t h a n tile rr + d a t a ( f o r t h e r a l i o rr+/rr In tile r e g i o n 0.7 < x < 0.9 tire rr
see s u b s e c t . 5.6. photoproduction
c r o s s s e c t i o n is larger t h a n
the rr+ c r o s s s e c t i o n . T h i s is m a i n l y d u e to rrA(1 2 3 6 ) p r o d u c t i o n : at q 2 = 0 m o r e rr A ++ t h a n rr+A 0 are p r o d u c e d (see figs. 7a, b) [22]. N e x t w e s h o w in figs. 10a, b a n d t a b l e s 10a, b tire n o r m a l i z e d i n v a r i a n t c r o s s sect i o n ) ' / o m t a v e r a g e d o v e r p 2 < 0.2 G e V 2, as a f u n c t i o n o f q2 in small x - i n t e r v a l s . T h e 7r+ a n d rr
d a t a i n c r e a s e w i t h i n c r e a s i n g Iq2i f r o m [q2i = 0.2 G e V 2 t o
Iq 2 I =
0.6 G e V -~. F o r c o m p a r i"s o n r e s u l t s f"r o m 7r-+ p h o t o p r o d u c t l o' n are given f o r 2 ~ + • 2.4 < W < 2.8 G e V , also a v e r a g e d o v e r P'F < 0.2 G e V - . T h e 7r p h o t o p r o d u c t l o n v a l u e s lie s i g n i f i c a n t l y b e l o w t h e e l e c t r o p r o d u c t i o n v a l u e s at lq2t ~ 0.2 G e V 2. T h e c o r r e c t i o n s d u e to t h e l o s s e s o f l - p r o n g e v e n t s are i n c l u d e d in the rr+ p h o t o p r o d u c t i o n d a t a [6] (see s u b s e c t . 5.4). F o r the 7r- d a t a (fig. 10b) t h e d i f f e r e n c e b e t w e e n t h e c r o s s s e c t i o n s at q 2 = 0 a n d [q21 ~ 0.2 G e V 2 is s m a l l e r .
+ . . L D a m m a n n et al., Inclusive ~ d i s t r t b u t t o n s
407
In figs. 10a, b one sees a similar tendency with respect to q2 as in fig. 9: )'/o.. 2 /" 2 tot increases (or is nearly constant) for Iq 1~ 0.3 GeV and then decreases with rising Iq2j. Within the statistical significance of our data, this q2dependence off/Oto t is the same for all given x-intervals. We mention that such a decrease ofj'/Oto t with increasing ]q2i as seen in figs. 9 and 10a, b f o r x > 0.4 has not been found in the a+ electroproduction experiment of Lazarus et al. [10] in the range 0.15 < x < 0.05, performed at a somewhat higher energy W = 3 GeV. There,JTOtotWas found to be rather constant at Iq21 = 0.3, 0.6 and 1.2 GeV 2.
5.6. Charge ratio n+/n In the previous subsections we pointed to the differences in t h e x and q2 dependence of the rr+ compared with the ~ cross sections. To see this different behaviour .
R- do(~ )
-do--~
Zi--"
r
~f,p ~ t
÷
.
+onythmg
" (~2~o.2o~v 2) I~
I
u
I
I
--I---~ q2=0 AHHM I I
~ I
t
_,~_1
I
__~ ,
+-~--*--'-+ -~-+4,-q,_ 0,1
I
]
I
I +
0.2
+ 21
0,3<1q21< 0.Z,GeV 2 I I I
+
I
I_~_
I
i~ -
~ -+-+++q'- + +
1 0,4
-t~
0
+ O.S
t
O~
_~_ I
.0.6 x= Pll/pmNax
I
i 0.8
i --r~igtt '
1.0
Fig. 11. R a t i o R = da(n+)/do(~-) o f the cross sections d 2 o / d x d p } for n + and rr- data, aver2 aged over P T < 0 . 2 G e V 2, as a f u n c t i o n o f x, for different q2 intervals. T h e data points at q 2 = 0 marked AHHM are taken from ref. {6]. Kinematic range: same as in fig. 8.
