- Email: [email protected]
c K+p interactions
Nuclear Physics B140 (1978) 389-408 © North-Holland Publishing Company
INCLUSIVE PRODUCTION CROSS SECTIONS OF RESONANCES IN 32 GeV/c K+p INTERACTIONS France-Soviet Union and CERN-Soviet Union Collaborations
P. GRANET, L. MOSCA, J. SAUDRAIX, J.C. SCHEUER and D. VILANOVA DPhPE, CEN- Saclay, France H. BLUMENFELD LPNHE, UniversitO de Paris VI, France V.P. HENRI, J. KESTEMAN, J. LAURENT and R. WINDMOLDERS Facultb des Sciences, Universitb de l'Etat, Mons, Belgique E. DE WOLF *'**, S. TAVERNIER * and F. VERBEURE ** Interuniversity Institute for High Energies, ULB-VUB, Brussels, Belgium I.V. AJINENKO, P.V. CHLIAPNIKOV, L.N. GERDYUKOV, P.A. GORBUNOV, V.M. PEREVOZTCHIKOV and A.M. RYBIN IHEP, Serpukhov, USSR Received 14 November 1977 (Revised 9 March 1978)
The inclusive production of resonances is systematically studied in K+p interactions at 32 GeV/c. Total production cross sections are given for three baryon resonances, five vector and three 2+ tensor mesons. We also compare the central and fragmentation components of the total production cross sections with quark model predictions.
1. Introduction The amount of data on inclusive production of resonances has grown considerably during the last few years. Among the reasons for this, we can note that: (a) this study completes those made on stable particles; (b) direct production is not the dominant process for the common stable particles; (c) in view of the interpretation of lepton production in hadron-hadron collisions it is of interest to know the inclusive production cross sections of mesons having a non-negligible decay branch* Navorser van het IIKW, Belgium. ** Also at Universitaire Instening Antwerpen, Wilrijk. 389
390
P. Granet er al. / Inclusive production cross sections
ing fraction into leptons; (d) finally, this is a way of testing models which predict production cross-section ratios in given phase-space regions, and among them, quark models now seem particularly promising. Fully inclusive studies of resonances are in general difficult because of small signal-to-background ratios due to the low production cross section and, in bubble chambers, because of the important fraction of unidentified decay particles. In particular, the large systematic errors in the cross-section determination are essentially due to the unknown background shape. In addition, in hydrogen bubble chambers, even if large, the 7r° detection efficiency is so small that inclusive p+ and co studies have not been performed. Above ~25 GeV/e, very little is known about inclusive resonance production except for p ° and A++(1232) [ 1]. The latter has been studied in restricted kinematical regions and it is often difficult to compare cross sections due to a lack of systematics in the methods used; in particular, in some cases, no background subtraction and no corrections for Breit-Wigner tails have been performed. Using a method described in sect. 2, the inclusive cross section is determined for each of the following 11 baryon and meson resonances, produced in K+p interactions at 32 GeV/c: A++(1232),
~;+(1385),
K*+(892),
K*°(892),
K*°(1420),
f.
>2+(1385) K*-(892),
po,
qS,
K*+(1420),
These cross sections are presented in sects. 3 to 5 and are compared in sect. 6 with quark model predictions.
2. Experimental method This study is based on a sample of 88 000 measured events coming from an exposure of the 4.7 m MIRABELLE hydrogen bubble chamber to an RF-separated K + beam of 32.1 GeV/c at the Serpukhov accelerator. The present statistics correspond to ~5 events//ab and a general description of experimental details can be found in ref. [2]. 2.1. Mass spectra
Outgoing charged tracks are not identified except for those of momentum less than 1.2 GeV/e, for which a pion-proton separation by means of ionization is possible, and the rare cases of four-constraint kinematical fit assignments (~5% of the inelastic events). Therefore, for the invariant-mass calculation, the masses of unidentified particles are selected depending, for a given state, on the decay mode under
P. Granet et al. /Inclusive production cross sections
391
study (K+rr - for K *°, K+K - for ~, etc .... ). The resonances are detected as an accumulation of events on a smooth background in the invariant spectra so obtained. In this procedure, the underlying assumption is that combinations coming from wrong mass assignments contribute mostly to the background. This is not true in the p ° analysis where the reflection of the K*°(892) (see subsect. 4.2) imposes a special treatment. 2.2. Fitting procedure
In principle, the inclusive total and differential cross sections could be obtained by fitting the relevant mass distributions to the well-known formula do dM
- -
= BW
• PS
+ BG,
where BG stands for background, BW for the resonant Breit-Wigner function and PS for the phase-space distribution. However, since we are dealing here with inclusive reactions involving a variable and generally unknown number of final state particles, the phase-space distribution cannot be calculated properly. Therefore, we assume that it can be represented by the same empirical function as the background and use the modified formula do dM = BG(1 + alBW ) . The total cross section for resonance production OR is then related to the fitted value of the parameter al by OR
=
0/1 f B G • BW • dM,
where the integral extends over the whole experimental distribution. We have used relativistic Breit-Wigner functions of the form [3] M F(M) BW=-p* (M2 - Mr2)2 +M,2V~(M) ' with
[p*\21+l p(M) P(M) = r T [ ~ - )
p(M~j
(1)
The attenuation factors t9(/14)have been chosen equal to 1/M for the meson resonences and equal to [(M + roB) 2 -- r n ~ ] / M 2 for the baryon ones; mB and rn M are the decay baryon and meson masses. The background is always well described by a product of two terms, involving at most 4 free parameters, which take into account
P. Granet et al. / Inclusive production cross sections
392
possible threshold effects and/or quasi-exponential background far from the threshold mass Mth :
BG = a2 (M - Mth)a3 e - a 4 M - a S M 2 . The masses and widths used in the fits are critical for cross-section determinations. The mass Mr and the natural width FN (which is related to F T ofeq. (1), as discussed in subsect. 2.3) of the resonances are given the values from the Particle Data Group tables [4].
2.3. Resolution Junction and determination of the width I'T The shape of the experimental resonance signal depends on FN and on the resolution function G(&M) which is usually assumed to be Gaussian:
1
F 1 [zxm~v]
G(&M) = N / ~ ~M e x p L - 2 ~ 6 - ~ ] J &M is the difference between the true and the measured values of the invariant mass M, and 6M is the experimental error on this mass, which is kept fixed and estimated on the whole resonance region. This leads to complicated Breit-Wigner and Gaussian curves convolutions. In contrast, following the authors of ref. [5], we calculate explicitly the experimental error distribution q(SM) in the resonance region using the estimated errors on track parameters. A typical example of these distributions is shown in fig. 1a for the K%r- invariant-mass spectrum, in the K*°(892) mass region defined as 0.8 < M(K+rr - ) < 1.0 GeV. Its shape is far from being Gaussian and can be described by the formula 8M
e__(~-~/6M)2
where 6M is the most probable value of 6M. Assuming this analytical form, a more correct resolution function
W(~XM): f q ( ~ G(zXM,~M) d(6M) is obtained, which is found to be a Breit-Wigner [5] centered on zero with total width at half maximum FR = 2x/2 8 M . Then, the observed mass distribution is the result of the convolution of 2 BreitWigner curves: one with parameters Mr and I'N (the resonance), the other with mass and width parameters zero and I'R (the resolution), that is again a Breit-Wigner function centered on Mr with total width I" T = I" N + I~R ,
P. Granet et al. /Inclusive production cross sections
K+p ---.. K+lrl.-X
~
..=
I
-- """*""" .... o . . . . ' . .
,oooj-
"~
g
/
'
,o
,o
6M (MeV)
~o
o
,,o'
K+P ---,. K+rr-X
I "~ ' r
,~ ~
500
25
393
•
2
,
'
,
,
'i,
&
~,o
M(rr*rr-), MeV
°"_,~,'
'o'
,g
AM (MeV)
Fig. 1. Examples of error distributions on invariant-mass systems and of resolution functions in K+p interactions at 32 GeV/c: (a) the error distribution of the K%r- invariant mass in the K*0(892) region, defined as 0.8 < M(K%r-) < 1.0 GeV; (b) the effective-mass distribution of the K0 charged decay products; (c) the resolution function R(AM) as a function of AM, the difference between the true mass and the measured mass of the K%r- mass system in the range 0.8 < M(K%r-) < 1.0 GeV (partial sample). The solid and dashed curves represent least squared fits of Breit-Wigner and Gaussian curves, respectively, to the data.
the value of which is imposed in the fits. As a check, figs. l b and c show the experimental . + n - invariant-mass spectrum of K ° decays, and the calculated resolution function R (ZXM) for the K+Tr- invariantmass system in the K*°(892) mass region. These resolution functions are well described by Breit-Wigner distributions (full lines), whereas the agreement with Gaussian curves (dashed lines) is rather poor. Table 1 gives for each studied resonance the resolution I'R and the total width I' x imposed in the fits. 2.4. Goodness o f fits and consistency checks All the results presented here correspond to satisfactory fits (x2/NDF ~ 1). The systematic effects, generally large, are taken into account in the quoted errors. The total cross sections are always corrected for unseen decay modes using k n o w n branching fractions [4]. The kinematical production regions are investigated, except for states which are weakly produced, and some distributions are systematically shown for selected intervals of the c.m. rapidity variable V*
E* +P~
1 In-
When data at 5, 8.25 and 16 GeV/c [6] are available, cross sections are evaluated in the same way and compared to our values.
