Data on inclusive jet production in the transverse-momentum (p_⊥) range 0-8 GeV/c for 200-GeV/c p, π^-, π^+, K^-, K^+, and p incident on a hydrogen target are presented. The jet cross section is fully corrected for losses and biases, and compared with the predictions of a model based on quantum chromodynamics. Both the absolute cross section and the inclusive charged-particle distributions inside and outside the jet are in qualitative agreement with the model

Abrams, R.

Ashford, V.

Bromberg, C.

Delzenero, R.

Dzierba, A.

Erhan, S.

Fox, G.

Goldberg, H.

Gomez, R.

Haggerty, H.

Juhala, R.

Kropac, W.

Lorenz, E.

Malamud, E.

Margulies, S.

McLeod, D.

Medinnis, M.

Mori, S.

Pine, J.

Rohlf, J.

Schlein, P.

Solomon, J.

Stampke, S.

Stanek, R.

Yung, K.

English

Caltech Authors - Main

VOLUME 43, NUMBER 8 PHYSICAL REVIEW LETTERS 20 AuGusT 1979 
Experimental Tests of Quantum Chromodynamics in High-pl. Jet Production 
in 200-Ge VIc Hadron-Proton Collisions 
C. Bromberg,< a) G. Fox, R. Gomez, J. Pine, J. Rohlf, S. Stampke, and K. Yung 
California Institute of Technology, Pasadena, California 91125 
and 
S. Erhan, E. Lorenz,<bl M. Medinnis, and P. Schlein 
University of California, Los Angeles, California 90024 
and 
V. Ashford,Cc) H. Haggerty, R. Juhala,Cdl E. Malamud, and S. Mori 
Fermi National Accelerator lAboratory, Batavia, illinois 60510 
and 
R. Abrams, R. Delzenero, H. Goldberg, S. Margulies, D. McLeod, J. Solomon, and R. stanek 
University of Illinois at Chicago .. Circle, Chicago, Illinois 60680 
and 
A Dzierba and W. Kropac<el 
Indiana University, Bloomington, Indiana 47401 
(Received 11 June 1979) 
Data on inclusive jet production in the transverse-momentum (pJ.) range 0-8 GeV /c 
for 200-GeV/c p, 1r-, 1r+, K-, K+, and]) incident on a hydrogen target are presented. 
The jet cross section is fully corrected for losses and biases, and compared with the pre-
dictions of a model based on quantum chromodynamics. Both the absolute cross section 
and the inclusive charged-particle distributions inside and outside the jet are in qualita-
tive agreement with the model. 
We have investigated 200-GeV/c hadron-proton 
collisions with a large-aperture spectrometer by 
triggering on jets of particles of high collective 
transverse momentum at 90o in the c.m. system. 
Earlier results from this experiment and details 
of the apparatus are described by Bromberg et 
al. 1- 4 Trigger jets are defined, in this analysis, 
as the collection of all particles in a 1. 5-sr cone 
near 90°, and are discussed in greater detail by 
Rohlf5 and by Bromberg et al. 6 The results re-
ported here are insensitive to the exact size of 
this cone. The incident hadron was tagged with 
four Cerenkov counters and contaminations in the 
beam flavor selection were negligible. 
Previous data on jet production1' 2' 7 have shown 
the cross section to be at least two orders of mag-
nitude larger than that for a single particle with 
the same transverse momentum. More precise 
statements are hampered by uncertainties in in-
terpretation of the data. Difficulties include trig-
ger biases, and ambiguities of jet definition re-
sulting from low-momentum particles. These 
questions can only be answered in the context of 
a model. s- 10 We have modeled the interactions 
as 
beam +P- four jets. 
The initial step in this formulation was to use 
the quantum-chromodynamic (QCD) approach dis-
cussed by Feynman, Field, and Fox, 11 which re-
lates hadron jet production to a sum of contribu-
tions of quark (q) and gluon (g) two-body scatter-
ings such as 
qq-qq, qg-qg, etc. 
The importance of including the gluon contribu-
tions has been pointed out by others. 12' 13 The 
model's success in describing other high-P J. phe-
nomena justifies its use in our experiment. The 
model is not an exact formulation of the QCD pre-
