- Email: [email protected]
cπ−p interactions
Nuclear Physics B53 (1973) 43-61. North-Holland Pubhshmg Company
S I X - P R O N G E V E N T S P R O D U C E D IN 5 GeV/c
7r-p INTERACTIONS
Berlin - D u b n a Collaboration
U. GENSCH, K. LANIUS, A. MEYER and H.J. SCHREIBER Institut fur ttochenergiephysik der Akademie der lCtssenschaften der DDR, Zeuthen/Berlin A. CONSTANTINESCU, W.W. GLAGOLEV, P.M. LEBEDEV and I.S. SAITOV Joint Institute ]'or Nuclear Research, Dubna
Received 26 October 1972
Abstract. Results are presented from a study of 3 184 six-prong n"p interactions at 5 GeV/c m the Dubna 1 m hydrogen bubble chamber. Cross sections for the various reacnon channels axe given and their energy dependence is discussed. The emphasis of this paper is on exhib~nng the semi-inclusiveparticle spectra in sufficient detail ,so that it wdl be possible to use it for testing models and developing new concepts. In particular, invariant d~strlbutions are plotted against the scaled longitudinal momentum x, the rapidrty y and the longitudinal momentum PL m the lab system The net charge per x as well as y interval is also presented. It is found that the isotroplc pion component is inconsistent with the Bose-Einstein formula. Compaxlson with data at other energies is made whenever possible.
1. Introduction In this paper we present results of stx-prong events produced in ~r-p interactions at 5 GeV/c incident lab momentum. Six-prong n - p events have already been studied at 3.2 (ref. [1 ]), 3.9 (ref. [2]), 4.2 (ref. ]3]), 5.5 (ref. [4]), 6 (ref. [5]), 7 (ref. [6-101), 10 (ref. [11]), 11 (ref. [12, 13]) and 16 GeV/c (ref. [14]). Previous results of this experiment have already been reported in ref. [15]. Most of the past investigations of hadron-hadron colhsions examine phenomena in few-body final states of rip, Kp and other interactions. In recent years however a growing interest in many-body reactions in observable and nowadays a large part of experimental and theoretical studies have been directed to understand some gross features of the transition matrix element by means of measuring only one particle in the final state, irrespective of how many other particles are produced in the col-
44
u. Gensch et al., 5 GeV/c n - p interactions
lislon. The study of SLx-prong events may be considered as a task somewhere m between few body investigations and the analysis of inclusive reactions" there are at least six particles in the final state and accordingly, the number of independent variables is at least 14. Hence the extraction of information about the production mechanism will be in general more difficult than in two- or three-body final states. On the other hand, using a bubble chamber one is not forced from the first to measure only one final particle in multibody collistons since the momenta of all charged particles can in principle be measured. However, the information about produced neutrals is lost in general. Since data are needed for testing and developing new ideas, the purpose of this paper ~s to make avadable our data m sufficient detail so that they can be effectwely used in this area of research. Necessarily many of the features of the six- and more-body final states studied in this experiment are of a statistical nature. In sect. 4 we present some of these features and compare them with those at other energies whenever possible. Our particular interest was directed to production mechanism of secondaries, investigating transverse- and c.m. longitudinal-momentum distributions, production-angle distribution, rapidity dtstribution etc., and to the question whether there are correlations between these varmbles. Some attempts have been made to study two-particle correlations in subsect. 4.4.
2. Experimental procedure The events of this experiment came from some 500 000 pictures taken in the Dubna 1 m hydrogen bubble chamber exposed to an unseparated n - beam at 4.9 GeV/c with I% resolution. A total of about 3 500 SLx-prong events with neither visible strange-particle production nor Dalitz pairs were found in a double scan of the film. The events were measured on convenuonal film-plane measuring machines and processed through the CERN chain of programs: THREStt, GRIND, SLICE and SUMX. Events which failed in THRESH or GRIND were remeasured. A total of 3 183 events was included in our final sample. The events were divided among the reaction channels * n - p ~ p 2rr + 3n'- ,
(1)
p 27r+ 37r-n ° ,
(2)
n 37r+ 37r- ,
(3)
p 2rr + 3rr- Z° ,
(4)
n 37r+ 31r- Z° .
(5)
* The symbol Z° represents more than one ~r° in reaction (4) or one or more ~r° m reaction (5).
45
U. Gensch et al., 5 Ge V/c 7r-p interactions
All events giving a satisfactory fit were checked for consistency of the observed ionisation with that gwen by the fitting program. Ambiguities between different constraint classes were resolved in favour of the higher constraint class, and for an n-fold ambiguity within a given constraint class, the event was assigned to each possible channel weighted by a factor of 1/n or by accepting that channel with the at least three times higher probability. A break of this rule was the ambiguity among channel (3) and (4). Here, both hypothesis have been accepted with a weight ~ [16]. This event selection technique results to a < 5% background in the four-constraint reaction (1), < 10% and < 20% background in the one-constraint reactions (2) and (3), respectively.
3. Cross sections The number of events assigned to each reaction channel and the cross sections for this experiment are given in table 1. The errors presented for the cross sections are only statistical ones. Estimates of the systematical errors in the fit channels (1), (2) and (3) were given in sect. 2. The cross sections compared with measurements at other energies are shown in fig. 1. The lines drawn through the experimental points are only to guide the eye. The total 6-prong cross section increases with increasing momentum over the whole energy range explored. For fitted reaction channels the cross section rises from threshold up to a maximum and than decreases at higher lab momentum. The no-fit channels behave similarly to the topological cross section itself, rising steadily with increasing momentum from threshold up to the highest energy measured, so that the higher the energy the larger is the amount of multi-neutral events in a given experiment. Our 5 GeV/c data indicate that at such small energies the total six-prong cross section is governed by the cross section of the fit channels or, in other words, six- and seven-body final states dominate the sixprong events at 5 GeV/c although phase space allows besides one nucleon a maximum of 15 plons to be produced. Table I Number of events used In the analysis and cross sections l"mal state a) .
.
No. of events .
.
.
.
n - p ---,p 2rr+ 3n n-p'-*p2n+3n-lr °
n-pon3n+3n n - p ~ p 2n + 3n- Z° Tr-p~ n 3n+ 3~r' zO ]
.
.
.
.
.
.
.
.
.
.
.
(?ross section (,ub) .
.
.
.
.
.
.
.
.
.
903 1157 331 5
246 +- 10 331 -* 12 93-+ 6
792 5
227 ~ 14
a) The symbol Z° is defined In the text.
.
.
.
.
.
.
.
.
.
46
U (;ensch et al., 5 Ge V/c rr- p mteractzons m
_
F
,--- ~.p--iN ~ET~AcTIONS r
r~
r
L L
z
~
0
i" l.,
,
" ,t,,-
!
0 IJ
oI D
i
<*i
/": ~, .L /
[ 1
s
,b PLab ' GeV/e
,'s
~. ] 2o
}'lg 1. Variation of sr<-prong cross sections m r r p Interactions as a function of the momentum
Plab of the incoming plon. 4. General features of the data
Sxmple properties of particle producnon in many-body reactions may be described by single-particle distributions which are obtained by integrating of the manydnnensxonal phase-space d~strlbutions over the molnenta of all partmles except the one whmh ~s being studied. Because of the azxmuthal symmetry of the initial state one needs only two variables instead of three, so that a two-dimensional distributxon contains complete information on the production of a particle at fixed incident energy. 4.1 D i s t r i b u t i o n s o f transl,erse a n d c m . l o n g z t u d i n a l m o m e n t u m
In fig. 2 plots of transverse momentum, PT, v e r s u s the c.m. longitudinal momentum, p~, for the final proton and charged pions of the total six-prongs are presented. The following features can be observed (a) Protons tend to populate regions at negative p~_ and small PTValues. (b) Plons of both charge tend to cluster near the center of the plot.
U. Gensch et al., 5 Ge V/c ~r-p mteracttons
w'-p
.......
6 prongs
AT 5 GeV/c
47
7
" OH- •
uJ
z <[
4
.-
~-
1 1
01,
-2
-I
0
,1
°1
*2
cm LONGITUDINAL MOMENTUM GeV/c
Fig. 2. Distributions of transverse m o m e n t u m versus c m. longitudinal m o m e n t u m for plons and protons produced m six-prong ~r-p interactzons at 5 GeV/c
[
tr-p
AT 5 GeV/c
6prongs
]
! ?IOS w'" PARTICLES
0551 if" PARTICLES
2/,40 p PARTICLES 1200
,
II00
0
SO
O2
06
02
Q6
0,2
0.6
TRANSVERSE MOMENTUM, GeV/c Fig. 3. Transverse m o m e n t u m d~stnbutlons of p~ous and protons produced m six-prong ~r-p interactions at 5 GeV/c. The dashed curves represent our best fits as described m the text.