L Dammann et al., Inclusive ~r-+distributions
408
R= do(~') doltC) I
%'vp ~ n : = + a n y t h i n g ( p2 < 0,2 GeV2) I
I
I
I I
I
AHH-~t- _4_+__,__ --iF-- 4 , - + + T
I
0.4
t
/
-+--4-'--*---
I
I
_4,_-~ :
-*-~-
I
!
0.5
II
~-
I
++
++ -*-~__~_ -*--~--q-
+
I
,-,--*--*--~F~-+O.6
,
0 0
-
+-*-+ o[2
0.7
__,_÷-*-+J'-0.8 <,.~ 0.g '
I
o'.~
I
o.~ lq~l [OeV2]
l:ig. 12. RatioR=do(n+)/do(Tr )ofthecrosssectionsd2o/dxdp}forn+andTr d a t a , avera g e d o v e r p 3f < 0 . 2 G e V 2 , as a f u n c t i o n o f q 2 f o r d i f f e r e n t x intervals. T h e d a t a p o i n t s a t q 2 = 0 m a r k e d A H H M are t a k e n f r o m ref. [6]. K i n e m a t i c r a n g e : s a m e as in fig. 8.
T a b l e 11 C r o s s s e c t i o n r a t i o R = d u ( r r + ) / d o ( r r - ) as a f u n c t i o n o f x in the k i n e m a t i c r a n g e : 2.5 < W < 2 . 8 G e V , o 2 60 ° <0<+60 ,pT < 0.2GeV 2 x
Iq21 ( G e V 2 ) 0. l
0.40 - 0.45 0.45 - 0.50 0.50-0.55 0.55 0.60 0.6(/ 0.65 0.65 - 0.70 0.70 - 0.75 0.75- 0.80 0.80 0.85 0.85-0.90 0.90 0.95
0.2
1.47 -+ 0.2(i 1.23 .+ 0 . 0 9 1.52+-0.11 1.37 -+ 0 . 1 0 1.34±0.11 1.75 -+ 0 . 1 7 1.14 +- 0 . 1 3 1.25+-0.17 1.08+-0.19 0.80+-0.21
0.2
--0.3
1.52 +. 0 . 1 6 1.35 .+ 0 . 0 8 1.32_+0.07 1.45 ± 0 . 0 7 1.45.+0.08 1.62 -+ 0 . 0 9 1.42 -+ 0 . 0 9 1.31-+0.10 1.28-+0.11 0.78+0.08 0 . 1 4 +. 0 . 0 6
0.3
0.4
1 . 5 0 +- 0 . 1 8 1.48 -+ 0 . 1 0 1.30_+0.08 1.24 +- 0 . 0 7 1.69-+0.10 1.51 +- 0 . 1 0 1.29 -+ 0 . 0 9 1.29+-0.10 1.06-+0.08 0.61-+0.06 0 . 2 1 -+ 0 . 0 4
0.4
0.5
1,27 + (t.28 1,41 -+ 0 . 1 6 1,50+-0.14 1,57 +- 0 . 1 4 1.65-+0.15 1,64 -+ 0 . 1 6 1 . 7 0 -+ 0 . 1 8 1.39+-0.16 1.34-+0.16 0.66_+0.08 0 . 2 0 +- 0 . 0 5
0.5
-0.6
2.09 ± 0.52 2.15-+0.39 2 . 6 5 -+- 0 . 4 6 2.27+-0.38 1.89 -+ 0 . 3 5 2 . 4 4 +- 0 . 5 0 1.61-+0.30 1.55-+0.29 1.01+0.18 0 . 3 9 -+ 0 . 1 2
+
.
.
.