dictions. Known simplifications include the ap-
proximate handling of the parton transverse-mo-
menta wave functions and the neglect of inelastic 
processes, such as qq -qqg. 
In the model, there are four jets in the final 
state, which arise from the two scattered con-
stituents, the beam remains, and the target re-
mains; each of these is fragmented into hadrons 
by use of a jet generator developed by Field and 
Feynman. 14- 16 The function D (z), which denotes 
the probability that a quark (gluon) fragments in-
to a hadron with a fraction z of the quark (gluon) 
momentum, is fixed to agree with lepton experi-
© 1979 The American Physical Society 565 
VOLUME 43, NUMBER 8 PHYSICAL REVIEW LETTERS 20 AUGUST 1979 
ments. 17• 18 Only mesons are produced in this 
model, and scale breaking in the fragmentation 
is not included. 
The four-jet Monte Carlo events were tracked 
through the spectrometer windows and the calo-
rimeter response was modeled. 5• 6 The events 
were then written out on magnetic tape, in the 
same format as the real data, and processed by 
the same software as the real events. A partial 
comparison of the data with the four-jet simula-
tion is given in Fig. 1, where final-state charged-
particle distributions are plotted versus z = p 
• Pie/1Pietl 2 , where pis the individual charged-
particle momentum, and Piet is the trigger jet 
momentum (4 GeV/c <IPietl< 5 GeV/c for these 
plots). The plots are divided into (a) trigger side, 
z >0; and (b) away side, z <0. The total charged-
particle multiplicities come out about the same. 
The average values are 10.3 for the data, and 9.5 
for the Monte Carlo simulations. The z distribu-
tions on the trigger side match reasonably well, 
the difference being a somewhat softer distribu-
tion in the data. Moreover, the away-side agree-
ment is striking. Comparable agreement was ob-
tained in both rapidity and p J. distributions. The 
discrepancies between theory and experiment 
could easily be due to the aforementioned simpli-
fications in the formulation of the model. 
These Monte Carlo events were used to study 
different approaches to the definition of a jet, 
and calculate the jet acceptance of our apparatus, 
including both geometrical and calorimeter reso-
lution effects. The calorimeter size in this ex-
periment was found to be well suited for meas-
uring these jets.5• 6 The collective p J. of all par-
ticles entering the trigger calorimeter was on 
(a) 
l do-
er dz 10o 
10-1 o DATA 
- MONTE CARI:.O 
10
-
2 o.o 0.2 0.4 0.6 0.8 
z 
0.2 0.4 0.6 0.8 1.0 
-z 
FIG. 1. Comparison of charged-particle z distribu-
tions between data and QCD-based four-jet model on 
(a) trigger side and (b) away side. 
566 
the average only about 100 MeV/c less than the 
generated trigger-jetp J.• when we apply the fidu-
cial cuts, IYI <0.2 and lc;ol <20°, where y is the 
c. m. rapidity and c;o is the azimuthal angle of the 
jet. The observedp J. is decreased by trigger-
jet particles missing the calorimeter but in-
creased by beam, target, or away-side jet par-
ticles entering the calorimeter. For our calorim-
eter these effects roughly cancel. 
The acceptance-corrected cross section for 
pp-jet+X is shown in Fig. 2. The jetpJ. is meas-
ured With very good resolution. 19 Data were tak-
en with six different calorimeter trigger thresh-
olds; in addition, a sample of events were re-
corded in which no calorimeter requirements 
were made. This enabled us to measure the 
cross section over a range of nine orders of mag-
nitude. Different bias regions (which have differ-
ent acceptances due to different trigger efficien-
cies) overlapped and thus served as a check of 
the net acceptance correction. The data have a 
p J. dependence of exp(- 3.2p J.) over the entire 
measured range. The single-particle data of 
Antreasyan et al. 20 are shown, with the numbers 