48
U Gensch et aL, 5 GeV/c n-p interactions
These features indicate that the leading particle effect for the proton is weak but present, i.e. in six-prong events at 5 GeV/c lab momentum the incident proton tends to conserve its direction of motion and its initial energy. The leading particle effect for the n - meson is small and strongly suppressed by the existence of more than one negative p~on per event. In fig. 3 we present the transverse momentum distributions for the charged pions and protons. The pions reveal a behaviour very similar in shape to each other. The protons exhibit a larger average transverse momentum. However, the general trend of this distribution, namely a rising behaviour at low PT values and after the maximum a quite fast fall-off as PT increases is unchanged with respect to the pion d~stnbutions. In past investigations the nature of these spectra in the multi-GeV range has been an interesting problem. Still no conclusion which formula gives the best description can be drawn. Therefore we have tried to describe our data according to the linear distribution [17].
d o/dp T -- ap T exp ( -bPT ) ,
(6)
the Boltzmann distribution: d o/dPT = aPT exp (-bp2),
(7)
the thermodynamical model [18]:
do/dPT = aPTlaKl(ta/To) , 02 = p2T + m 2 ,
(8)
a formula obtained from the thermodynamlcal model for m2/2p~- ~ 0 [19]:
d a/dp T = ap T exp (-PT/To),
(9)
and the Planck distribution:
do/dPT=PT#m { ~ (+)n+l Kl(nla/T 0)/~n (+-)n+l K2(nm/TO)
(10)
It turns out that our pion spectra are best described * by formula (8) with ×2/NDF = 2.1. The value T0(w- ) obtained was 103 MeV while T0(n +) turns out to be 95 MeV. Among the distributions we have tried, formula (I0) gives comparatively the best fit (x2/NDF = 1.0) with T O = 87 MeV for the proton spectrum. Our best fit results are shown as dashed curves m fig. 3. In order to discriminate between these several ansatzes we have calculated the moments and test functions as gwen in ref. [20]. Neither one however is adequate for the PT distributions of the charged secondaries in our experiment. The average transverse and longitudinal momenta of the nucleons and plons in the total st,x-prong sample as well as for each channel separately are summarized in table 2. While the < p~ > values for both charged pions are equal to each other in each indiwdual channel, for the n + meson is significantly smaller than for • The x2/NDF obtained by using eq. (10) is only shghtly larger.
Table 2 Average values of transverse and longitudinal m o m e n t u m for nucleons and plons at 5 GeV/c lab m o m e n t u m
Final state a)
< pT >
(MeV/c)
proton
neutron
n÷
~-
n°
< P[ >
tMeV/c)
proton
neutron
rr*
~r-
7r°
total stx-prongs
378 *- 4
238-+
3 251 ±
2
-120- + 8
2 2 -+
7r-p -* p 2n ~ 3~r-
396 ± 7
274-+
7 300±
7
-124-+ 13
20-+ 12
28*- 15
l r - p "-* p 2rr* 3 n - r r °
376 ± 6
7 232-+5
-114-+ 10
18-+
8
17-+ 10
35-+ 19
10± 18
.,r - p
~
n 37r ÷
3n-
7r-p ~ p 2n ÷ 37r- Z °
231 ± 5 250-+
363-+ 11 2 4 4 ± 13 243-* 13 378 -+ 8
n - p ~ n 3n ÷ 3 n - Z °
a) The symbol Z ° is defined m the te':t.
207±
9 205-+ 11
210.- 10 190-+
9
-135± - 1 2 4 -+ 18
19
3
18-+
3
19 ± 13
14 ± 15
1 8 -+ 14
7 2 16
26±6 Xa
I
2"
50
U G e n s c h et a l , 5 G e V / c n - p i n t e r a c t i o n s
F.... • proton L
~7-p-- p 2 rr "3:rr "
V rr" (
z
t
o • ~-
~
tit It)
,
!
t
,
> it)
z <~ o:;
!
7
t
,J
, ....
?r-p~p2~"3~
• proton ;
?r" V fr"
,J
.
500~ >
!
;
!
300-
i
.~e
`5
10
P Lab
GeV/¢
Fig. 4. A v e r a g e t r a n s v e r s e m o m e n t a o f s e c o n d a r i e s p r o d u c e d in r r - p ~ p 2rr ÷ 3 n - a n d n -p --, p 2n ÷ 3 n - * r ° as a f u n c t i o n o f t h e i n c o m i n g rr m o m e n t u m , Plab-
/
r-p 6 prongs . . . . i ........ `500i' 7105rr ° PARTICLES tl J'lg551I'-I "~t--~T/'" I'~PARTICLES[_[ J
AT 5 GeV/c
l /
2440 p PARTICLES ~300
ZOO
2.50-
[ P00
!
0i__ -1
.
0
]_ . -I
.
.
.
. 0
[.. . . . -1
•. . . . . 0
COS 8 "
Fig 5. P r o d u c t i o n a n g u l a r d i s t r i b u t i o n s o f c h a r g e d s e c o n d a r i e s p r o d u c e d in s i x - p r o n g n - p ratera c t i o n at 5 G e V / c
U Gensch et al., 5 Ge V/c 7r-p mteracttons
51
the rr - in reactions (1) and (2) The difference is probably due to copious A ++ (1236) production [21 ] m these reactions which is a source of n + mesons with low transverse momentum [22]. The average transverse momenta for final nucleons are in general about 100 MeV/c larger than for ptons. The values of thexr longitudinal components establish the leading particle character. In fig. 4 we present the behavlour o f < P T > for pions and nucleons in reaction (1) and (2) versus incident lab momentum. Our 5 GeV/c data points establish the trend expected from higher energy data down to small energies. The proton possesses the largest < PT > values in the energy range explored. Its difference from the pion values seems to be independent of Plab. It seems further that the average transverse momenta tend to approach a limit at high energies for both types of secondaries. The fact that < PT >rr ÷ < ( PT > n - IS observed at Plab ~> 10 GeV/c too; however, any energy dependence of this difference cannot be established. 4.2. P r o d u c t i o n angular d i s t r i b u t i o n s
Fig. 5 displays the emission angle distribution for the charged secondaries, the 7r+, 7r- mesons and the proton for all st,x-prong events. Obviously, the interaction cannot be described by phase space alone so that even as a first approximation phase space cannot be used for the description of the data. A measure of the deviation o f phase space is the asymmetry ratio A = ( F - B ) / ( F + B). The asymmetry values obtained for the pamcles produced m all six-prong events as well as m the fit channels (1) --(3) are hsted m table 3. For the reactions (1) --- (3) they are compared with the results ofTr p experiments at 5.5 (ref. [4]), 6 (ref. [5]), 7 (ref. [8]), 10 (ref. [11]) and 16 GeV/c (ref. [14]) in fig. 6. It is evident that the asymmetry of baryons and the rr- meson is more pronounced at higher energies. The rr÷ meson reveals a shght positive (however energy independent) asymmetry ratio. It seems further that below 6 GeV/c in the seven-particle final state (3) the neutron is more peaked backward than the proton in the corresponding reaction (2). Recently the question arose [23] whether there is an isotropic component of particle production m high-energy collisions and whether the energy distribution of this part obeys the Bose-Einstein functxon. As observed on fig. 5, the production angular distributions are anisotropic. For smaller values of E*, the amsotropy deTable 3 Asymmetry rano A = (F - B)/(F + B) m 5 GeV/c rr p interactions proton total six-prongs -0.24 ± 0 02 n - p -, p 21r*3rr-0.26±003 rr'-p~p2n*3rr"n ° -0.22± 0.03 n - p --' n 3~r*3zr-
÷
..
neutron
/r
/r
- 0 30 +-0.05
0.07 ± 0.01 0.03±002 0.06 ± 0.02 0.09 -+ 0.03
0.04 ± 0.01 0.04± 002 0.06 ± 0.02 0.09 ± 0.03 0.04 ± 0.03
7,t o
U. Gensch et al., 5 GeV/c *r-p mteracttons
52
•0 ~
•
/
1 i
....
_,.,.,.:
L'
.........
...................
: .........
[
-05,
,.
it
~-t
t~
~ ~"
- - .
~.os[ --
I
~-0sii
+
--I
i
t .............................
0 ~ ..... ¢_~
u
{"
*t
_"........
i
",,.
pro~
~
i
<{
! ,
f
~-p ~ p 2 zr*3~'-Tr*
q-
,
---+--
i
-
,,~n'*
I
. I
l
7 r - p ~ n 3 ;7" 3 ~--
.4~vv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0 .....
.". . . . . . . . .
!
i# !
-05"
•
rwutron
=
rr -°
vrrJ
5
10
]
1
15
PLal) ' GeV/c l"lg 6 A s y m m e t r y
a function
r a u o A = ( F - B)/(F + B) f o r sccondanes p r o d u c e d m reactions ( 1 ) - ( 3 ) as
of t h e m o m e n t u m
o f t h e i n c o m i n g p~on
creases markedly and below 400 MeV the p]on distribuhons are isotropic. Given isotropy, all information resides solely in the energy spectrum, so that the non-Lorentzinvanant density distribution may be written as d3N/d3p - 4 r r l , E , dN/dE* = F(E*).