1. Darnrnann et al., Inclusive rr- dtstrtbuttons
409
Table 12 Cross section ratioR = dc~lrr )/do(~r ) as a lunctlon ofq in the kinematic range: 2.5 < W< 2.8GeV, 60 ° < ~ < +60 ° ,p-~-< O.2 GeV2 +
•
Iq21 (GeV 2 )
2
x 0.4
0.10 0.15 0.15 0.20 0.20 0.25 0.25 - 0.30 0.30-0.35 0.35 - 0.40 0.40 - 0.45 0.45 0.50 0.50 0.55 1/.55 - 0.60
,
0.5
1.38-+0.16 1.28-+0.10 1.39+--0.09 1.32 -+ 0.09 1.41-+0.11 1.48 -+ 0.13 1.26 -+ 0.15 1.72-+0.27 2.15 -+ 0.53
0.5
0.6
1.52±0,17 1.45+0.08 1.45-+0.07 1.35 -+ 0.07 1.35-+0.07 1.22 ± 0.07 1.54 -+ 0.12 1.52 ± 0.16 2.44 -+ 0.37 2.45 + 0.55
0.6 - 0.7
0.7
0.8
1.30-+0.19 1.55-+0.10 1.52-+0.08 1.53 -+ 0.09 1.54-+0.09 1.68 -+ 0.11 1.55 -+ 0.12 1.73-+0.19 2.20 -+ 0.34 1.91 -+ 0.40
1.27+-0.29 1.15-+0.11 1.49-+0.10 1.24 + 0.09 1.25+0.09 1.34 + 0.10 1.50 + 0.14 1.52-+0.18 1.95 -+ 0.32 2.00-+ 0.49
0.8 - 0.9 1.03-+0.60 0.98-+0.14 1.13-+0.11 1.04 -+ 0.09 0.83-+0.07 0.93 -+ I).08 0.96 -+ 0.10 1.11+-0.15 1.31 + 0.21 1.39-+ 11.31
o f the 7r+ and lr cross sections more clearly, we show the r a t i o R = do0r+)/doOr - ) of the cross sections d 2 o / d x dp2T as a function o f x in fig. 1 1 and table 1 1, and as a function o f q 2 in fig. 12 and table 12. The cross sections d 2 o ( ~ + ) / d x dp 2 and d 2 o ( r r - ) / d x dPT have been averaged over p ~ < 0.2 GeV 2. Radiative corrections do not significantly influence the values of R as m e n t i o n e d above. For comparison the ratio obtained in p h o t o p r o d u c t i o n [6] is given, also as an average over p . ~ < 0.2 GeV 2. F r o m fig. 11 we see that in all bins o f q 2, R is i n d e p e n d e n t o f x up t o x ~ 0.7. Above x ~ 0.8, R falls to nauch smaller values. We m e n t i o n again the exclusion of ep ~eTr+n events which would mainly contribute to the region 0,9 < x < 1 (see subsect. 5.4.). While at q2 = 0 the n u m b e r of p r o d u c e d lr + equals the n u m b e r o f ~ r - (at 0.4 < x < 0.7), the ratio R increases with increasing Iq2i up to R ~ 2 at iq21 ~ 0.6 GeV 2 (see fig. 12). We m e n t i o n that in the e x p e r i m e n t [9] p e r f o r m e d at iq2[ 1.15GeV 2andp{,~0aratioof2<~R<~3hasbeenfoundintheregion 0.4 < x < 0.7 (see figs. 7a, b).
6, S u m m a r y 1. The invariant n + and n cross sections dn not significantly depend on the azinmthal angle qS, i.e. d2aT/'Ckr dPT and d2Ol/dX dp 2 are small c o m p a r e d with d2Ou/dX dp 2 + e d2OL/dX dp 2. (see fig. 3). 2. For b o t h the lr + and ~ data the p 2 distributions show an a p p r o x i m a t e ex2 The slope depends ponential behaviour apart from the region o f very small PT" strongly on x (in the region 0.4 < x < 1) but varies very little with q2 t h r o u g h o u t the region 0.3 < Iq21 < 0.6 GeV2; however, it is smaller than in p h o t o p r o d u c t i o n (see fig. 6).