indicating the jet/single-particle ratios. Also 
shown in Fig. 2 are the QCD predictions. 11 The 
upper curve is the cross section for producing a 
jet (quark, gluon) of a given energy. The bottom 
107 
105 
d3cr 103 E-
dp3 
nb 
10 1 (GeV/cl2 
10-1 
lo-3 
10-5 0 
0 
<>o 
• 0 0 --· QCD ENERGY 
~0 - QCD P.L 
20 .q. 
! -<;>-
2 3 4 
P.L GeV/c 
• 
5 6 7 
FIG. 2. Invariant cross section (empty squares) for 
pp- jet+ X compared with QCD predictions. Also 
shown are the single-particle data, (11"+ +71"-)/2, from 
Ref. 20 (full triangles). The numbers incidate the jet/ 
single-particle ratio. (See text for a discussion of the 
QCD predictions). 
VOLUME 43, NUMBER 8 PHYSICAL REVIEW LETTERS 20 AUGUST 1979 
curve, which is about a factor of 15 lower, is the 
cross section for producing a jet of given p .~., 
with some energy going into mass of the jet parti-
cles, and transverse momentum of these parti-
cles about the jet {quark, gluon) axis. The lower 
curve, which is the prediction for what we have 
measured, is about a factor of 3 lower than the 
data, independent of p J..· Notice that the large jet 
cross section is characteristic of QCD10• 11 and we 
know of no other theories (e.g., a phase model as 
discussed in Ref. 1) that gives this. 
The ratio of jet production by incident protons 
to that by incident 1r- is shown in Fig. 3(a). No 
acceptance correction is used here, for it cancels 
upon taking the ratio. As seen in other experi-
ments,21•22 the ratio approaches the ratio of the 
total cross sections at low p .1. and falls sharply at 
~111-ill . (a) 1.5 
1.0 ~+•i-
0.5 
-t ++-
1.5 K+ K- (b) []-
·-
... .. 
1.0 
(c) 
(d) 
0.5 
2 3 4 5 6 7 
PJ.. GeV/c 
FIG. 3. (a} The beam ratio p;w- for jet production 
(empty squares) compared with single-particle produc-
tion (solid triangles) from this experiment (pJ. divided 
by 0.8) and the beam ratio p/w+ for jet production from 
Corcoran et al. 21 (crosses). (b) The beam ratios K- /w-
and K + jw+. (c) The beam ratio w+ /1r- and the single-
particle data from this experiment (pJ. divided by 0.8). 
(d) The beam ratio pfP. 
high p J.· We expect pions to make high-p .1. jets 
more easily than protons because the pion has on-
ly two valence quarks, which therefore each car-
ry on the average a larger fraction of the incident 
momentum than the three valence quarks of the 
proton. Also shown in Fig. 3(a) are the data from 
this experiment on the ratio of cross sections a 
a(pp -h +X)/a(1T"P -h +X), 
where h is a single charged hadron produced at 
90° in the c.m. system. The single-particle data 
agree with the jet data when the former p .1. scale 
is divided by about 0.8. This is consistent with 
the single high-p .~. hadron having originated from 
a quark or gluon which had on the average 15%-
20% more momentum, as suggested by both the 
theoretical11 and experimental1 analyses of single-
particle production. The datum point in the p .L 
bin 7-8 GeV/c represents thirteen 1r"P events 
and no pp events from roughly equal beam fluxes. 
These highest-p .~. events are indeed jetlike; they 
have about 80% of the kinematically allowed en-
ergy going into about 15% of the hemisphere. Jet 
data from Ref. 21 is superimposed for compari-
son with this experiment. Figure 3 also shows 
the cross-section ratios 
a(Jcp- jet +X)/ a(1r"P- jet +X), 
a(K1~P- jet+X)/a(7T+p- jet+X), 
a(1r+p- jet +X)/a(1T"P - jet+X), 
a(pp- jet +X)/a(Jip- jet +X). 
These cross sections are consistent with the hy-
pothesis that high-p .1. jet production depends only 
on the number of valence quarks in the incident 
beam (with other parameters fixed). This has 
been observed for high-P J.. single-particle produc-
tion. 4' 22 
This Letter represents a comprehensive but 
qualitative test of QCD. The current theory still 
has many uncertainties10• 11 and this, plus the 