Fig. 7 shows a semilogarithmic plot of the experimental distributions, (4rip*E*) -1 dN/dE*, for n +, 7r- and proton, ttowever, a fit to the pion data using the Bose-Einstein function F ( E * ) = (e E*/kT - 1) -1
(1 1)
reveals no satisfactory success; the X2 probability turns out to be < 10- 2 for the n as well as the 7r+ sample. Thus, we may conclude low-energy n's in six-prongs at 5 GeV/e are inconsistent with formula (11) or, in other words, they are not distributed m a manner analogous to photons m "blackbody radiation". It Is "also evident from fig. 7 that a simple exponential fails to describe the energy distribution at low c.m. energies too.
U Gensciz et al, 5 Ge V/c *r-p interactions
rfp
6
prongs
7105 7r* PARTICLES
53
AT 5 G e V / c 9551
w"
PARTICLES
2/./.0 p PARTICLES
C3 O
\
Z
'
'
0k, c m
I.lg. 7
044 ENERGY , GeV
104
I~
Energy distribution of charged secondaries produced in six-prong rr-p interactions at 5
(;eV/c 4. 3. The mvariant distributions as a f u n c t i o n o f x , y and PL
The single-particle distribution in an inclusive reaction may be described by the expression d o/dPT dp~_ = ) ~1 / ' ( P L, ' PT' s).
(12)
According to Feynman [24], the invariant structure function f ( p E , PT, s) should approach a lltnttmg distribution of only two variables at very high energies. One of these variables is the transverse momentum, the other one is either the longitudinal momentum in the lab (projectile) system or the reduced c.m. longitudinal momen-* tum, x - PL/Pm~x" Thls scahng suggestion has been extended by Koba, Nielsen and Olesen [25] to the so-called semi-inclusive reactions a + b ~ c + (n
1) charged particles + any neutrals,
(13)
where in addition to the knowledge of the momentum and nature of particle c the number of charged particles produced is known. Bubble chamber experiments are most suitable to investigate semi-inclusive reactions since the total number of charged particles created is simply obtained by counting the tracks per event. Provided scaling works in reclusive reactions then the authors of ref. [25] suggest a scalIng law In semi-inclusive reactions:
forn~>.
U Gensch et al., 5 Ge V/c n - p interactions
54
w-p
6 prongs
AT 5 GeV/c
t
-05
0
-0.5
O
oo I
-0.8
0
0.8
SCALED LONG MOMENTUM . x = pL / Pn,,ax
Fig. 8 [nvarlant structure fun~.tlon for pions and protons produced in six-prong n - p interactions at 5 GeV/c as a function of the scaled longitudinal m o m e n t u m x
The semi-reclusive spectra for the charged pions and proton as a function o f x are presented in fig. 8. The plon spectra reveal a very symmetric behaviour at x = 0, while about ~ of the protons have x values smaller than zero. Unfortunately there are not yet other semi-inclusive data published m order to test the scaling hypothesis according to ref. [25]. ~'p
G ~ s
-/-
71057r* PARTICLES
~,51 n'" PARTICLESI
0i
o
°
I
24/,0 p PARTICLES ,
!
¢
I 102
z
AT 5 GeV/c
101
1 -2
Q
-2 S
O
-2 5
(1
5
RAPIDITY
Ftg. 9. Rapidity distribution of charges secondaries produced in six-prong 7r-p interactions at 5 GeV/c.
U. Gensch et aL, 5 Ge V/c n - p mteractzons
6 prongs
7/" p .
.
.
.
.
.
.
.
.
.
55
AT S GeV/c
.
.
.
.
.
.
.
.
.
1
.
.
0
J2o
L
i
f .....
-0.2
0
02
04
/ ..... -'02
0
02
i 04
~ 02
]o 04
06
08
LONGITUDINAL MOMENTUM IN THE TARGET REST SYSTEM
Fig. 10 Energy-weighted lab longitudinal momentum distributions of plons and protons produced In six-prong rr-p interactions at 5 GeV/c.
In fig. 9 we present the invariant cross section as a function of the rapidity [24] E* + p~ y=~ lnE._p [ .
(15)
The asymmetry in the proton case observed in the x variable is also evident in the rapidity. The pion distributions are again symmetric and very close to each other. Benecke, Chou, Yang and Yen [26] suggest plotting data In term of s, PT and the longitudinal momentum in the lab system, PL. The hypothesis of limiting fray'henration of ref. [26] is easily shown to be the same as the Feynman prediction, provided that x 2 ~ 4(p 2 + m2)/s, where m is the mass of the detected particle. Fig. 10 displayes the pion and proton distributions in terms of PL. Plotting data in one of the rest systems of the incident particles offers the possibility to test besides hmiting fragmentation the hypothesis of factorizatton. By factorizatlon we mean, if pomeron exchange dominates than the mvariant cross section for a given target (projectile) should be independent of the projectile (target) particle, so that appropriate semi-inclusive data at other energies might be compared with that on fig. 10. Since the invariant cross section depends at fLxed s on two variables, e.g. the transverse momentum PT and the scaled longitudinal momentum x, it is of mterest to ask if there are correlations between these two variables. In order to study this problem we have plotted the invariant cross section for the n± semi-inclusive data against x in intervals ofp2T , seen in fig. l I. The variation of the spectra with increasing p2T illustrates that the structure function cannot be written as a product of two functions, one of them only depending onp2T, the other only on x; i.e.
u. Gensch et al., 5 Ge V/c n - p mteractions
56
rr-p
I 1o'It~
"
,
o
i
10
,
I
~-,-~-,-~,~
_I"e-,-tl..,_~-~o~,.o~ :"u
~os , ,
r"° i 01"p1T
-
,4,,
l
F"',-,"--~'-u ,;o;.otl
log) 04 -0,4 O0 SCALED LONG MOMENTUM
Fig 11. [nvarmnt structure funcnon for as a function o f x m steps of p-I-.
p2) *
0~
+
//-
-04
f(x,
AT 5 OeV/c
,
~..~,~,,;.oo~
1'I I
"1o
6prongs
n+
0.4
and Tr- mesons produced in six-prongs at 5 GeV/c
g ( x ) h(p~.) .
The question can be repeated using the rapidity, y , instead o f x . In fig. 12 we p lot the n u m b e r o f ~± mesons as a function o f y for various intervals in p2. T Within our limited statistics it is evident from that figure, that f O ' , p2) Is inconsistent with factorization for the n - as well as for the n + meson. Moreover, the 7r- distribution
-p
AT 5 GeV/c
6 prongs
--
I
S.
i
- i
O:p~,OO5
I0z. c~
'iI
IJd ._J cj
t,n,-
nJj
10 I :
<
"kl
I0 T
2 2 -2 RAPIDITY Fig. 12. Rapidity distributions for n ÷ and n - mesons produced m stx-prongs at 5 GeV/c m steps -2
of p-I-.
0
U. Gensch et al., 5 GeV/c n - p interactions
7/"- p
prongs
a) 005~
_.
AT 5 C~Vlc
T Z,X "~ b)
-005~-
57
Z--Y
T
I __.~
.
.
-0,8
.
.
I
0
1
i .......
.1_
(18
-2
SCALEDLONGMOMENTUM, x
0
J i
2
RAPIDITY.y
Fig. 13. Net charge distributions as (a) a function of the scaled longttudmal m o m e n t u m x and (b) as a function of the rapidity y for stx-prongs produced in ~r-p interactions at 5 GeV/c.
for 0 ~< p2 < 0.05 (GeV/c) 2 reveals in comparison to the other spectra of this figure a shoulder at y ~> 1 establishing the leading particle effect. This effect has not been seen in the p~integrated x and y distributions (see figs. 8 and 9).
4.4. Charge distributions In studying high energy interactions certain parameters and quantum numbers are considered. The charge, which is one of the quantum numbers and one of the characteristics of the initial state has been rarely taken into account. When two particle collide, in our case the ~ - and p, then the question may arise, how does the charge behave over the x range [27]. In fig. 13 we plot dQ/dx as well as dQ/dy defined as dzdQ- d N1N t o{dN t_a _l
__
_dN _
}
,
z=x,y.