'
394
P. Granet et al. / bwlusive production cross sections
Table 1 Experimental resolution F R (total width at hall" maximum of the resolution function R(AM-)) and widths FT of the Breit-Wignerfunction imposed in the fits for observed resonances Resonance
Decay used
I" R (MeV)
I"T (MeV)
Ax++(1232)
pTr+
10
120
~+(1385) 2+(1385) K*+(892)
An+ ATrK0rr+
10 10 10
45 45 60
K*+(1420) K*0(892) K*0(1420) K*-(892) /90
KOTr+ K+TrK+~rKO~r7r+rr-
10 15 15 10 10
120 65 125 60 160
f
rr+zr-
10
180
0
K+K-
5
10
Consistency checks were also performed comparing results obtained for differential, semi-inclusive (not presented here) and total distributions.
3. Baryon resonance production A++(1232) is known to be abundantly produced in K+p interactions [1] in the small m o m e n t u m transfer t(p, A++) region. We have determined the total cross section of the reaction K+p 4 A++(1232) X , pTr+ distributions; p stands for dividing the data in t bins and using " mvanant-mass " " identified protons (in this case, the pn + distributions would be biased for - t > 0.6 GeV 2) or unidentified particles with a proton mass assignment. A selection of spectra is shown in fig. 2; the curves are a representation of Breit-Wigner plus background and pure background, respectively. Clearly the total distribution of fig. 2f cannot be used, because of the very important background. In fig. 3 are presented the four-momentum transfer and the c.m. rapidity differential distributions. The t distribution was fitted with a curve of the form A e m ÷ c t 2 (solid line of fig. 3a). The integral of this curve, in the 0.1 to 5 GeV 2 range, and the contribution to the cross section of the - t < 0.1 GeV 2 region, leads to a total cross section of 0A++(1232)
1.6 + 0.3 m b .
(The integration of a linear function, which underestimates this cross section, gives
P. Granet et al. / Inclusive production cross sections
395
K+p .p11'+X ----~ T u --T-la) 0.2<-t<~3 GeV= 1.5
i
r
(b)
w
r
.<. (c)
0.5<-t<0.6
+
1.0
1.O A
>.
0.5 o.s
0
.D E
0
o
"O
20
I (o)
1,5<-t <3.0
(d)
40 ~
I I t 3.0,¢-t<10
~
o
1.0,¢-t <1.5
I
I
If} 1101
J %o
•
20
i
• °o% •
"o lO
I
Total
I i
%o %%%%
5( •
e
1.0
i
i
114
1.8
0
1.0
L
J 1.4
M(p
0 1.8
~
!
1.0
1,4
1.8
~T+), G e V
Fig. 2. Inclusive pTr+ invariant-mass distribution for selected f o u r - m o m e n t u m transfer t(p, prr +) intervals and for the total sample. The upper curves are the results of fitting the 1 . 0 7 5 - 1 . 7 9 5 mass regions with a p-wave Breit-Wigner plus background; the latter is represented by the lower curves.
a lower limit of 1.3 - 0.2 mb.) The total cross section is approximately two times the value obtained using identified protons only, which amounts to 0.9 -+ 0.1 rob. Our total cross section value can be compared with 16 GeV/c results [7]
K*p
+(1232) X
• ~+
5 (a)
(b) 2
>=
ol
J~ E b "O
+
O.1 0.05
,
I
1
I
L
2
--t (GeV 2)
0 -2
j -1
,
,
,k ,k ,k
O
y*
Fig. 3. Differential cross sections for A++(1232) inclusive production: (a) the f o u r - m o m e n t u m transfer t(p, A) distribution; (b) the c.m. rapidity distribution. The curve represents a quadratic fit to the data.
396
P. Granet et al. / Inclusive production cross sections
4.57 + 0.l l, 2.00 +- 0.10 and 1.76 -+ 0.07 mb for 7r+p, rr-p and K - p interactions, respectively. Applying the same technique to 8.25 and 16 GeV/c K+p data [6], cross sections of 2.3 + 0.3 and 1.8 -+ 0.3 mb are obtained. This indicates, in K+p interactions, a small decrease (o4+ + cc '-Plabn--O'3~J of the A ++ inclusive production cross section with increasing incident momentum. As shown in fig. 3b, the largest fraction o f this production is confined to the proton fragmentation region. The second baryon resonance investigated is the ~+(1385) state using its Art+ decay mode (figs. 4a and b). The weak but definitely present signal corresponds to a cross section of o+(1385) = 140 + 40 ~ b , coming, as expected, essentially from the proton fragmentation region (for y* < - 1 ,
K÷p
=An÷X
T
ta)
4
Total
(b)
y*,.,:-I
1.1
o E
b
1,0
2 1 0
] ~
O.S
_ _ ~ 1.2 1,4
t 1.6
_
'
I 18,
0i
1,2
1~4
i
1.6
1'.8
M [A1T+I,GeV
K+ p.._.Xl"t'- X F
~
(~)
7----
f
7~ 7
Total
;
--
tu)
O
1.4
1.6
i
ilo
! /,,°~, ,
o) .... 1.2
1.4
1.6
1,8
o 1.2
1.8
M (A TI"), G e V
Fig. 4. Invariant-mass distributions of An+ and ~,Tr- systems for selected rapidity intervals and for the total samples. The curves represent the best fits to the data, performed with a p-wave Breit-Wigner plus background, in the 1.26-1.80 GeV mass range.
P. Granet et al. / Inclusive production cross sections
397
the cross section is estimated to be 80 + 30 ~£b). This production is ~3 times smaller that the corresponding one observed in K - p interactions at 32 GeV/c [8]. When examining the An- mass spectrum (fig. 4c), Z+(1385) production is also seen with a cross section equal to o~O38s)
60-+ 20/Jb.
It should be stressed that the kinematical region defined as 0 < y * < 1 (fig. 4d) contains the quasi-whole signal, indicating that, although less peripheral than the ~+(1385), the ]2+(1385) also comes mainly from a fragmentation process. No detectable Z-(1385) or Z-(1385) signal is observed.
4. Vector-meson production
4.1. K*+(892), K +°(892) and K*-(892) production Preliminary results on K*+(892) production have already been presented [9] and the new data (fig. 5) confirm our previous analysis. The cross section of neutral K* cannot be obtained as easily because of background problems; in fig. 6 are shown typical do/dM distributions for the K+Tr- system where unidentified positive
K*p (a) -0.6 < y ' < - 0 . 4
6i
,.K°1"r*X
(b)
O.2
0.8
(C)
6
i
i '
>'I
f
0
(d)
:E "o
. . . . . . .
,¢",W,
!
1.2
(e)
6
1.8
I
~
+
If)
Total
i +~ 40
"o
2i
4
0-8
1.0
1.2
0 0.6
,
1,o
1
0 0.6
........
0.8
1.0
1.2
J
0
0.6
0.8
1.0
1.2
M (K°'n'÷), G e V Fig. 5. Effective KOn + mass distributions for different c.m. rapidity intervals and for the total sample. The curves are the results of fitting the 0 . 6 4 - 1 . 2 0 GeV mass region with a p-wave Breit-Wigner plus background.
398
P. Granet et al. / Inclusive production cross sections
K+p ._~K+TI.- X f
(a)
i
i
- 0 . 6 ,c y*,C-0.2
30
A
{b)
lol~ , ~
lO
61
o
I (d)
~; "0
6
"0
4
I
ol
1.2.(y*< 1.4
3~
I
t to)
(el
0.2< y'< 0.4
2O
>. E
,
151
b
i
r
0.8,c y*< 1.0
10
I
o
1 . 8 < y ' < 2.0
I If)
I
I
Total
200
100
o
•
0.6
0,8
10
1.2
0".6
t
0.8
i
1.0
1.2
0 0.6
i 0 8
L 1.0
__~ 1.2
M (K+Tr-), GeV Fig. 6. E f f e c t i v e K+Tr - mass d i s t r i b u t i o n s for d i f f e r e n t c e n t e r o f mass r a p i d i t y i n t e r v a l s a n d for the t o t a l sample. The curves are the results o f f i t t i n g the 0 . 6 6 - 1 . 2 0 G e V m a s s r e g i o n w i t h a p-wave Breit-Wigner plus b a c k g r o u n d .
(negative) particles are assumed to be K*(n-). As is well-known, K*(892) production in KN interactions is mainly due to the beam fragmentation process; this is also true in 32 GeV/c K+p interactions (see fig. 7 where the d o / d y * distributions of the two K*(892) are compared). Besides common production regions, these two resonances have also similar cross sections 0K,+(892)
=
3.2 + 0.3 m b ,
0K,o(892) = 3.4 + 0.4 m b . The energy dependence of K*(892) production can be analyzed using data at 5, 8.25 and 16 GeV/c [6] ; the inclusive cross sections, almost constant between 5 and 16 GeV/c, increase by about 1 mb between 16 and 32 GeV/c (fig. 8a). The ratio K°/(K° + ~0) in 32 GeV/c K÷p interactions being ~10%, as previously noted [10], we looked for a possible K.*-(892) production. A small signal (not shown) is seen and the estimated cross section is O ~ , _ ( 8 9 2 ) = 1 8 0 -+ 1 2 0 / ~ b .
This production is essentially central, the cross section in the interval [y*l < 1 amounting to 160 + 100 ~b.