relatively low energy of our data, renders more 
quantitative comparisons impossible at present. 
We will discuss these points more fully in Refs. 
5 and 6, and discuss there the discrepancies in 
Figs. 1 and 2 between theory and experiment. 
still it should be realized that the data summa-
rized in this Letter are being compared with ab-
solute, parameter-free predictions of a fundamen-
tal theory of the strong interactions. Viewed in 
this light, we feel that the success of the theory 
is impressive. 
We are grateful for the assistance of the staffs 
567 
VOLUME 43, NUMBER 8 PHYSICAL REVIEW LETTERS 20 AUGUST 1979 
of the Accelerator Division, Meson Department, 
and Research Services at Fermilab. We thank 
Rick Field for use of his jet-making software, 
and useful discussions, and G. Ray Beausoleil 
for his assistance with the beam Cerenkov anal-
ysis. This work was supported in part by the 
U. S. Department of Energy under Contract No. 
DE-AC-03079ER0068 and No. E(ll-1)-2009, and 
the National Science Foundation under Grants No. 
PHY-76-80660 and No. MPS-73-04640. 
(a) Present address: Michigan state University, East 
Lansing, Mich. 48824. 
(blpermanent address: Max-Planck-Institut fUr Phy-
sik und Astrophysik, Munich, Germany. 
(c) present address: Brookhaven National Laboratory, 
Upton, N.Y. 11973. 
(dlpresent address: McDonnell-Douglas Corporation, 
St. Louis, Mo. 63121. 
(elpresent address: Hughes Aircraft Corporation, Los 
Angeles, Cal. 90024. 
1c. Bromberg et al., Phys. Rev. Lett. 38, 1447 (1977), 
and Nucl. Phys. B134, 189 (1978). 
2C. Bromberg et al., in Proceedings of the Eighth In-
ternational Symposium on Multiparticle Dynamics, Kay-
sersberg, France, 1977, edited by R. Arnold, J. B. 
Gerber, and P. SchCibelin (Centre National de la Re-
cherche Scientifique, strasbourg, France, 1977). 
3c. Bromberg et al., Phys. Rev. Lett. 42, 1202 
(1979). 
4c. Bromberg et al., Phys. Rev. Lett. 43, 561 (1979) 
(this issue). 
5J. Rohlf, unpublished. 
568 
6C. Bromberg et al., "Jet Production in 200 GeV /c 
Hadron-Proton Collisions" (to be published). 
7w. Selove et al., in Proceedings of the Nineteenth 
International Conference on High Energy Physics, 
Tokyo, Japan, 1978, edited by S. Homma, M. Kawa-
guchi, and H. Miyazawa (Physical Society of Japan, 
Tokyo, 1979). 
8G. C. Fox, in Particles and Fields-1977, edited by 
G. H. Tomas, A. B. Wicklund, and P. Schreiner (Amer-
ican Institute of Physics, New York, 1978). 
9M. Della Negraet al., Nucl. Phys. B127, 1 (1977). 
10M. Jacob and P. V. Landshoff, Phys. Rep. 48, 285 
(1978). -
11R. P. Feynman, R. D. Field, and G. C. Fox, Nucl. 
Phys. B128, 1 (1977), and Phys. Rev. D 18, 3320 
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Lett. 70B, 234 (1977). 
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(1978). 
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15R. D. Field and R. P. Feynman, Nucl. Phys. B136, 
1 (1978). 
16R. D. Field, private communication. 
17J. Dakin et al., Phys. Rev, D 10, 1401 (1974). 
18G. Hanson et al., Phys. Rev. Lett. 35, 1609 (1975). 
19The resolution depends on the jet structure (Refs. 1 
and 6). For an average jet of p .L = 5 GeV /c made up of 
60% charged particles, 15% hadronic neutrals, and 25% 
electromagnetic neutrals, the jet p.L resolution is 6%. 
20D. Antreasyan et al., Phys. Rev. Lett, 38, 112 (1977). 
21M. D. Corcoran et al., Phys. Rev. Lett-:-41, 9 (1978). 
22G. Donaldson et al., Phys. Rev. Lett. 36:1110 
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Experimental Tests of Quantum Chromodynamics in High-p_⊥ Jet Production in 200-GeV/c Hadron-Proton Collisions

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Experimental Tests of Quantum Chromodynamics in High-p_⊥ Jet Production in 200-GeV/c Hadron-Proton Collisions

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