(15)
Here Ntota I corresponds to the total number of events. Since the initial charge is zero the area above the line dQ/dZ = 0 is equal to the area below that line. The distribution dQ/dx (fig. 13a) reveals a positive net charge over the x range - 0 . 6 to - 0 . 2 . This effect is due to the proton whose contribution is strongest in that x interval. With increasing x the distribution rapidly changes sign to give a negative enhancement near x = + 0, 1. The negative net charge at positive x comes from the dominance of n - particles in that region. One would a priori expect that besides positive (negative) net charge at negative (positive) x values the to-
58
u (;ensch et al., 5 GeV/c n- p mteracttons
tal charge near x = 0 vanishes Contrary to that we observe strong negative charge, so that one may conclude from fig. 13a that (i) leading parucle effects are also present for the n - meson and (u) these effects e x t e n d out to and b e y o n d x = 0. In addition to the net charge per x interval we show m fig. 13b the charge distribution dQ/dy plotted against y, the rapidity, d Q / d y is charactertzed by two negative enh a n c e m e n t s near y = +- 1, a region where the negative p~ons d o m i n a t e over the posltwe ones. The proton contribution is negligtble for lyl >~ I due to kinematics (see also fig. 9). Near y = 0 the net charge is poslttve since the proton and n + mesons d o m i n a t e here over the negattve charged plons. 4.5. Two-partwle correlations It was orxgmally p o m t e d out by G o l d h a b e r et al. [28] and then by Bartke et al. [29] that the distributions o f angle between the pair of pions depend on whether the pions have hke or unlike charges ( G G L P effect). An investigation o f these distributtons has been made for plons m our total six-prongs as well as in reactions (1), (2) and (3). For each o f these reactions and for each pair of charged pions, we have determined the q u a n t i t y 3' = B / F where B denotes the n u m b e r of plon pairs with opening angle greater than 90 ° and F denotes the n u m b e r of pairs with angles less than 90 °, "/++, 7 - - and 3'+- refer to pairs of posltwe plons, negative pions and to pairs o f plons of unhke charge, respecttvely. The 3' values for this e x p e r i m e n t are presented m table 4 calculated m b o t h the overall c.m. system of the reaction and m the rest system o f the p~ons. The 3'++ are found to be smaller than 3 ' - - for reaction (1) and (2) as well as for the overall sample, irrespectively of the rest system in which they have been calculated. The 5 G e V / c n + e x p e r i m e n t [30] has shown on the contrary that 3'++ 3> 3 ' - . Fable 4 Correlation parameter 7 for plon pairs of hke and unhke charge
.
overall c m. system
3'÷+
7--
3'+ -
total six-prongs n - p ~ p 2zr~"3n -
1.08 ± 0 04
1.19 ± 0.03
1 54 ± 0 02
1 06 ± 0 09
1 32 ± 0.05
1 69 ± 0.04
n - p ~ p 2 n ÷31r-rr°
1 06 ± 006
1.20+- 003
1 47 ± 003
n--p--* n 3rr*3n-
1 15 ± 0.08
1 05 ± 0.07
1.57 ~- 0.04
plon rest system
3'++
3'--
3'+-
total six-prongs
1.20 ± 0.05
1.35 ± 0.04
1 84 -* 0.03
n-p~p2n+3n -
1.11 ± 0.09
1 59± 0.06
2.21 ± 0.05
lr p--* p 2n÷3;,r-Tr°
1 22 ± 0.07
1.36 ± 0 05
1.70 ± 0.04
n - p --' n 3n ÷ 3rr-
1 26 ± 0 09
1 19 ± 0.09
1 89 ± 0 05
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
59
U. Gensch et al., 5 GeV/c lr- p mteracttons
IN O V E R A L L ,~ ~
c m
t
1
i
'I--t
t
t
,--
~---
-~
r* If'*-
I • It'-"
,
.
]
l
, -
rr p - n 3 n " 3 / r " I
ISr-
• v
I
;'r-p -- p 2 ft" 3 n ' " rr *
/
,o I
.~
rr-p - p 2 r r ' 3 ~ r "
~s-
10It-
SYSTEM
:
r ** Ie-
v
r e-
=
~ '~
.
.
.
,'5
.
PLaI~
,
'
GeV/c
Iqg. 14 The values -,t+ , ~++ and 7 - - calculated m the overall c.m., as a function of the metdent rr momentum, Plab. This effect could be attributed to the leadmg lr as argued in ref. [12]. However, following this argument one might expect that this effect is more d o m i n a n t the higher the energy is. In fig. 14 the values for the three fitted reactions obtained in the overall c.m. system are shown. There seems to be the trend that T +-, largest below 7 GeV/c, decreases continuously as Plab increases, so that It ~s comparable w~th T - or T ++ or even smaller at 16 GeV/c. The difference between T ++ and " 7 - - m reaction ( l ) and (2) is only estabhshed at our energy and does not grow with increasing energy as e x p e c t e d from leading particle influence alone.
5. Conclusion In studying 3 184 six-prong 7r-p interactions at 5 GeV/c, it was first noted that rarely more than one rr° is present m the final state. The d o m i n a t i n g reaction channels are r:- p --,- p 27r+ 31r - and rr -p ~ p 2rr + 3rr- rr°. A very general feature o f the six-prongs is already revealed by the study o f individual final--state p a m c l e s . It is found that the productions do not follow the relati-
U. (;ensch et al , 5 Ge V/c lr-p interactions
60
vistic statistical phase space. F r o m the description of transverse m o m e n t a usmg several formulas it was c o n c l u d e d that the gross features are accounted for by the therm o d y n a m l c a l model (8) for mesons and the Planck distribution (10) for baryons, i.e. the PT spectra are governed by statistical laws. Further, it has been found that the energy behaviour o f the lsotroptc c o m p o n e n t of the cos 0* distribution for plons is inconsistent with the Bose-Einstein formula (1 1). In order to open the possibility of testmg the scaling hypothesis as well as factor. tzation in semi-inclusive reactions we presented the invariant distributions as a function o f x , y and PL" It has been found that for the 7r- and 7r+ mesons the invarlant structure function is inconsistent with factorlzation into a product g(x) h(p2T ) or g(v) h(p2). In addition we presented the net charge p e r t a n d y mterval in our sixprong data. F r o m dQ]dx some leading particle features of the ~r- were observed also b e y o n d x = 0. The general features o f the G G L P effect observed in this e x p e r i m e n t are very similar to those in pp annihilation where it was originally studied. However, any interpretation ts made difficult since the angular correlations are perturbed by the presence of resonance and the rr- leading particle effect. We are deeply Indebted to the operating crews of the p r o t o n synchrotron at Dubna and the 1 m Dubna hydrogen bubble chamber. We would like to thank the scanning, measuring and c o m p u t i n g staffs at each of our laboratories.
References [I] [2] [31 [4] [5] [6] [71 [8] [9] [101 {ll] [12] [131 [14] [151 [16] 117] [18]
R.H. Allen and V.G. Lind, Bull Am. Phys. Soc. 13 (19681 589. K. Abe et al , Phys. Rev D2 (1970) 91 R.A. Luke and V.G. Lind, Bull. Am. Phys. Soc. 13 (19681 589 F Bomsectal.,Phys. Rev. 162(1967) 1328 K.F. Suenetal,Phys. Rev D1 (19701 54. M,A l.laz and J E. Campbell, Nucl Phys. B7 (1968) 175 M,A. Ijaz and J E Campbell, Nuovo Clmento 61A (1969) 307. J E. CampbellandM.A. Ijaz, Nucl. Phys B12 (19691549. P L Berenyl et al., Bull Am. Phys, Soc. 12 (19671 684. P.L. Berenyl et al., Nucl. Phys. B37 (1972) 621. M Bardamn et al., lnsntute of Nuclear Research, Warsaw, report 51 I/VI (19641. P. Daroman et al., CERN report Th-68-7 (19681 226. P Daroman, A Dandm and L. Mosca, paper submitted to the Collt~qulum on high multlphclty hadrontc interactions, Paris, 1970 (unpubhshed) B Junknrannet al,Nucl Phys. BS(19681471 V.V Glagolev et al, paper submitted to the 15111 Int. ('onf on high energy physics, Klev, 1970 (unpubhshed) M.R Atalanand I,S. Saltov, Jomt Institute for Nuclear Research, Dubna, report 13-6(186 (1971) G Coccom, J Koesterand J H Perkms, UCRLreport 10022 (1961) R. Hagedorn, NuovoOmentoSuppl 3(19651 147
U. Gensch et al., 5 Ge V/c n - p interactions
61
[19] R. Hagedorn, CERN preprmt TH/851 (1967). [201 T.F. Hoang, Nucl. Phys. B38 (1972) 333 [21 ] Berhn-Dubna Collaboration, paper submitted to the Int Conf. on high energy physics, Batavia, 1972. [22] U. Gensch and H.J. Schrelber, Berhn preprint PHE 7 1 - 15 (1971) [23] J. Erwm et al., Phys. Rev. Letters 27 (1971) 1534. [24] R.P. Feynman, Proc. of the 3rd Int. Conf. on high energy colhslons, Stony Brook, 1969; Phys. Rev. Letters 23 (1969) 1415. [25] Z. Koba, H.B. Nielsen and P. Olesen, Phys. Letters 38B (1972) 25. [26] J. Benecke, T.T Chou, C.N. Yang and E. Yen, Phys. Rev. 188 (1969) 2159. [27] L. Van flove, Proc. of the Colloqumm on multiparticle dynamics, Helsmki, 1971. [28] G. Goldhaber et al., Phys. Rev. 120 (1960) 300. [291 J. Bartke et al., Phys. Letters 24B (1967) 163. [30] H. Drevermann et al., Phys. Rev. 161 (1967) 1356.