399
P. Granet et al. /Inclusive production cross sections
K+p--,, K*(892) X I
(a)
'
I
'
I
i
i
K m÷
+
E *>, "0
0
"0
2
I
~
f
i
I
I
t
,.o
(b)
+ o -2
l,
J,
l -1
0
1
2
y. Fig. 7. c.m. rapidity differential cross sections at 32 GeV/c for the inclusive reactions: (a) K+p -~K*+(892)X and (b) K+p --, K *0(892)X.
4.2. p a n d ~ p r o d u c t i o n
Due to the very small n o detection efficiency in hydrogen bubble chambers, p± and co inclusive production are completely unknown. Using events having at least 2 measured photons, we formed the invariant-mass combinations M(n+n°), M ( n - n °) and M(n+n-n°), where n ° stands for diphoton systems with 0.13 ( M ( 7 7 ) 0.14 GeV (corresponding to the 2 upper points of the insert in fig. 9). No signals are observed either in the n±n ° spectra (not shown) or in the 7r+Tr-Tr° distribution presented in fig. 9 and it is even difficult to give upper limits of the production cross sections. This is mainly due to low statistics (400 n°'s only, as a consequence of large n + n - n ° combination weights (mean value ~ 450)) and to the large dispersion of weights. The study o f p ° production is easier, although, until now, no results were published in K±p interactions due to strong K*°(892) reflection. The problem arises from the misidentification of K + which are treated as n +'s. The contaminated region extends from threshold to M(zr+n - ) ~ 0.78 GeV and peaks at ~0.6 GeV. Neverthe-
400
P. Granet et al. / Inclusive productio~z cross sectio~ls K*p I
(a)
I
I
(~
I
,.K*X i
r
I
]
K " ÷(e92) K * ° (o92)
.o
E c 0
OH
o w
I
ot=.
(b)
I
I ~tlll
(o°
K*"{142o) K*°(142o)
, 0
+ 2
J
J
l 5
I i I ]1 10 PI.b
20
J
50
(GeV/c)
F'ig. 8. Total cross sections of (a) K*(892) and (b) K*(1420l inclusively produced in K~p interactions at 5, 8.25, 16 (;eV/c [6] and 32 GcV/c (this experiment).
less, f o r y * < 0 ( r e m e m b e r the fact that the K *° is mainly produced in the forward hemisphere and its rr+~r- reflection too), we can neglect this c o n t a m i n a t i o n to evaluate the O° cross section in the backward hemisphere (figs. 10a to c). Tile cross section thus o b t a i n e d is oo0(y,
=
1.3-+ 0.3 m b .
In the forward hemisphere, the c o n t a m i n a t i o n is i m p o r t a n t and we use two distinct m e t h o d s to evaluate this cross section. In a first m e t h o d we fit the po outside the 0.6 to 0.78 GeV c o n t a m i n a t e d region. The constraints, o f course, are not as strong as in the backward hemisphere * because we use roughly one h a l f o f the BreitWigner curve. As an example, such a fitted distribution is shown in fig. 10d; the dashed lines indicate the u n f i t t e d (interpolated) region. This procedure leads to the value OpOfv,>o ) = 1.6 -+ 0.5 mb. The second m e t h o d [11] is based on additional * We checked that tile values obtained with these cuts in the .v* < 0 regions are in agreement with the cross sections calculated without cuts.
401
P. Granet et al. / Inclusive production cross sections
K*p
,.l"r * Tr - yy X
2ooot
++
10001-
!
o ~..,.,..,,~t ..,÷,÷÷, 4O0
0.08
19
0.12 M Iyy)
(3
0.16 , GoV
E "10
b
"0
200
o
o. 4
0.6
I 0.8
I
I 1.o
M (Tt*1T- n°), GeV Fig. 9. The inclusive invariant-mass distribution of the n+n-~ 0 system produced in K+p interactions at 32 GeV/c; the insert shows the diphoton effective-mass distribution and n0's are selected by the 0.13 < M(3,3,) < 0.14 GeV requirement.
kinematical arguments, namely the fact that the K*°(892) reflection is not present in the p0 mass region, if we use only events satisfying the condition cos 0r+ > 0.4 (On+ is the angle between the line of flight of the n+rr - system and the n+ in the po rest frame). Figs. 10e and f represent the n+n - invariant-mass distributions obtained using this cut. To achieve the cross-section evaluation we have to extrapolate the angular distribution, which is found to be compatible with isotropy for cos 0 + > 0.4 (do/d cos 0 + cc 1 + a COS20n+, with a = 0.0 -+ 0.5). Thus, the second cross-section estimation of the po forward hemisphere production is Ooo(y, > o) = 1.9 +- 0.6 mb and the mean of these two estimates yields ooO(y,>o)
= 1.8 +- 0.5 m b .
This leads to a total inclusive cross section of o o=3.1-+0.6mb. p We note that this po production is smaller than in n-*p collisions [1], where an important p production occurs via beam fragmentation, and than in pp interactions [1], for which the inelastic cross section is about 2 times higher than in K÷p colli-
402
P. Granet et al. / Inclusive production cross sections
K * p --.'rr+'rr - X I
21
(a)
-1.6< y - < - 1.4
[b)
i
i
-0.2
I
/c)
1
60
5
2O
0
i
r
y*< 0
.CI
E
v
o
o (d)
_
I
1.2
(el
:E
i
I
I
o
1.20.4
I
t
t
If]
y*>O Cos 8" • 0.4
0.6
0.8
10
0 0.4
016
t 0.8
0 110
0.4
1.0
1.2
M ('n'*~-), GeV Fig. l(k Inclusive n+~r- invariant-mass distributions for selected c.m. rapidity intervals. The upper stolid curves are tile results of fitting the 0.49-1.09 GeV mass region with a p-wave Breit-Wigner plus background; the latter is represented by the lower solid curves. In the forward hemisphere regions, where the data are not fitted over tile whole mass range (first method), the dashed curves show the fit interpolations in the 0.6 < M(~+Tr- ) < 0.79 GeV mass interval (d). (e) and (f) represent partial distributions in forward hemisphere regions obtained with the c o s O r + t.'tlt l l l e t h o d .
sions. The pO rapidity distribution looks roughly symmetrical and has its m a x i m u m at y* ~ 0 (fig. 1 la). 4.3. (~ p r o d u c t i o n
The inclusive study o f this state is difficult because of its small p r o d u c t i o n cross Section and there are only a few e x p e r i m e n t s [ 12] where total inclusive cross sections are available. Despite an i m p o r t a n t background in the K+K - mass distributions (fig. 12), the $ signal is clearly observed even in the total sample owing to its small width and the good resolution in the <~mass region (['R ~ 5 MeV). Its production proceeds mainly via beam fragmentation and central emission seems very small; the strong difference b e t w e e n ~ and pO rapidity distributions is clearly shown on fig. 11. Our value o f the inclusive cross section % = 0.48 + 0.10 mb is a p p r o x i m a t e l y as large as the corresponding one d e t e r m i n e d in 150 GeV pp interactions [12]. The cross sections derived from the 8.25 and 16 G e V / c K+p data [6]
P. Granet et al. / Inclusive production cross sections i
(a)
I
'
I
'
I
403
'
l
K*p--.p° X
+++++++++++ vE >,,
b
'10
(b)
K* p--,.(I) X
0,4
0.2
0 -2
-1
0
1
2
y*
Fig. 11. c.m. rapidity differential cross sections for inclusive production of o 0 and ~ mesons.
'O'F-0 [a)
K*p .K*K- X
y~
100
---F
-
Ib)
-0"2
l
~
[ 15~
IC)
0 . 6 < y ~ <1.0
30 10~-
20
I
10 .I0
E
o
t
(d) 1.0
b
(e)
6
"0 25
098
,!o2
,1o8
0
0,8
I
--
yN>O
f
,1o2
o
20G
I if)
t Total
100 S
,1o6
0 .....
0,8
,1o2
1!o8
M (K÷K-), GeV Fig. 12. Tile effective K+K invariant-mass spectra for different c.m. rapidity intervals and for the total sample. The curves represent the best fits to the data, performed ~ith a p-wave BreitWigner plus background, in the 0.989 1.081 (;eV mass range.
404
t'. (;ranet et al. / Inclusive production cross sections
K÷p
.K÷K- X (y*>O)
r (al
825
T [b}
--
-
16 G e V I c
(c)
3 2 GeWc
3C
8 f;:
--
GeV/c
2c
lO
"0
1C
~~ i,J
° lI i ,
"0
0
0.98
0 1102
1106
0.98
1.02
1.06
0.98
1.02
1.06
M (K ÷ K - ) , GeV
Fig. 13. Comparison of K+K - invariant-mass spectra (forward hemisphere only) at 8.25, 16 and 32 GeV/c incident momentum. The curves are the results of fitting the 0.989 1.081 GeV mass region with a p-wave Breit-Wigner plus background.
indicate that ~ production increases with energy in K÷p interactions: the cross sections for y* > 0 are equal to 170 -+ 4 0 , 2 5 0 + 80 and 410 + 70 pb at 8.25, 16 and 32 GeV/c, respectively (fig. 13). In a restricted interval of the Feynman x variable (x > 0.4), our calculated cross section (0.23 -+ 0.04 rob) is significantly lower than the corresponding value (0.43 -+ 0.11 rob) given by a 43 GeV/c K - p electronic experiment [ 1 ], while for x > 0 it is 15 times bigger than the corresponding value in a 16 GeV/c n - p experiment [ 13] where q~ production, according to the Zweig rule, is expected to be much smaller than in Kp collisions.