+
410
L D a m m a n n et al., Inclusive n distributions
3. T h e i n v a r i a n t n+ and 7r cross s e c t i o n s f decrease w i t h rising x ( w i t h i n 0.4 < x < 0.7). This d e s c e n t is r a t h e r flat at q2 = 0 b u t b e c o m e s m o r e p r o n o u n c e d w i t h increasing Iq2i (see figs. 7 a n d 8). 4. T h e i n v a r i a n t n+ a n d n cross sections)'~ divided by the total inelastic cross section Oto t ( q " W), are larger at Iq21 ~ 0.2 G e V 2 t h a n for p h o t o p r o d u c t i o n ; for [q21 ~ 0.2 G e V 2 .['/Otot(q" "), W) decreases again (see fig. 9). •
5. In the interval 0.4 < x < 0.8 the ratio R = do(rr+)/do(Tr -) increases w i t h increasing tq2l f r o m R ~ I (at q2 = 0) to R ~ 2 (at Iq2l ~ 0.6 G e V 2) (see fig. 12). We like to t h a n k all o t h e r m e m b e r s of o u r g r o u p for t h e i r e x c e l l e n t technical assistance. T h e s u p e r i o r p e r f o r m a n c e o f the S y n c h r o t r o n crew in p r o v i d i n g the intense p o s i t r o n b e a m is gratefully a c k n o w l e d g e d . We also t h a n k the H a l l e n d i e n s t , the K~iltetechnik a n d the R e c h e n z e n t r u m for their valuable c o o p e r a t i o n . M a n y discussions w i t h Drs. H. Meyer a n d B.H. Wiik have b e e n very valuable.
References [1] 11. Kendall, K. Berkelman and .I. Bjorken in Int. Symposium on electron and photon interactions at high energies, Cornell University, 1971, ed. N.B. Mistry. [2] K.C. Moffeit et al., Phys. Rev. D5 (1972) 1603. [3] W.P. Swanson et al., Phys. Rev. Letters 27 (1971) 1472. [4] A.M. Boyarski et al., as quoted by 13. Wiik, talk at the Cornell Conference (1971). [5] Aachen-Hamburg-Heidelberg-M~inchen Collaboration, as quoted by 13. Wiik, talk at the Cornell Conference ( 1971 ). 16] Aachen-ltamburg-Heidelberg-Miinchen Collaboration, Inclusive photoproduction of rr+ and p at energies up lo 6.3 (;eV, and comparison to electroproduction, Contribution no. 668 to the 16th int. Conf. on high energy physics, Chicago, 1972, and private communications• [7] H. Burfcindt et al., DESY 72/75 (1972); B.H. Wiik, private communication. [8] A. Sot'air et al., Nucl. Phys. B42 (1972) 369. [9] J.C. Adler et al., Nucl. Phys. B46 (19721 415; W. Fehrenbach Hamburg, thesis. [ 10] E. Lazarus et al., Phys. Rev. Letters 29 (1972) 743. [11] V. Eckhardt et al., DESY 72•67 (19621. [12] C.J. Bebek et al., contribution no. 952 to Chicago Conference (1972). [131 See e.g.S.M. Berman, Phys. Rev. 135 (1964) 1249. [141 C. Driver et al., Nucl. Phys. B30 (19711 245. [15] J. Ralhje, ttamburg thesis (1971), DESY F32-71/3 (19711. [16] G. llofmann, Hamburg thesis (1971), DESY t"32-71/2 (1971). [17] P. Karow, ltamburg thesis (19711, DESY F32-71/1 (1971). [18] LW. Mo and YS. Tsai, Rev. Mod. Phys. 41 (19691 205. [ 19] 1. Dammann el al., DESY 72]70 (1972). [2(1] H. Cheng and T.T. Wu, Phys. Rev. 183 (19691 1324; J.D. Bjorken, J. Kogut and D. Soper, Phys. Rev. D3 (1971) 1382; It.T. Nieh, Phys. Letters B38 (1972) 100. [21] F.W. Brasse et al., Nucl. Phys. B39 (19721421. [22] A.M. Boyarski et al., Phys. Rev. Letters 25 (1970) 695.