S I X - P R O N G E V E N T S P R O D U C E D IN 5 GeV/c
7r-p INTERACTIONS
Berlin - D u b n a Collaboration
U. GENSCH, K. LANIUS, A. MEYER and H.J. SCHREIBER Institut fur ttochenergiephysik der Akademie der lCtssenschaften der DDR, Zeuthen/Berlin A. CONSTANTINESCU, W.W. GLAGOLEV, P.M. LEBEDEV and I.S. SAITOV Joint Institute ]'or Nuclear Research, Dubna
Received 26 October 1972
Abstract. Results are presented from a study of 3 184 six-prong n"p interactions at 5 GeV/c m the Dubna 1 m hydrogen bubble chamber. Cross sections for the various reacnon channels axe given and their energy dependence is discussed. The emphasis of this paper is on exhib~nng the semi-inclusiveparticle spectra in sufficient detail ,so that it wdl be possible to use it for testing models and developing new concepts. In particular, invariant d~strlbutions are plotted against the scaled longitudinal momentum x, the rapidrty y and the longitudinal momentum PL m the lab system The net charge per x as well as y interval is also presented. It is found that the isotroplc pion component is inconsistent with the Bose-Einstein formula. Compaxlson with data at other energies is made whenever possible.
1. Introduction In this paper we present results of stx-prong events produced in ~r-p interactions at 5 GeV/c incident lab momentum. Six-prong n - p events have already been studied at 3.2 (ref. [1 ]), 3.9 (ref. [2]), 4.2 (ref. ]3]), 5.5 (ref. [4]), 6 (ref. [5]), 7 (ref. [6-101), 10 (ref. [11]), 11 (ref. [12, 13]) and 16 GeV/c (ref. [14]). Previous results of this experiment have already been reported in ref. [15]. Most of the past investigations of hadron-hadron colhsions examine phenomena in few-body final states of rip, Kp and other interactions. In recent years however a growing interest in many-body reactions in observable and nowadays a large part of experimental and theoretical studies have been directed to understand some gross features of the transition matrix element by means of measuring only one particle in the final state, irrespective of how many other particles are produced in the col-
44
u. Gensch et al., 5 GeV/c n - p interactions
lislon. The study of SLx-prong events may be considered as a task somewhere m between few body investigations and the analysis of inclusive reactions" there are at least six particles in the final state and accordingly, the number of independent variables is at least 14. Hence the extraction of information about the production mechanism will be in general more difficult than in two- or three-body final states. On the other hand, using a bubble chamber one is not forced from the first to measure only one final particle in multibody collistons since the momenta of all charged particles can in principle be measured. However, the information about produced neutrals is lost in general. Since data are needed for testing and developing new ideas, the purpose of this paper ~s to make avadable our data m sufficient detail so that they can be effectwely used in this area of research. Necessarily many of the features of the six- and more-body final states studied in this experiment are of a statistical nature. In sect. 4 we present some of these features and compare them with those at other energies whenever possible. Our particular interest was directed to production mechanism of secondaries, investigating transverse- and c.m. longitudinal-momentum distributions, production-angle distribution, rapidity dtstribution etc., and to the question whether there are correlations between these varmbles. Some attempts have been made to study two-particle correlations in subsect. 4.4.
2. Experimental procedure The events of this experiment came from some 500 000 pictures taken in the Dubna 1 m hydrogen bubble chamber exposed to an unseparated n - beam at 4.9 GeV/c with I% resolution. A total of about 3 500 SLx-prong events with neither visible strange-particle production nor Dalitz pairs were found in a double scan of the film. The events were measured on convenuonal film-plane measuring machines and processed through the CERN chain of programs: THREStt, GRIND, SLICE and SUMX. Events which failed in THRESH or GRIND were remeasured. A total of 3 183 events was included in our final sample. The events were divided among the reaction channels * n - p ~ p 2rr + 3n'- ,
(1)
p 27r+ 37r-n ° ,
(2)
n 37r+ 37r- ,
(3)
p 2rr + 3rr- Z° ,
(4)
n 37r+ 31r- Z° .
(5)
* The symbol Z° represents more than one ~r° in reaction (4) or one or more ~r° m reaction (5).
45
U. Gensch et al., 5 Ge V/c 7r-p interactions
All events giving a satisfactory fit were checked for consistency of the observed ionisation with that gwen by the fitting program. Ambiguities between different constraint classes were resolved in favour of the higher constraint class, and for an n-fold ambiguity within a given constraint class, the event was assigned to each possible channel weighted by a factor of 1/n or by accepting that channel with the at least three times higher probability. A break of this rule was the ambiguity among channel (3) and (4). Here, both hypothesis have been accepted with a weight ~ [16]. This event selection technique results to a < 5% background in the four-constraint reaction (1), < 10% and < 20% background in the one-constraint reactions (2) and (3), respectively.
3. Cross sections The number of events assigned to each reaction channel and the cross sections for this experiment are given in table 1. The errors presented for the cross sections are only statistical ones. Estimates of the systematical errors in the fit channels (1), (2) and (3) were given in sect. 2. The cross sections compared with measurements at other energies are shown in fig. 1. The lines drawn through the experimental points are only to guide the eye. The total 6-prong cross section increases with increasing momentum over the whole energy range explored. For fitted reaction channels the cross section rises from threshold up to a maximum and than decreases at higher lab momentum. The no-fit channels behave similarly to the topological cross section itself, rising steadily with increasing momentum from threshold up to the highest energy measured, so that the higher the energy the larger is the amount of multi-neutral events in a given experiment. Our 5 GeV/c data indicate that at such small energies the total six-prong cross section is governed by the cross section of the fit channels or, in other words, six- and seven-body final states dominate the sixprong events at 5 GeV/c although phase space allows besides one nucleon a maximum of 15 plons to be produced. Table I Number of events used In the analysis and cross sections l"mal state a) .
.
No. of events .
.
.
.
n - p ---,p 2rr+ 3n n-p'-*p2n+3n-lr °
n-pon3n+3n n - p ~ p 2n + 3n- Z° Tr-p~ n 3n+ 3~r' zO ]
.
.
.
.
.
.
.
.
.
.
.
(?ross section (,ub) .
.
.
.
.
.
.
.
.
.
903 1157 331 5
246 +- 10 331 -* 12 93-+ 6
792 5
227 ~ 14
a) The symbol Z° is defined In the text.
.
.
.
.
.
.
.
.
.
46
U (;ensch et al., 5 Ge V/c rr- p mteractzons m
_
F
,--- ~.p--iN ~ET~AcTIONS r
r~
r
L L
z
~
0
i" l.,
,
" ,t,,-
!
0 IJ
oI D
i
<*i
/": ~, .L /
[ 1
s
,b PLab ' GeV/e
,'s
~. ] 2o
}'lg 1. Variation of sr<-prong cross sections m r r p Interactions as a function of the momentum
Plab of the incoming plon. 4. General features of the data
Sxmple properties of particle producnon in many-body reactions may be described by single-particle distributions which are obtained by integrating of the manydnnensxonal phase-space d~strlbutions over the molnenta of all partmles except the one whmh ~s being studied. Because of the azxmuthal symmetry of the initial state one needs only two variables instead of three, so that a two-dimensional distributxon contains complete information on the production of a particle at fixed incident energy. 4.1 D i s t r i b u t i o n s o f transl,erse a n d c m . l o n g z t u d i n a l m o m e n t u m
In fig. 2 plots of transverse momentum, PT, v e r s u s the c.m. longitudinal momentum, p~, for the final proton and charged pions of the total six-prongs are presented. The following features can be observed (a) Protons tend to populate regions at negative p~_ and small PTValues. (b) Plons of both charge tend to cluster near the center of the plot.
U. Gensch et al., 5 Ge V/c ~r-p mteracttons
w'-p
.......
6 prongs
AT 5 GeV/c
47
7
" OH- •
uJ
z <[
4
.-
~-
1 1
01,
-2
-I
0
,1
°1
*2
cm LONGITUDINAL MOMENTUM GeV/c
Fig. 2. Distributions of transverse m o m e n t u m versus c m. longitudinal m o m e n t u m for plons and protons produced m six-prong ~r-p interactzons at 5 GeV/c
[
tr-p
AT 5 GeV/c
6prongs
]
! ?IOS w'" PARTICLES
0551 if" PARTICLES
2/,40 p PARTICLES 1200
,
II00
0
SO
O2
06
02
Q6
0,2
0.6
TRANSVERSE MOMENTUM, GeV/c Fig. 3. Transverse m o m e n t u m d~stnbutlons of p~ous and protons produced m six-prong ~r-p interactions at 5 GeV/c. The dashed curves represent our best fits as described m the text.