5 . 2 + Tensor meson production In this experiment it has not been possible to obtain the A2 (dominant decay mode On) and f' (production probably too small) inclusive cross sections. Compared to K*(892), the.K*(1420) (and particularly the K*+(1420)) is more difficult to observe because o f its lower production rate, its Kn branching fraction o f only 50%, and its relatively large width (there is an advantage in the fact that the background in this mass region is smaller than in the 0.9 GeV region). The same remarks concerning the cross section and the width are also valid for the f resonance. In fig. 14 are displayed the n+n- and K+n - invariant-mass spectra. Evidence is found for f and K*°(1420) production: of = 0.8 -+ 0.3 m b , OK,0(1420 )
1.0 + 0.2 m b .
P. Granet et al. / Inclusive production cross sections
405
K + p__.,.TT+ T1.- X r
i ! 25
ol
~>
L
1.2
OB
(b
. . . .
2
16
M I'rr +'n'- ), G e V .Q
E K * p ---~ K*IT- X "O
b
"O
25 t
"~..._'
I
5 '
o8c 0
1.1
~ "
Si+
i
~
1.3
1.5
_
_
_
_
1.7
_
1.9
M ( K + I ~ - ) , GeV Fig. 14. The invariant-mass distributions of n+n - and K+n systems produced in tile inclusive reactions (a) K+p ~ rr+rr-X, (b) K+p ~ K+Tr X (total sample) and (c) K+p -~ K+rr X (c.m. rapidity interval 1.4 < y* < 1.6). The curves are the results o1" fits to the data, perfornled with d-wave Breit-Wigner plus background, in the 0.91 1.81 and 1.20 1.80 GeV mass regions for the rr+rr- and K+r: - systems, respectively. The inserts represent the data and the results of the fits when the fitted backgrounds are subtracted.
F o r the c h a r g e d K * ( 1 4 2 0 ) , t h e p r e s e n t statistics do n o t allow to q u o t e an accurate cross s e c t i o n ; nevertheless, o u r data are c o m p a t i b l e with a value 0"K,+(1420 )
=
+0.4 mr, 0.3 - 0 . 3 . . . . .
N o s t r o n g energy d e p e n d e n c e is observed for e i t h e r charged or n e u t r a l K * ( 1 4 2 0 ) (fig. 8b), w h e n our results are c o m p a r e d to cross sections derived f r o m 5, 8.25 a n d 16 G e V / c d a t a [6]. No a t t e m p t was m a d e to calculate d i f f e r e n t i a l cross sections because o f t h e w e a k n e s s o f the signals.
P. Granet et al. /Inclusive production cross sections
406
6. Comparison with quark m o d e l predictions Predictions o f cross-section ratios for inclusive particle p r o d u c t i o n and in par-
ticular for g3 + baryons and vector mesons, have been given in the framework of the additive quark m o d e l by Anisovich and S h e k h t e r [14]. This m o d e l is supposed to be valid at sufficiently high energy and predictions are m a d e for b o t h f r a g m e n t a t i o n and central regions. A t intermediate energies, the c o m p a r i s o n w i t h the data is made difficult by the fact that several p r o d u c t i o n mechanisms can c o m p e t i t i v e l y overlap in a given kinematical region. Therefore, the definitions o f the kinematical regions given in table 2 are s o m e w h a t arbitrary and are p r o p o s e d in order to make this comparison possible. F o r b o t h central and fragmentation regions, the strange-quark suppression factor X, which is the only free p a r a m e t e r o f the m o d e l , was fixed to 3 [141
Table 2 Comparison of experimental inclusive cross sections ratios, for 3+ baryons and vector mesons produced in K+p interactions at 32 GeV/c, with quark model predictions in different kinematical regions Resonance cross-section ratios
Kinematical production regions
Experimental values
/x++(1232)
proton fragmentation Oy • < -1
0.94 -+ 0.15
K + fragmentation total - 2ay, < 0
2.5 -+ 0.6 - - - 1_+. 10.4 _+0.3 2.2
K+ fragmentation
0.41 -+ 0.07
ay, > 0 total - 2Oy, < 0
2.2 -+ 0.4
Z+(1385) K*0(892) K*+(892)
K*+(892) K*0(892) K*+(892)
- 0.18 -+ 0.05
0.9 -+ 0.5 1.0 -+ 0.3
central
0.2 -+ 0.1 --=0.2_+0.1 1.0 -+ 0.3
Crly*l < 1
K*+(892)
2Oy* < 0
K*+(892)
=12-+5
central 2Cry, < O
K*-(892)
p0
0.08 + 0.03
central
2.6 -+ 0.6
2Oy, < 0
1.0 -+ 0.3
-
-
-
0.9 -+ 0.6
2.6 -+ 1 . 0
Quark model predictions
4.5 to 9
0.75
0.25
1
P. Granet et al. / Inclusive production cross sections
407
Surprisingly (for the reasons mentioned above), the overall data are in reasonable agreement with this very simple quark model, except for the K.*-(892)K*+(892) ratio in the central region.
7. Conclusions The inclusive cross sections obtained in this experiment are summarized in table 3. The most unportant conclusions are as follows. (a) The average number of resonances per inelastic event is large; for the only states analyzed here and neglecting the multiple-counting effects due to associated productions it amounts to ~0.9. (b) Concerning ~+ baryon production, the A*+(1232) total cross section is substantially higher than the one calculated using identified protons only and 2~+(1385) production is smaller than in K - p interactions. (c) The cross sections of the K*+(892), K*°(892) and po vector mesons are of the order of 3 mb and 0 production is about 6 times smaller. This last proceeds mainly, as the K*'s, via beam fragmentation while the pO is emitted rather symmetrically around y* = 0. The inclusive cross sections of these states and their properties are comparable to those observed in 32 GeV/c K - p interactions, where a similar study has been made [11]. (d) Tensor-meson production (K*°(1420), K*+(1420) and f) is 3 to 4 times smaller than vector-meson production. (e) The predictions of the naive quark model of Anisovich and Shekhter are in general agreement with the data,
Table 3 Smnmary of inclusive production of resonances in 32 GeV/c K+p interactions Resonance
Cross section (rob)
Main kinematical production region
~++(1232) )2+(1385) S+(1385) K*+(892) K'0(892) 1(*-(892) p0 0
1.6 ± 0.3 0.14 ± 0.04 0.06 ± 0.02 3.2 -+ 0.3 3.4 e 0.4 0.18 ± 0.12 3.1 ± 0.6 0.48 -+ 0.10 +0.4 0.3_0.3 1.0 ± 0.2 0.8 -+ 0.3
proton fragmentation proton fragmentation beam fragmentation beam fragmentation beam fragmentation central central beam fragmentation
K*+(1420) K*0(1420) f
408
P. Granet et al. / Inclusive production cross sections
We wish to thank the many physicists and technicians of CERN, Saclay and Serpukhov who contributed generously to make this experiment possible and the 5, 8.25 and 16 GeV/c K+p collaborations for permitting us to use their data.
References [1] P.V. Chliapnikov, Rapporteur's talk at 18th Int. Conf. on high-energy physics, Tbilisi, 1976. [2] P.V. Chliapnikov et al., Nucl. Phys. B131 (1977) 93. [3] J.D. Jackson, Nuovo Cim. 34 (1964) 1644. [4t Particle Data Group, Rev. Mod. Phys. 48 (1976) S1. [5] W.T. Eadie et al., Statistical methods in experimental physics, (North-Holland, Amsterdam. 19711. [6] Private communications from Brussels and CERN Collaboration (5 and 8.25 GeV/c), and Birmingham, Brussels, CERN, Mons, Saclay, Serpukhov and Universit~ de Paris VI Collaboration (16 GeV/c). [71 J. Bartke et al., Nucl. Phys. Bl37 (1978) 189. [81 U. Gensch et al., France-Soviet Union and Cl'RN-Soviet Union Collaborations, Inclusive resonance production in K p interactions at 32 GeV/c, Paper presented at 18th Int. Conf. on high-energy physics, Tbilisi, 1976. [91 M. de Beer et al., France-Soviet Union and CERN-Soviet Union Collaborations, Inclusive K*+(892) production in 32 GeV/c K+p interactions, Paper presented at 18th Int. Conf. on high-energy physics, Tbilisi, 1976. I10l P.V. Chliapnikov et al., France-Soviet Union and CERN-Soviet Union Collaborations, Nucl. Phys. B133 (1978) 93. I 11 I C. Lewin et al., France-Soviet Union and CERN-Soviet Union Collaborations, Inclusive vector meson production in K p interactions at 32 GeV/c, Paper submitted to European Conf. on particle physics, Budapest, 1977. I 121 O production : C. Louedec et al., Nuovo Cim. 41A (19771 166 ( K - p , 14.3 GeV/c); V. Blobcl et al., Phys. Lett. 59B (19751 88 (pp, 24 GeV/c); K.J. Anderson et al., Phys. Rev. Lctt. 37 (19761 799 (pp, 15(1 GeV/c). [131 B. Ghidini et al., Phys. Lett. 68B (1977) 186. [141 V.V. Anisovich and V.M. Shekhter, Nucl. Phys. B55 (1973) 455.
INCLUSIVE PRODUCTION CROSS SECTIONS OF RESONANCES IN 32 GeV/c K+p INTERACTIONS France-Soviet Union and CERN-Soviet Union Collaborations
P. GRANET, L. MOSCA, J. SAUDRAIX, J.C. SCHEUER and D. VILANOVA DPhPE, CEN- Saclay, France H. BLUMENFELD LPNHE, UniversitO de Paris VI, France V.P. HENRI, J. KESTEMAN, J. LAURENT and R. WINDMOLDERS Facultb des Sciences, Universitb de l'Etat, Mons, Belgique E. DE WOLF *'**, S. TAVERNIER * and F. VERBEURE ** Interuniversity Institute for High Energies, ULB-VUB, Brussels, Belgium I.V. AJINENKO, P.V. CHLIAPNIKOV, L.N. GERDYUKOV, P.A. GORBUNOV, V.M. PEREVOZTCHIKOV and A.M. RYBIN IHEP, Serpukhov, USSR Received 14 November 1977 (Revised 9 March 1978)
The inclusive production of resonances is systematically studied in K+p interactions at 32 GeV/c. Total production cross sections are given for three baryon resonances, five vector and three 2+ tensor mesons. We also compare the central and fragmentation components of the total production cross sections with quark model predictions.
1. Introduction The amount of data on inclusive production of resonances has grown considerably during the last few years. Among the reasons for this, we can note that: (a) this study completes those made on stable particles; (b) direct production is not the dominant process for the common stable particles; (c) in view of the interpretation of lepton production in hadron-hadron collisions it is of interest to know the inclusive production cross sections of mesons having a non-negligible decay branch* Navorser van het IIKW, Belgium. ** Also at Universitaire Instening Antwerpen, Wilrijk. 389
390
P. Granet er al. / Inclusive production cross sections
ing fraction into leptons; (d) finally, this is a way of testing models which predict production cross-section ratios in given phase-space regions, and among them, quark models now seem particularly promising. Fully inclusive studies of resonances are in general difficult because of small signal-to-background ratios due to the low production cross section and, in bubble chambers, because of the important fraction of unidentified decay particles. In particular, the large systematic errors in the cross-section determination are essentially due to the unknown background shape. In addition, in hydrogen bubble chambers, even if large, the 7r° detection efficiency is so small that inclusive p+ and co studies have not been performed. Above ~25 GeV/e, very little is known about inclusive resonance production except for p ° and A++(1232) [ 1]. The latter has been studied in restricted kinematical regions and it is often difficult to compare cross sections due to a lack of systematics in the methods used; in particular, in some cases, no background subtraction and no corrections for Breit-Wigner tails have been performed. Using a method described in sect. 2, the inclusive cross section is determined for each of the following 11 baryon and meson resonances, produced in K+p interactions at 32 GeV/c: A++(1232),
~;+(1385),
K*+(892),
K*°(892),
K*°(1420),
f.
>2+(1385) K*-(892),
po,
qS,
K*+(1420),
These cross sections are presented in sects. 3 to 5 and are compared in sect. 6 with quark model predictions.
2. Experimental method This study is based on a sample of 88 000 measured events coming from an exposure of the 4.7 m MIRABELLE hydrogen bubble chamber to an RF-separated K + beam of 32.1 GeV/c at the Serpukhov accelerator. The present statistics correspond to ~5 events//ab and a general description of experimental details can be found in ref. [2]. 2.1. Mass spectra
Outgoing charged tracks are not identified except for those of momentum less than 1.2 GeV/e, for which a pion-proton separation by means of ionization is possible, and the rare cases of four-constraint kinematical fit assignments (~5% of the inelastic events). Therefore, for the invariant-mass calculation, the masses of unidentified particles are selected depending, for a given state, on the decay mode under
P. Granet et al. /Inclusive production cross sections
391
study (K+rr - for K *°, K+K - for ~, etc .... ). The resonances are detected as an accumulation of events on a smooth background in the invariant spectra so obtained. In this procedure, the underlying assumption is that combinations coming from wrong mass assignments contribute mostly to the background. This is not true in the p ° analysis where the reflection of the K*°(892) (see subsect. 4.2) imposes a special treatment. 2.2. Fitting procedure
In principle, the inclusive total and differential cross sections could be obtained by fitting the relevant mass distributions to the well-known formula do dM
- -
= BW
• PS
+ BG,
where BG stands for background, BW for the resonant Breit-Wigner function and PS for the phase-space distribution. However, since we are dealing here with inclusive reactions involving a variable and generally unknown number of final state particles, the phase-space distribution cannot be calculated properly. Therefore, we assume that it can be represented by the same empirical function as the background and use the modified formula do dM = BG(1 + alBW ) . The total cross section for resonance production OR is then related to the fitted value of the parameter al by OR
=
0/1 f B G • BW • dM,
where the integral extends over the whole experimental distribution. We have used relativistic Breit-Wigner functions of the form [3] M F(M) BW=-p* (M2 - Mr2)2 +M,2V~(M) ' with
[p*\21+l p(M) P(M) = r T [ ~ - )
p(M~j
(1)
The attenuation factors t9(/14)have been chosen equal to 1/M for the meson resonences and equal to [(M + roB) 2 -- r n ~ ] / M 2 for the baryon ones; mB and rn M are the decay baryon and meson masses. The background is always well described by a product of two terms, involving at most 4 free parameters, which take into account
P. Granet et al. / Inclusive production cross sections
392
possible threshold effects and/or quasi-exponential background far from the threshold mass Mth :
BG = a2 (M - Mth)a3 e - a 4 M - a S M 2 . The masses and widths used in the fits are critical for cross-section determinations. The mass Mr and the natural width FN (which is related to F T ofeq. (1), as discussed in subsect. 2.3) of the resonances are given the values from the Particle Data Group tables [4].
2.3. Resolution Junction and determination of the width I'T The shape of the experimental resonance signal depends on FN and on the resolution function G(&M) which is usually assumed to be Gaussian:
1
F 1 [zxm~v]
G(&M) = N / ~ ~M e x p L - 2 ~ 6 - ~ ] J &M is the difference between the true and the measured values of the invariant mass M, and 6M is the experimental error on this mass, which is kept fixed and estimated on the whole resonance region. This leads to complicated Breit-Wigner and Gaussian curves convolutions. In contrast, following the authors of ref. [5], we calculate explicitly the experimental error distribution q(SM) in the resonance region using the estimated errors on track parameters. A typical example of these distributions is shown in fig. 1a for the K%r- invariant-mass spectrum, in the K*°(892) mass region defined as 0.8 < M(K+rr - ) < 1.0 GeV. Its shape is far from being Gaussian and can be described by the formula 8M
e__(~-~/6M)2
where 6M is the most probable value of 6M. Assuming this analytical form, a more correct resolution function
W(~XM): f q ( ~ G(zXM,~M) d(6M) is obtained, which is found to be a Breit-Wigner [5] centered on zero with total width at half maximum FR = 2x/2 8 M . Then, the observed mass distribution is the result of the convolution of 2 BreitWigner curves: one with parameters Mr and I'N (the resonance), the other with mass and width parameters zero and I'R (the resolution), that is again a Breit-Wigner function centered on Mr with total width I" T = I" N + I~R ,
P. Granet et al. /Inclusive production cross sections
K+p ---.. K+lrl.-X
~
..=
I
-- """*""" .... o . . . . ' . .
,oooj-
"~
g
/
'
,o
,o
6M (MeV)
~o
o
,,o'
K+P ---,. K+rr-X
I "~ ' r
,~ ~
500
25
393
•
2
,
'
,
,
'i,
&
~,o
M(rr*rr-), MeV
°"_,~,'
'o'
,g
AM (MeV)
Fig. 1. Examples of error distributions on invariant-mass systems and of resolution functions in K+p interactions at 32 GeV/c: (a) the error distribution of the K%r- invariant mass in the K*0(892) region, defined as 0.8 < M(K%r-) < 1.0 GeV; (b) the effective-mass distribution of the K0 charged decay products; (c) the resolution function R(AM) as a function of AM, the difference between the true mass and the measured mass of the K%r- mass system in the range 0.8 < M(K%r-) < 1.0 GeV (partial sample). The solid and dashed curves represent least squared fits of Breit-Wigner and Gaussian curves, respectively, to the data.
the value of which is imposed in the fits. As a check, figs. l b and c show the experimental . + n - invariant-mass spectrum of K ° decays, and the calculated resolution function R (ZXM) for the K+Tr- invariantmass system in the K*°(892) mass region. These resolution functions are well described by Breit-Wigner distributions (full lines), whereas the agreement with Gaussian curves (dashed lines) is rather poor. Table 1 gives for each studied resonance the resolution I'R and the total width I' x imposed in the fits. 2.4. Goodness o f fits and consistency checks All the results presented here correspond to satisfactory fits (x2/NDF ~ 1). The systematic effects, generally large, are taken into account in the quoted errors. The total cross sections are always corrected for unseen decay modes using k n o w n branching fractions [4]. The kinematical production regions are investigated, except for states which are weakly produced, and some distributions are systematically shown for selected intervals of the c.m. rapidity variable V*
E* +P~
1 In-
When data at 5, 8.25 and 16 GeV/c [6] are available, cross sections are evaluated in the same way and compared to our values.