48
U Gensch et aL, 5 GeV/c n-p interactions
These features indicate that the leading particle effect for the proton is weak but present, i.e. in six-prong events at 5 GeV/c lab momentum the incident proton tends to conserve its direction of motion and its initial energy. The leading particle effect for the n - meson is small and strongly suppressed by the existence of more than one negative p~on per event. In fig. 3 we present the transverse momentum distributions for the charged pions and protons. The pions reveal a behaviour very similar in shape to each other. The protons exhibit a larger average transverse momentum. However, the general trend of this distribution, namely a rising behaviour at low PT values and after the maximum a quite fast fall-off as PT increases is unchanged with respect to the pion d~stnbutions. In past investigations the nature of these spectra in the multi-GeV range has been an interesting problem. Still no conclusion which formula gives the best description can be drawn. Therefore we have tried to describe our data according to the linear distribution [17].
d o/dp T -- ap T exp ( -bPT ) ,
(6)
the Boltzmann distribution: d o/dPT = aPT exp (-bp2),
(7)
the thermodynamical model [18]:
do/dPT = aPTlaKl(ta/To) , 02 = p2T + m 2 ,
(8)
a formula obtained from the thermodynamlcal model for m2/2p~- ~ 0 [19]:
d a/dp T = ap T exp (-PT/To),
(9)
and the Planck distribution:
do/dPT=PT#m { ~ (+)n+l Kl(nla/T 0)/~n (+-)n+l K2(nm/TO)
(10)
It turns out that our pion spectra are best described * by formula (8) with ×2/NDF = 2.1. The value T0(w- ) obtained was 103 MeV while T0(n +) turns out to be 95 MeV. Among the distributions we have tried, formula (I0) gives comparatively the best fit (x2/NDF = 1.0) with T O = 87 MeV for the proton spectrum. Our best fit results are shown as dashed curves m fig. 3. In order to discriminate between these several ansatzes we have calculated the moments and test functions as gwen in ref. [20]. Neither one however is adequate for the PT distributions of the charged secondaries in our experiment. The average transverse and longitudinal momenta of the nucleons and plons in the total st,x-prong sample as well as for each channel separately are summarized in table 2. While the < p~ > values for both charged pions are equal to each other in each indiwdual channel,
Table 2 Average values of transverse and longitudinal m o m e n t u m for nucleons and plons at 5 GeV/c lab m o m e n t u m
Final state a)
< pT >
(MeV/c)
proton
neutron
n÷
~-
n°
< P[ >
tMeV/c)
proton
neutron
rr*
~r-
7r°
total stx-prongs
378 *- 4
238-+
3 251 ±
2
-120- + 8
2 2 -+
7r-p -* p 2n ~ 3~r-
396 ± 7
274-+
7 300±
7
-124-+ 13
20-+ 12
28*- 15
l r - p "-* p 2rr* 3 n - r r °
376 ± 6
7 232-+5
-114-+ 10
18-+
8
17-+ 10
35-+ 19
10± 18
.,r - p
~
n 37r ÷
3n-
7r-p ~ p 2n ÷ 37r- Z °
231 ± 5 250-+
363-+ 11 2 4 4 ± 13 243-* 13 378 -+ 8
n - p ~ n 3n ÷ 3 n - Z °
a) The symbol Z ° is defined m the te':t.
207±
9 205-+ 11
210.- 10 190-+
9
-135± - 1 2 4 -+ 18
19
3
18-+
3
19 ± 13
14 ± 15
1 8 -+ 14
7 2 16
26±6 Xa
I
2"
50
U G e n s c h et a l , 5 G e V / c n - p i n t e r a c t i o n s
F.... • proton L
~7-p-- p 2 rr "3:rr "
V rr" (
z
t
o • ~-
~
tit It)
,
!
t
,
> it)
z <~ o:;
!
7
t
,J
, ....
?r-p~p2~"3~
• proton ;
?r" V fr"
,J
.
500~ >
!
;
!
300-
i
.~e
`5
10
P Lab
GeV/¢
Fig. 4. A v e r a g e t r a n s v e r s e m o m e n t a o f s e c o n d a r i e s p r o d u c e d in r r - p ~ p 2rr ÷ 3 n - a n d n -p --, p 2n ÷ 3 n - * r ° as a f u n c t i o n o f t h e i n c o m i n g rr m o m e n t u m , Plab-
/
r-p 6 prongs . . . . i ........ `500i' 7105rr ° PARTICLES tl J'lg551I'-I "~t--~T/'" I'~PARTICLES[_[ J
AT 5 GeV/c
l /
2440 p PARTICLES ~300
ZOO
2.50-
[ P00
!
0i__ -1
.
0
]_ . -I
.
.
.
. 0
[.. . . . -1
•. . . . . 0
COS 8 "
Fig 5. P r o d u c t i o n a n g u l a r d i s t r i b u t i o n s o f c h a r g e d s e c o n d a r i e s p r o d u c e d in s i x - p r o n g n - p ratera c t i o n at 5 G e V / c
U Gensch et al., 5 Ge V/c 7r-p mteracttons
51
the rr - in reactions (1) and (2) The difference is probably due to copious A ++ (1236) production [21 ] m these reactions which is a source of n + mesons with low transverse momentum [22]. The average transverse momenta for final nucleons are in general about 100 MeV/c larger than for ptons. The values of thexr longitudinal components establish the leading particle character. In fig. 4 we present the behavlour o f < P T > for pions and nucleons in reaction (1) and (2) versus incident lab momentum. Our 5 GeV/c data points establish the trend expected from higher energy data down to small energies. The proton possesses the largest < PT > values in the energy range explored. Its difference from the pion values seems to be independent of Plab. It seems further that the average transverse momenta tend to approach a limit at high energies for both types of secondaries. The fact that < PT >rr ÷ < ( PT > n - IS observed at Plab ~> 10 GeV/c too; however, any energy dependence of this difference cannot be established. 4.2. P r o d u c t i o n angular d i s t r i b u t i o n s
Fig. 5 displays the emission angle distribution for the charged secondaries, the 7r+, 7r- mesons and the proton for all st,x-prong events. Obviously, the interaction cannot be described by phase space alone so that even as a first approximation phase space cannot be used for the description of the data. A measure of the deviation o f phase space is the asymmetry ratio A = ( F - B ) / ( F + B). The asymmetry values obtained for the pamcles produced m all six-prong events as well as m the fit channels (1) --(3) are hsted m table 3. For the reactions (1) --- (3) they are compared with the results ofTr p experiments at 5.5 (ref. [4]), 6 (ref. [5]), 7 (ref. [8]), 10 (ref. [11]) and 16 GeV/c (ref. [14]) in fig. 6. It is evident that the asymmetry of baryons and the rr- meson is more pronounced at higher energies. The rr÷ meson reveals a shght positive (however energy independent) asymmetry ratio. It seems further that below 6 GeV/c in the seven-particle final state (3) the neutron is more peaked backward than the proton in the corresponding reaction (2). Recently the question arose [23] whether there is an isotropic component of particle production m high-energy collisions and whether the energy distribution of this part obeys the Bose-Einstein functxon. As observed on fig. 5, the production angular distributions are anisotropic. For smaller values of E*, the amsotropy deTable 3 Asymmetry rano A = (F - B)/(F + B) m 5 GeV/c rr p interactions proton total six-prongs -0.24 ± 0 02 n - p -, p 21r*3rr-0.26±003 rr'-p~p2n*3rr"n ° -0.22± 0.03 n - p --' n 3~r*3zr-
÷
..
neutron
/r
/r
- 0 30 +-0.05
0.07 ± 0.01 0.03±002 0.06 ± 0.02 0.09 -+ 0.03
0.04 ± 0.01 0.04± 002 0.06 ± 0.02 0.09 ± 0.03 0.04 ± 0.03
7,t o
U. Gensch et al., 5 GeV/c *r-p mteracttons
52
•0 ~
•
/
1 i
....
_,.,.,.:
L'
.........
...................
: .........
[
-05,
,.
it
~-t
t~
~ ~"
- - .
~.os[ --
I
~-0sii
+
--I
i
t .............................
0 ~ ..... ¢_~
u
{"
*t
_"........
i
",,.
pro~
~
i
<{
! ,
f
~-p ~ p 2 zr*3~'-Tr*
q-
,
---+--
i
-
,,~n'*
I
. I
l
7 r - p ~ n 3 ;7" 3 ~--
.4~vv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0 .....
.". . . . . . . . .
!
i# !
-05"
•
rwutron
=
rr -°
vrrJ
5
10
]
1
15
PLal) ' GeV/c l"lg 6 A s y m m e t r y
a function
r a u o A = ( F - B)/(F + B) f o r sccondanes p r o d u c e d m reactions ( 1 ) - ( 3 ) as
of t h e m o m e n t u m
o f t h e i n c o m i n g p~on
creases markedly and below 400 MeV the p]on distribuhons are isotropic. Given isotropy, all information resides solely in the energy spectrum, so that the non-Lorentzinvanant density distribution may be written as d3N/d3p - 4 r r l , E , dN/dE* = F(E*).