'
394
P. Granet et al. / bwlusive production cross sections
Table 1 Experimental resolution F R (total width at hall" maximum of the resolution function R(AM-)) and widths FT of the Breit-Wignerfunction imposed in the fits for observed resonances Resonance
Decay used
I" R (MeV)
I"T (MeV)
Ax++(1232)
pTr+
10
120
~+(1385) 2+(1385) K*+(892)
An+ ATrK0rr+
10 10 10
45 45 60
K*+(1420) K*0(892) K*0(1420) K*-(892) /90
KOTr+ K+TrK+~rKO~r7r+rr-
10 15 15 10 10
120 65 125 60 160
f
rr+zr-
10
180
0
K+K-
5
10
Consistency checks were also performed comparing results obtained for differential, semi-inclusive (not presented here) and total distributions.
3. Baryon resonance production A++(1232) is known to be abundantly produced in K+p interactions [1] in the small m o m e n t u m transfer t(p, A++) region. We have determined the total cross section of the reaction K+p 4 A++(1232) X , pTr+ distributions; p stands for dividing the data in t bins and using " mvanant-mass " " identified protons (in this case, the pn + distributions would be biased for - t > 0.6 GeV 2) or unidentified particles with a proton mass assignment. A selection of spectra is shown in fig. 2; the curves are a representation of Breit-Wigner plus background and pure background, respectively. Clearly the total distribution of fig. 2f cannot be used, because of the very important background. In fig. 3 are presented the four-momentum transfer and the c.m. rapidity differential distributions. The t distribution was fitted with a curve of the form A e m ÷ c t 2 (solid line of fig. 3a). The integral of this curve, in the 0.1 to 5 GeV 2 range, and the contribution to the cross section of the - t < 0.1 GeV 2 region, leads to a total cross section of 0A++(1232)
1.6 + 0.3 m b .
(The integration of a linear function, which underestimates this cross section, gives
P. Granet et al. / Inclusive production cross sections
395
K+p .p11'+X ----~ T u --T-la) 0.2<-t<~3 GeV= 1.5
i
r
(b)
w
r
.<. (c)
0.5<-t<0.6
+
1.0
1.O A
>.
0.5 o.s
0
.D E
0
o
"O
20
I (o)
1,5<-t <3.0
(d)
40 ~
I I t 3.0,¢-t<10
~
o
1.0,¢-t <1.5
I
I
If} 1101
J %o
•
20
i
• °o% •
"o lO
I
Total
I i
%o %%%%
5( •
e
1.0
i
i
114
1.8
0
1.0
L
J 1.4
M(p
0 1.8
~
!
1.0
1,4
1.8
~T+), G e V
Fig. 2. Inclusive pTr+ invariant-mass distribution for selected f o u r - m o m e n t u m transfer t(p, prr +) intervals and for the total sample. The upper curves are the results of fitting the 1 . 0 7 5 - 1 . 7 9 5 mass regions with a p-wave Breit-Wigner plus background; the latter is represented by the lower curves.
a lower limit of 1.3 - 0.2 mb.) The total cross section is approximately two times the value obtained using identified protons only, which amounts to 0.9 -+ 0.1 rob. Our total cross section value can be compared with 16 GeV/c results [7]
K*p
+(1232) X
• ~+
5 (a)
(b) 2
>=
ol
J~ E b "O
+
O.1 0.05
,
I
1
I
L
2
--t (GeV 2)
0 -2
j -1
,
,
,k ,k ,k
O
y*
Fig. 3. Differential cross sections for A++(1232) inclusive production: (a) the f o u r - m o m e n t u m transfer t(p, A) distribution; (b) the c.m. rapidity distribution. The curve represents a quadratic fit to the data.
396
P. Granet et al. / Inclusive production cross sections
4.57 + 0.l l, 2.00 +- 0.10 and 1.76 -+ 0.07 mb for 7r+p, rr-p and K - p interactions, respectively. Applying the same technique to 8.25 and 16 GeV/c K+p data [6], cross sections of 2.3 + 0.3 and 1.8 -+ 0.3 mb are obtained. This indicates, in K+p interactions, a small decrease (o4+ + cc '-Plabn--O'3~J of the A ++ inclusive production cross section with increasing incident momentum. As shown in fig. 3b, the largest fraction o f this production is confined to the proton fragmentation region. The second baryon resonance investigated is the ~+(1385) state using its Art+ decay mode (figs. 4a and b). The weak but definitely present signal corresponds to a cross section of o+(1385) = 140 + 40 ~ b , coming, as expected, essentially from the proton fragmentation region (for y* < - 1 ,
K÷p
=An÷X
T
ta)
4
Total
(b)
y*,.,:-I
1.1
o E
b
1,0
2 1 0
] ~
O.S
_ _ ~ 1.2 1,4
t 1.6
_
'
I 18,
0i
1,2
1~4
i
1.6
1'.8
M [A1T+I,GeV
K+ p.._.Xl"t'- X F
~
(~)
7----
f
7~ 7
Total
;
--
tu)
O
1.4
1.6
i
ilo
! /,,°~, ,
o) .... 1.2
1.4
1.6
1,8
o 1.2
1.8
M (A TI"), G e V
Fig. 4. Invariant-mass distributions of An+ and ~,Tr- systems for selected rapidity intervals and for the total samples. The curves represent the best fits to the data, performed with a p-wave Breit-Wigner plus background, in the 1.26-1.80 GeV mass range.
P. Granet et al. / Inclusive production cross sections
397
the cross section is estimated to be 80 + 30 ~£b). This production is ~3 times smaller that the corresponding one observed in K - p interactions at 32 GeV/c [8]. When examining the An- mass spectrum (fig. 4c), Z+(1385) production is also seen with a cross section equal to o~O38s)
60-+ 20/Jb.
It should be stressed that the kinematical region defined as 0 < y * < 1 (fig. 4d) contains the quasi-whole signal, indicating that, although less peripheral than the ~+(1385), the ]2+(1385) also comes mainly from a fragmentation process. No detectable Z-(1385) or Z-(1385) signal is observed.
4. Vector-meson production
4.1. K*+(892), K +°(892) and K*-(892) production Preliminary results on K*+(892) production have already been presented [9] and the new data (fig. 5) confirm our previous analysis. The cross section of neutral K* cannot be obtained as easily because of background problems; in fig. 6 are shown typical do/dM distributions for the K+Tr- system where unidentified positive
K*p (a) -0.6 < y ' < - 0 . 4
6i
,.K°1"r*X
(b)
O.2
0.8
(C)
6
i
i '
>'I
f
0
(d)
:E "o
. . . . . . .
,¢",W,
!
1.2
(e)
6
1.8
I
~
+
If)
Total
i +~ 40
"o
2i
4
0-8
1.0
1.2
0 0.6
,
1,o
1
0 0.6
........
0.8
1.0
1.2
J
0
0.6
0.8
1.0
1.2
M (K°'n'÷), G e V Fig. 5. Effective KOn + mass distributions for different c.m. rapidity intervals and for the total sample. The curves are the results of fitting the 0 . 6 4 - 1 . 2 0 GeV mass region with a p-wave Breit-Wigner plus background.
398
P. Granet et al. / Inclusive production cross sections
K+p ._~K+TI.- X f
(a)
i
i
- 0 . 6 ,c y*,C-0.2
30
A
{b)
lol~ , ~
lO
61
o
I (d)
~; "0
6
"0
4
I
ol
1.2.(y*< 1.4
3~
I
t to)
(el
0.2< y'< 0.4
2O
>. E
,
151
b
i
r
0.8,c y*< 1.0
10
I
o
1 . 8 < y ' < 2.0
I If)
I
I
Total
200
100
o
•
0.6
0,8
10
1.2
0".6
t
0.8
i
1.0
1.2
0 0.6
i 0 8
L 1.0
__~ 1.2
M (K+Tr-), GeV Fig. 6. E f f e c t i v e K+Tr - mass d i s t r i b u t i o n s for d i f f e r e n t c e n t e r o f mass r a p i d i t y i n t e r v a l s a n d for the t o t a l sample. The curves are the results o f f i t t i n g the 0 . 6 6 - 1 . 2 0 G e V m a s s r e g i o n w i t h a p-wave Breit-Wigner plus b a c k g r o u n d .
(negative) particles are assumed to be K*(n-). As is well-known, K*(892) production in KN interactions is mainly due to the beam fragmentation process; this is also true in 32 GeV/c K+p interactions (see fig. 7 where the d o / d y * distributions of the two K*(892) are compared). Besides common production regions, these two resonances have also similar cross sections 0K,+(892)
=
3.2 + 0.3 m b ,
0K,o(892) = 3.4 + 0.4 m b . The energy dependence of K*(892) production can be analyzed using data at 5, 8.25 and 16 GeV/c [6] ; the inclusive cross sections, almost constant between 5 and 16 GeV/c, increase by about 1 mb between 16 and 32 GeV/c (fig. 8a). The ratio K°/(K° + ~0) in 32 GeV/c K÷p interactions being ~10%, as previously noted [10], we looked for a possible K.*-(892) production. A small signal (not shown) is seen and the estimated cross section is O ~ , _ ( 8 9 2 ) = 1 8 0 -+ 1 2 0 / ~ b .
This production is essentially central, the cross section in the interval [y*l < 1 amounting to 160 + 100 ~b.
399
P. Granet et al. /Inclusive production cross sections
K+p--,, K*(892) X I
(a)
'
I
'
I
i
i
K m÷
+
E *>, "0
0
"0
2
I
~
f
i
I
I
t
,.o
(b)
+ o -2
l,
J,
l -1
0
1
2
y. Fig. 7. c.m. rapidity differential cross sections at 32 GeV/c for the inclusive reactions: (a) K+p -~K*+(892)X and (b) K+p --, K *0(892)X.
4.2. p a n d ~ p r o d u c t i o n
Due to the very small n o detection efficiency in hydrogen bubble chambers, p± and co inclusive production are completely unknown. Using events having at least 2 measured photons, we formed the invariant-mass combinations M(n+n°), M ( n - n °) and M(n+n-n°), where n ° stands for diphoton systems with 0.13 ( M ( 7 7 ) 0.14 GeV (corresponding to the 2 upper points of the insert in fig. 9). No signals are observed either in the n±n ° spectra (not shown) or in the 7r+Tr-Tr° distribution presented in fig. 9 and it is even difficult to give upper limits of the production cross sections. This is mainly due to low statistics (400 n°'s only, as a consequence of large n + n - n ° combination weights (mean value ~ 450)) and to the large dispersion of weights. The study o f p ° production is easier, although, until now, no results were published in K±p interactions due to strong K*°(892) reflection. The problem arises from the misidentification of K + which are treated as n +'s. The contaminated region extends from threshold to M(zr+n - ) ~ 0.78 GeV and peaks at ~0.6 GeV. Neverthe-
400
P. Granet et al. / Inclusive productio~z cross sectio~ls K*p I
(a)
I
I
(~
I
,.K*X i
r
I
]
K " ÷(e92) K * ° (o92)
.o
E c 0
OH
o w
I
ot=.
(b)
I
I ~tlll
(o°
K*"{142o) K*°(142o)
, 0
+ 2
J
J
l 5
I i I ]1 10 PI.b
20
J
50
(GeV/c)
F'ig. 8. Total cross sections of (a) K*(892) and (b) K*(1420l inclusively produced in K~p interactions at 5, 8.25, 16 (;eV/c [6] and 32 GcV/c (this experiment).
less, f o r y * < 0 ( r e m e m b e r the fact that the K *° is mainly produced in the forward hemisphere and its rr+~r- reflection too), we can neglect this c o n t a m i n a t i o n to evaluate the O° cross section in the backward hemisphere (figs. 10a to c). Tile cross section thus o b t a i n e d is oo0(y,
=
1.3-+ 0.3 m b .
In the forward hemisphere, the c o n t a m i n a t i o n is i m p o r t a n t and we use two distinct m e t h o d s to evaluate this cross section. In a first m e t h o d we fit the po outside the 0.6 to 0.78 GeV c o n t a m i n a t e d region. The constraints, o f course, are not as strong as in the backward hemisphere * because we use roughly one h a l f o f the BreitWigner curve. As an example, such a fitted distribution is shown in fig. 10d; the dashed lines indicate the u n f i t t e d (interpolated) region. This procedure leads to the value OpOfv,>o ) = 1.6 -+ 0.5 mb. The second m e t h o d [11] is based on additional * We checked that tile values obtained with these cuts in the .v* < 0 regions are in agreement with the cross sections calculated without cuts.
401
P. Granet et al. / Inclusive production cross sections
K*p
,.l"r * Tr - yy X
2ooot
++
10001-
!
o ~..,.,..,,~t ..,÷,÷÷, 4O0
0.08
19
0.12 M Iyy)
(3
0.16 , GoV
E "10
b
"0
200
o
o. 4
0.6
I 0.8
I
I 1.o
M (Tt*1T- n°), GeV Fig. 9. The inclusive invariant-mass distribution of the n+n-~ 0 system produced in K+p interactions at 32 GeV/c; the insert shows the diphoton effective-mass distribution and n0's are selected by the 0.13 < M(3,3,) < 0.14 GeV requirement.
kinematical arguments, namely the fact that the K*°(892) reflection is not present in the p0 mass region, if we use only events satisfying the condition cos 0r+ > 0.4 (On+ is the angle between the line of flight of the n+rr - system and the n+ in the po rest frame). Figs. 10e and f represent the n+n - invariant-mass distributions obtained using this cut. To achieve the cross-section evaluation we have to extrapolate the angular distribution, which is found to be compatible with isotropy for cos 0 + > 0.4 (do/d cos 0 + cc 1 + a COS20n+, with a = 0.0 -+ 0.5). Thus, the second cross-section estimation of the po forward hemisphere production is Ooo(y, > o) = 1.9 +- 0.6 mb and the mean of these two estimates yields ooO(y,>o)
= 1.8 +- 0.5 m b .
This leads to a total inclusive cross section of o o=3.1-+0.6mb. p We note that this po production is smaller than in n-*p collisions [1], where an important p production occurs via beam fragmentation, and than in pp interactions [1], for which the inelastic cross section is about 2 times higher than in K÷p colli-
402
P. Granet et al. / Inclusive production cross sections
K * p --.'rr+'rr - X I
21
(a)
-1.6< y - < - 1.4
[b)
i
i
-0.2
I
/c)
1
60
5
2O
0
i
r
y*< 0
.CI
E
v
o
o (d)
_
I
1.2
(el
:E
i
I
I
o
1.2
I
t
t
If]
y*>O Cos 8" • 0.4
0.6
0.8
10
0 0.4
016
t 0.8
0 110
0.4
1.0
1.2
M ('n'*~-), GeV Fig. l(k Inclusive n+~r- invariant-mass distributions for selected c.m. rapidity intervals. The upper stolid curves are tile results of fitting the 0.49-1.09 GeV mass region with a p-wave Breit-Wigner plus background; the latter is represented by the lower solid curves. In the forward hemisphere regions, where the data are not fitted over tile whole mass range (first method), the dashed curves show the fit interpolations in the 0.6 < M(~+Tr- ) < 0.79 GeV mass interval (d). (e) and (f) represent partial distributions in forward hemisphere regions obtained with the c o s O r + t.'tlt l l l e t h o d .
sions. The pO rapidity distribution looks roughly symmetrical and has its m a x i m u m at y* ~ 0 (fig. 1 la). 4.3. (~ p r o d u c t i o n
The inclusive study o f this state is difficult because of its small p r o d u c t i o n cross Section and there are only a few e x p e r i m e n t s [ 12] where total inclusive cross sections are available. Despite an i m p o r t a n t background in the K+K - mass distributions (fig. 12), the $ signal is clearly observed even in the total sample owing to its small width and the good resolution in the <~mass region (['R ~ 5 MeV). Its production proceeds mainly via beam fragmentation and central emission seems very small; the strong difference b e t w e e n ~ and pO rapidity distributions is clearly shown on fig. 11. Our value o f the inclusive cross section % = 0.48 + 0.10 mb is a p p r o x i m a t e l y as large as the corresponding one d e t e r m i n e d in 150 GeV pp interactions [12]. The cross sections derived from the 8.25 and 16 G e V / c K+p data [6]
P. Granet et al. / Inclusive production cross sections i
(a)
I
'
I
'
I
403
'
l
K*p--.p° X
+++++++++++ vE >,,
b
'10
(b)
K* p--,.(I) X
0,4
0.2
0 -2
-1
0
1
2
y*
Fig. 11. c.m. rapidity differential cross sections for inclusive production of o 0 and ~ mesons.
'O'F-0 [a)
K*p .K*K- X
y~
100
---F
-
Ib)
-0"2
l
~
[ 15~
IC)
0 . 6 < y ~ <1.0
30 10~-
20
I
10 .I0
E
o
t
(d) 1.0
b
(e)
6
"0 25
098
,!o2
,1o8
0
0,8
I
--
yN>O
f
,1o2
o
20G
I if)
t Total
100 S
,1o6
0 .....
0,8
,1o2
1!o8
M (K÷K-), GeV Fig. 12. Tile effective K+K invariant-mass spectra for different c.m. rapidity intervals and for the total sample. The curves represent the best fits to the data, performed ~ith a p-wave BreitWigner plus background, in the 0.989 1.081 (;eV mass range.
404
t'. (;ranet et al. / Inclusive production cross sections
K÷p
.K÷K- X (y*>O)
r (al
825
T [b}
--
-
16 G e V I c
(c)
3 2 GeWc
3C
8 f;:
--
GeV/c
2c
lO
"0
1C
~~ i,J
° lI i ,
"0
0
0.98
0 1102
1106
0.98
1.02
1.06
0.98
1.02
1.06
M (K ÷ K - ) , GeV
Fig. 13. Comparison of K+K - invariant-mass spectra (forward hemisphere only) at 8.25, 16 and 32 GeV/c incident momentum. The curves are the results of fitting the 0.989 1.081 GeV mass region with a p-wave Breit-Wigner plus background.
indicate that ~ production increases with energy in K÷p interactions: the cross sections for y* > 0 are equal to 170 -+ 4 0 , 2 5 0 + 80 and 410 + 70 pb at 8.25, 16 and 32 GeV/c, respectively (fig. 13). In a restricted interval of the Feynman x variable (x > 0.4), our calculated cross section (0.23 -+ 0.04 rob) is significantly lower than the corresponding value (0.43 -+ 0.11 rob) given by a 43 GeV/c K - p electronic experiment [ 1 ], while for x > 0 it is 15 times bigger than the corresponding value in a 16 GeV/c n - p experiment [ 13] where q~ production, according to the Zweig rule, is expected to be much smaller than in Kp collisions.