Fig. 7 shows a semilogarithmic plot of the experimental distributions, (4rip*E*) -1 dN/dE*, for n +, 7r- and proton, ttowever, a fit to the pion data using the Bose-Einstein function F ( E * ) = (e E*/kT - 1) -1
(1 1)
reveals no satisfactory success; the X2 probability turns out to be < 10- 2 for the n as well as the 7r+ sample. Thus, we may conclude low-energy n's in six-prongs at 5 GeV/e are inconsistent with formula (11) or, in other words, they are not distributed m a manner analogous to photons m "blackbody radiation". It Is "also evident from fig. 7 that a simple exponential fails to describe the energy distribution at low c.m. energies too.
U Gensciz et al, 5 Ge V/c *r-p interactions
rfp
6
prongs
7105 7r* PARTICLES
53
AT 5 G e V / c 9551
w"
PARTICLES
2/./.0 p PARTICLES
C3 O
\
Z
'
'
0k, c m
I.lg. 7
044 ENERGY , GeV
104
I~
Energy distribution of charged secondaries produced in six-prong rr-p interactions at 5
(;eV/c 4. 3. The mvariant distributions as a f u n c t i o n o f x , y and PL
The single-particle distribution in an inclusive reaction may be described by the expression d o/dPT dp~_ = ) ~1 / ' ( P L, ' PT' s).
(12)
According to Feynman [24], the invariant structure function f ( p E , PT, s) should approach a lltnttmg distribution of only two variables at very high energies. One of these variables is the transverse momentum, the other one is either the longitudinal momentum in the lab (projectile) system or the reduced c.m. longitudinal momen-* tum, x - PL/Pm~x" Thls scahng suggestion has been extended by Koba, Nielsen and Olesen [25] to the so-called semi-inclusive reactions a + b ~ c + (n
1) charged particles + any neutrals,
(13)
where in addition to the knowledge of the momentum and nature of particle c the number of charged particles produced is known. Bubble chamber experiments are most suitable to investigate semi-inclusive reactions since the total number of charged particles created is simply obtained by counting the tracks per event. Provided scaling works in reclusive reactions then the authors of ref. [25] suggest a scalIng law In semi-inclusive reactions:
forn~>
U Gensch et al., 5 Ge V/c n - p interactions
54
w-p
6 prongs
AT 5 GeV/c
t
-05
0
-0.5
O
oo I
-0.8
0
0.8
SCALED LONG MOMENTUM . x = pL / Pn,,ax
Fig. 8 [nvarlant structure fun~.tlon for pions and protons produced in six-prong n - p interactions at 5 GeV/c as a function of the scaled longitudinal m o m e n t u m x
The semi-reclusive spectra for the charged pions and proton as a function o f x are presented in fig. 8. The plon spectra reveal a very symmetric behaviour at x = 0, while about ~ of the protons have x values smaller than zero. Unfortunately there are not yet other semi-inclusive data published m order to test the scaling hypothesis according to ref. [25]. ~'p
G ~ s
-/-
71057r* PARTICLES
~,51 n'" PARTICLESI
0i
o
°
I
24/,0 p PARTICLES ,
!
¢
I 102
z
AT 5 GeV/c
101
1 -2
Q
-2 S
O
-2 5
(1
5
RAPIDITY
Ftg. 9. Rapidity distribution of charges secondaries produced in six-prong 7r-p interactions at 5 GeV/c.
U. Gensch et aL, 5 Ge V/c n - p mteractzons
6 prongs
7/" p .
.
.
.
.
.
.
.
.
.
55
AT S GeV/c
.
.
.
.
.
.
.
.
.
1
.
.
0
J2o
L
i
f .....
-0.2
0
02
04
/ ..... -'02
0
02
i 04
~ 02
]o 04
06
08
LONGITUDINAL MOMENTUM IN THE TARGET REST SYSTEM
Fig. 10 Energy-weighted lab longitudinal momentum distributions of plons and protons produced In six-prong rr-p interactions at 5 GeV/c.
In fig. 9 we present the invariant cross section as a function of the rapidity [24] E* + p~ y=~ lnE._p [ .
(15)
The asymmetry in the proton case observed in the x variable is also evident in the rapidity. The pion distributions are again symmetric and very close to each other. Benecke, Chou, Yang and Yen [26] suggest plotting data In term of s, PT and the longitudinal momentum in the lab system, PL. The hypothesis of limiting fray'henration of ref. [26] is easily shown to be the same as the Feynman prediction, provided that x 2 ~ 4(p 2 + m2)/s, where m is the mass of the detected particle. Fig. 10 displayes the pion and proton distributions in terms of PL. Plotting data in one of the rest systems of the incident particles offers the possibility to test besides hmiting fragmentation the hypothesis of factorizatton. By factorizatlon we mean, if pomeron exchange dominates than the mvariant cross section for a given target (projectile) should be independent of the projectile (target) particle, so that appropriate semi-inclusive data at other energies might be compared with that on fig. 10. Since the invariant cross section depends at fLxed s on two variables, e.g. the transverse momentum PT and the scaled longitudinal momentum x, it is of mterest to ask if there are correlations between these two variables. In order to study this problem we have plotted the invariant cross section for the n± semi-inclusive data against x in intervals ofp2T , seen in fig. l I. The variation of the spectra with increasing p2T illustrates that the structure function cannot be written as a product of two functions, one of them only depending onp2T, the other only on x; i.e.
u. Gensch et al., 5 Ge V/c n - p mteractions
56
rr-p
I 1o'It~
"
,
o
i
10
,
I
~-,-~-,-~,~
_I"e-,-tl..,_~-~o~,.o~ :"u
~os , ,
r"° i 01"p1T
-
,4,,
l
F"',-,"--~'-u ,;o;.otl
log) 04 -0,4 O0 SCALED LONG MOMENTUM
Fig 11. [nvarmnt structure funcnon for as a function o f x m steps of p-I-.
p2) *
0~
+
//-
-04
f(x,
AT 5 OeV/c
,
~..~,~,,;.oo~
1'I I
"1o
6prongs
n+
0.4
and Tr- mesons produced in six-prongs at 5 GeV/c
g ( x ) h(p~.) .
The question can be repeated using the rapidity, y , instead o f x . In fig. 12 we p lot the n u m b e r o f ~± mesons as a function o f y for various intervals in p2. T Within our limited statistics it is evident from that figure, that f O ' , p2) Is inconsistent with factorization for the n - as well as for the n + meson. Moreover, the 7r- distribution
-p
AT 5 GeV/c
6 prongs
--
I
S.
i
- i
O:p~,OO5
I0z. c~
'iI
IJd ._J cj
t,n,-
nJj
10 I :
<
"kl
I0 T
2 2 -2 RAPIDITY Fig. 12. Rapidity distributions for n ÷ and n - mesons produced m stx-prongs at 5 GeV/c m steps -2
of p-I-.
0
U. Gensch et al., 5 GeV/c n - p interactions
7/"- p
prongs
a) 005~
_.
AT 5 C~Vlc
T Z,X "~ b)
-005~-
57
Z--Y
T
I __.~
.
.
-0,8
.
.
I
0
1
i .......
.1_
(18
-2
SCALEDLONGMOMENTUM, x
0
J i
2
RAPIDITY.y
Fig. 13. Net charge distributions as (a) a function of the scaled longttudmal m o m e n t u m x and (b) as a function of the rapidity y for stx-prongs produced in ~r-p interactions at 5 GeV/c.
for 0 ~< p2 < 0.05 (GeV/c) 2 reveals in comparison to the other spectra of this figure a shoulder at y ~> 1 establishing the leading particle effect. This effect has not been seen in the p~integrated x and y distributions (see figs. 8 and 9).
4.4. Charge distributions In studying high energy interactions certain parameters and quantum numbers are considered. The charge, which is one of the quantum numbers and one of the characteristics of the initial state has been rarely taken into account. When two particle collide, in our case the ~ - and p, then the question may arise, how does the charge behave over the x range [27]. In fig. 13 we plot dQ/dx as well as dQ/dy defined as dzdQ- d N1N t o{dN t_a _l
__
_dN _
}
,
z=x,y.