5 . 2 + Tensor meson production In this experiment it has not been possible to obtain the A2 (dominant decay mode On) and f' (production probably too small) inclusive cross sections. Compared to K*(892), the.K*(1420) (and particularly the K*+(1420)) is more difficult to observe because o f its lower production rate, its Kn branching fraction o f only 50%, and its relatively large width (there is an advantage in the fact that the background in this mass region is smaller than in the 0.9 GeV region). The same remarks concerning the cross section and the width are also valid for the f resonance. In fig. 14 are displayed the n+n- and K+n - invariant-mass spectra. Evidence is found for f and K*°(1420) production: of = 0.8 -+ 0.3 m b , OK,0(1420 )
1.0 + 0.2 m b .
P. Granet et al. / Inclusive production cross sections
405
K + p__.,.TT+ T1.- X r
i ! 25
ol
~>
L
1.2
OB
(b
. . . .
2
16
M I'rr +'n'- ), G e V .Q
E K * p ---~ K*IT- X "O
b
"O
25 t
"~..._'
I
5 '
o8c 0
1.1
~ "
Si+
i
~
1.3
1.5
_
_
_
_
1.7
_
1.9
M ( K + I ~ - ) , GeV Fig. 14. The invariant-mass distributions of n+n - and K+n systems produced in tile inclusive reactions (a) K+p ~ rr+rr-X, (b) K+p ~ K+Tr X (total sample) and (c) K+p -~ K+rr X (c.m. rapidity interval 1.4 < y* < 1.6). The curves are the results o1" fits to the data, perfornled with d-wave Breit-Wigner plus background, in the 0.91 1.81 and 1.20 1.80 GeV mass regions for the rr+rr- and K+r: - systems, respectively. The inserts represent the data and the results of the fits when the fitted backgrounds are subtracted.
F o r the c h a r g e d K * ( 1 4 2 0 ) , t h e p r e s e n t statistics do n o t allow to q u o t e an accurate cross s e c t i o n ; nevertheless, o u r data are c o m p a t i b l e with a value 0"K,+(1420 )
=
+0.4 mr, 0.3 - 0 . 3 . . . . .
N o s t r o n g energy d e p e n d e n c e is observed for e i t h e r charged or n e u t r a l K * ( 1 4 2 0 ) (fig. 8b), w h e n our results are c o m p a r e d to cross sections derived f r o m 5, 8.25 a n d 16 G e V / c d a t a [6]. No a t t e m p t was m a d e to calculate d i f f e r e n t i a l cross sections because o f t h e w e a k n e s s o f the signals.
P. Granet et al. /Inclusive production cross sections
406
6. Comparison with quark m o d e l predictions Predictions o f cross-section ratios for inclusive particle p r o d u c t i o n and in par-
ticular for g3 + baryons and vector mesons, have been given in the framework of the additive quark m o d e l by Anisovich and S h e k h t e r [14]. This m o d e l is supposed to be valid at sufficiently high energy and predictions are m a d e for b o t h f r a g m e n t a t i o n and central regions. A t intermediate energies, the c o m p a r i s o n w i t h the data is made difficult by the fact that several p r o d u c t i o n mechanisms can c o m p e t i t i v e l y overlap in a given kinematical region. Therefore, the definitions o f the kinematical regions given in table 2 are s o m e w h a t arbitrary and are p r o p o s e d in order to make this comparison possible. F o r b o t h central and fragmentation regions, the strange-quark suppression factor X, which is the only free p a r a m e t e r o f the m o d e l , was fixed to 3 [141
Table 2 Comparison of experimental inclusive cross sections ratios, for 3+ baryons and vector mesons produced in K+p interactions at 32 GeV/c, with quark model predictions in different kinematical regions Resonance cross-section ratios
Kinematical production regions
Experimental values
/x++(1232)
proton fragmentation Oy • < -1
0.94 -+ 0.15
K + fragmentation total - 2ay, < 0
2.5 -+ 0.6 - - - 1_+. 10.4 _+0.3 2.2
K+ fragmentation
0.41 -+ 0.07
ay, > 0 total - 2Oy, < 0
2.2 -+ 0.4
Z+(1385) K*0(892) K*+(892)
K*+(892) K*0(892) K*+(892)
- 0.18 -+ 0.05
0.9 -+ 0.5 1.0 -+ 0.3
central
0.2 -+ 0.1 --=0.2_+0.1 1.0 -+ 0.3
Crly*l < 1
K*+(892)
2Oy* < 0
K*+(892)
=12-+5
central 2Cry, < O
K*-(892)
p0
0.08 + 0.03
central
2.6 -+ 0.6
2Oy, < 0
1.0 -+ 0.3
-
-
-
0.9 -+ 0.6
2.6 -+ 1 . 0
Quark model predictions
4.5 to 9
0.75
0.25
1
P. Granet et al. / Inclusive production cross sections
407
Surprisingly (for the reasons mentioned above), the overall data are in reasonable agreement with this very simple quark model, except for the K.*-(892)K*+(892) ratio in the central region.
7. Conclusions The inclusive cross sections obtained in this experiment are summarized in table 3. The most unportant conclusions are as follows. (a) The average number of resonances per inelastic event is large; for the only states analyzed here and neglecting the multiple-counting effects due to associated productions it amounts to ~0.9. (b) Concerning ~+ baryon production, the A*+(1232) total cross section is substantially higher than the one calculated using identified protons only and 2~+(1385) production is smaller than in K - p interactions. (c) The cross sections of the K*+(892), K*°(892) and po vector mesons are of the order of 3 mb and 0 production is about 6 times smaller. This last proceeds mainly, as the K*'s, via beam fragmentation while the pO is emitted rather symmetrically around y* = 0. The inclusive cross sections of these states and their properties are comparable to those observed in 32 GeV/c K - p interactions, where a similar study has been made [11]. (d) Tensor-meson production (K*°(1420), K*+(1420) and f) is 3 to 4 times smaller than vector-meson production. (e) The predictions of the naive quark model of Anisovich and Shekhter are in general agreement with the data,
Table 3 Smnmary of inclusive production of resonances in 32 GeV/c K+p interactions Resonance
Cross section (rob)
Main kinematical production region
~++(1232) )2+(1385) S+(1385) K*+(892) K'0(892) 1(*-(892) p0 0
1.6 ± 0.3 0.14 ± 0.04 0.06 ± 0.02 3.2 -+ 0.3 3.4 e 0.4 0.18 ± 0.12 3.1 ± 0.6 0.48 -+ 0.10 +0.4 0.3_0.3 1.0 ± 0.2 0.8 -+ 0.3
proton fragmentation proton fragmentation beam fragmentation beam fragmentation beam fragmentation central central beam fragmentation
K*+(1420) K*0(1420) f
408
P. Granet et al. / Inclusive production cross sections
We wish to thank the many physicists and technicians of CERN, Saclay and Serpukhov who contributed generously to make this experiment possible and the 5, 8.25 and 16 GeV/c K+p collaborations for permitting us to use their data.
References [1] P.V. Chliapnikov, Rapporteur's talk at 18th Int. Conf. on high-energy physics, Tbilisi, 1976. [2] P.V. Chliapnikov et al., Nucl. Phys. B131 (1977) 93. [3] J.D. Jackson, Nuovo Cim. 34 (1964) 1644. [4t Particle Data Group, Rev. Mod. Phys. 48 (1976) S1. [5] W.T. Eadie et al., Statistical methods in experimental physics, (North-Holland, Amsterdam. 19711. [6] Private communications from Brussels and CERN Collaboration (5 and 8.25 GeV/c), and Birmingham, Brussels, CERN, Mons, Saclay, Serpukhov and Universit~ de Paris VI Collaboration (16 GeV/c). [71 J. Bartke et al., Nucl. Phys. Bl37 (1978) 189. [81 U. Gensch et al., France-Soviet Union and Cl'RN-Soviet Union Collaborations, Inclusive resonance production in K p interactions at 32 GeV/c, Paper presented at 18th Int. Conf. on high-energy physics, Tbilisi, 1976. [91 M. de Beer et al., France-Soviet Union and CERN-Soviet Union Collaborations, Inclusive K*+(892) production in 32 GeV/c K+p interactions, Paper presented at 18th Int. Conf. on high-energy physics, Tbilisi, 1976. I10l P.V. Chliapnikov et al., France-Soviet Union and CERN-Soviet Union Collaborations, Nucl. Phys. B133 (1978) 93. I 11 I C. Lewin et al., France-Soviet Union and CERN-Soviet Union Collaborations, Inclusive vector meson production in K p interactions at 32 GeV/c, Paper submitted to European Conf. on particle physics, Budapest, 1977. I 121 O production : C. Louedec et al., Nuovo Cim. 41A (19771 166 ( K - p , 14.3 GeV/c); V. Blobcl et al., Phys. Lett. 59B (19751 88 (pp, 24 GeV/c); K.J. Anderson et al., Phys. Rev. Lctt. 37 (19761 799 (pp, 15(1 GeV/c). [131 B. Ghidini et al., Phys. Lett. 68B (1977) 186. [141 V.V. Anisovich and V.M. Shekhter, Nucl. Phys. B55 (1973) 455.