(15)
Here Ntota I corresponds to the total number of events. Since the initial charge is zero the area above the line dQ/dZ = 0 is equal to the area below that line. The distribution dQ/dx (fig. 13a) reveals a positive net charge over the x range - 0 . 6 to - 0 . 2 . This effect is due to the proton whose contribution is strongest in that x interval. With increasing x the distribution rapidly changes sign to give a negative enhancement near x = + 0, 1. The negative net charge at positive x comes from the dominance of n - particles in that region. One would a priori expect that besides positive (negative) net charge at negative (positive) x values the to-
58
u (;ensch et al., 5 GeV/c n- p mteracttons
tal charge near x = 0 vanishes Contrary to that we observe strong negative charge, so that one may conclude from fig. 13a that (i) leading parucle effects are also present for the n - meson and (u) these effects e x t e n d out to and b e y o n d x = 0. In addition to the net charge per x interval we show m fig. 13b the charge distribution dQ/dy plotted against y, the rapidity, d Q / d y is charactertzed by two negative enh a n c e m e n t s near y = +- 1, a region where the negative p~ons d o m i n a t e over the posltwe ones. The proton contribution is negligtble for lyl >~ I due to kinematics (see also fig. 9). Near y = 0 the net charge is poslttve since the proton and n + mesons d o m i n a t e here over the negattve charged plons. 4.5. Two-partwle correlations It was orxgmally p o m t e d out by G o l d h a b e r et al. [28] and then by Bartke et al. [29] that the distributions o f angle between the pair of pions depend on whether the pions have hke or unlike charges ( G G L P effect). An investigation o f these distributtons has been made for plons m our total six-prongs as well as in reactions (1), (2) and (3). For each o f these reactions and for each pair of charged pions, we have determined the q u a n t i t y 3' = B / F where B denotes the n u m b e r of plon pairs with opening angle greater than 90 ° and F denotes the n u m b e r of pairs with angles less than 90 °, "/++, 7 - - and 3'+- refer to pairs of posltwe plons, negative pions and to pairs o f plons of unhke charge, respecttvely. The 3' values for this e x p e r i m e n t are presented m table 4 calculated m b o t h the overall c.m. system of the reaction and m the rest system o f the p~ons. The 3'++ are found to be smaller than 3 ' - - for reaction (1) and (2) as well as for the overall sample, irrespectively of the rest system in which they have been calculated. The 5 G e V / c n + e x p e r i m e n t [30] has shown on the contrary that 3'++ 3> 3 ' - . Fable 4 Correlation parameter 7 for plon pairs of hke and unhke charge
.
overall c m. system
3'÷+
7--
3'+ -
total six-prongs n - p ~ p 2zr~"3n -
1.08 ± 0 04
1.19 ± 0.03
1 54 ± 0 02
1 06 ± 0 09
1 32 ± 0.05
1 69 ± 0.04
n - p ~ p 2 n ÷31r-rr°
1 06 ± 006
1.20+- 003
1 47 ± 003
n--p--* n 3rr*3n-
1 15 ± 0.08
1 05 ± 0.07
1.57 ~- 0.04
plon rest system
3'++
3'--
3'+-
total six-prongs
1.20 ± 0.05
1.35 ± 0.04
1 84 -* 0.03
n-p~p2n+3n -
1.11 ± 0.09
1 59± 0.06
2.21 ± 0.05
lr p--* p 2n÷3;,r-Tr°
1 22 ± 0.07
1.36 ± 0 05
1.70 ± 0.04
n - p --' n 3n ÷ 3rr-
1 26 ± 0 09
1 19 ± 0.09
1 89 ± 0 05
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
59
U. Gensch et al., 5 GeV/c lr- p mteracttons
IN O V E R A L L ,~ ~
c m
t
1
i
'I--t
t
t
,--
~---
-~
r* If'*-
I • It'-"
,
.
]
l
, -
rr p - n 3 n " 3 / r " I
ISr-
• v
I
;'r-p -- p 2 ft" 3 n ' " rr *
/
,o I
.~
rr-p - p 2 r r ' 3 ~ r "
~s-
10It-
SYSTEM
:
r ** Ie-
v
r e-
=
~ '~
.
.
.
,'5
.
PLaI~
,
'
GeV/c
Iqg. 14 The values -,t+ , ~++ and 7 - - calculated m the overall c.m., as a function of the metdent rr momentum, Plab. This effect could be attributed to the leadmg lr as argued in ref. [12]. However, following this argument one might expect that this effect is more d o m i n a n t the higher the energy is. In fig. 14 the values for the three fitted reactions obtained in the overall c.m. system are shown. There seems to be the trend that T +-, largest below 7 GeV/c, decreases continuously as Plab increases, so that It ~s comparable w~th T - or T ++ or even smaller at 16 GeV/c. The difference between T ++ and " 7 - - m reaction ( l ) and (2) is only estabhshed at our energy and does not grow with increasing energy as e x p e c t e d from leading particle influence alone.
5. Conclusion In studying 3 184 six-prong 7r-p interactions at 5 GeV/c, it was first noted that rarely more than one rr° is present m the final state. The d o m i n a t i n g reaction channels are r:- p --,- p 27r+ 31r - and rr -p ~ p 2rr + 3rr- rr°. A very general feature o f the six-prongs is already revealed by the study o f individual final--state p a m c l e s . It is found that the productions do not follow the relati-
U. (;ensch et al , 5 Ge V/c lr-p interactions
60
vistic statistical phase space. F r o m the description of transverse m o m e n t a usmg several formulas it was c o n c l u d e d that the gross features are accounted for by the therm o d y n a m l c a l model (8) for mesons and the Planck distribution (10) for baryons, i.e. the PT spectra are governed by statistical laws. Further, it has been found that the energy behaviour o f the lsotroptc c o m p o n e n t of the cos 0* distribution for plons is inconsistent with the Bose-Einstein formula (1 1). In order to open the possibility of testmg the scaling hypothesis as well as factor. tzation in semi-inclusive reactions we presented the invariant distributions as a function o f x , y and PL" It has been found that for the 7r- and 7r+ mesons the invarlant structure function is inconsistent with factorlzation into a product g(x) h(p2T ) or g(v) h(p2). In addition we presented the net charge p e r t a n d y mterval in our sixprong data. F r o m dQ]dx some leading particle features of the ~r- were observed also b e y o n d x = 0. The general features o f the G G L P effect observed in this e x p e r i m e n t are very similar to those in pp annihilation where it was originally studied. However, any interpretation ts made difficult since the angular correlations are perturbed by the presence of resonance and the rr- leading particle effect. We are deeply Indebted to the operating crews of the p r o t o n synchrotron at Dubna and the 1 m Dubna hydrogen bubble chamber. We would like to thank the scanning, measuring and c o m p u t i n g staffs at each of our laboratories.
References [I] [2] [31 [4] [5] [6] [71 [8] [9] [101 {ll] [12] [131 [14] [151 [16] 117] [18]
R.H. Allen and V.G. Lind, Bull Am. Phys. Soc. 13 (19681 589. K. Abe et al , Phys. Rev D2 (1970) 91 R.A. Luke and V.G. Lind, Bull. Am. Phys. Soc. 13 (19681 589 F Bomsectal.,Phys. Rev. 162(1967) 1328 K.F. Suenetal,Phys. Rev D1 (19701 54. M,A l.laz and J E. Campbell, Nucl Phys. B7 (1968) 175 M,A. Ijaz and J E Campbell, Nuovo Clmento 61A (1969) 307. J E. CampbellandM.A. Ijaz, Nucl. Phys B12 (19691549. P L Berenyl et al., Bull Am. Phys, Soc. 12 (19671 684. P.L. Berenyl et al., Nucl. Phys. B37 (1972) 621. M Bardamn et al., lnsntute of Nuclear Research, Warsaw, report 51 I/VI (19641. P. Daroman et al., CERN report Th-68-7 (19681 226. P Daroman, A Dandm and L. Mosca, paper submitted to the Collt~qulum on high multlphclty hadrontc interactions, Paris, 1970 (unpubhshed) B Junknrannet al,Nucl Phys. BS(19681471 V.V Glagolev et al, paper submitted to the 15111 Int. ('onf on high energy physics, Klev, 1970 (unpubhshed) M.R Atalanand I,S. Saltov, Jomt Institute for Nuclear Research, Dubna, report 13-6(186 (1971) G Coccom, J Koesterand J H Perkms, UCRLreport 10022 (1961) R. Hagedorn, NuovoOmentoSuppl 3(19651 147
U. Gensch et al., 5 Ge V/c n - p interactions
61
[19] R. Hagedorn, CERN preprmt TH/851 (1967). [201 T.F. Hoang, Nucl. Phys. B38 (1972) 333 [21 ] Berhn-Dubna Collaboration, paper submitted to the Int Conf. on high energy physics, Batavia, 1972. [22] U. Gensch and H.J. Schrelber, Berhn preprint PHE 7 1 - 15 (1971) [23] J. Erwm et al., Phys. Rev. Letters 27 (1971) 1534. [24] R.P. Feynman, Proc. of the 3rd Int. Conf. on high energy colhslons, Stony Brook, 1969; Phys. Rev. Letters 23 (1969) 1415. [25] Z. Koba, H.B. Nielsen and P. Olesen, Phys. Letters 38B (1972) 25. [26] J. Benecke, T.T Chou, C.N. Yang and E. Yen, Phys. Rev. 188 (1969) 2159. [27] L. Van flove, Proc. of the Colloqumm on multiparticle dynamics, Helsmki, 1971. [28] G. Goldhaber et al., Phys. Rev. 120 (1960) 300. [291 J. Bartke et al., Phys. Letters 24B (1967) 163. [30] H. Drevermann et al., Phys. Rev. 161 (1967) 1356.