- Email: [email protected]
Measurement of the inclusive jet cross section at the CERN pp collider
Volume 172; number 3,4
PHYSICS LETTERS B
22 May 1986
M E A S U R E M E N T OF THE INCLUSIVE JET CROSS SECTION AT THE CERN p~ COLLIDER UA1 Collaboration, C E R N , Geneva, Switzerland Aachen-Amsterdam (NIKHEF)-Annecy (LAPP)-Birmingham-CERN-HarvardH e l s i n k i - K i e l - I m p e r i a l College, L o n d o n - Q u e e n M a r y College, L o n d o n - M I T P a d u a - P a r i s (Coll6ge de F r a n c e ) - R i v e r s i d e - R o m e - R u t h e r f o r d Appleton L a b o r a t o r y Saclay ( C E N ) - V i c t o r i a - V i e n n a - W i s c o n s i n G. A R N I S O N a, M.G. A L B R O W a, O.C. A L L K O F E R b, A. A S T B U R Y c, B. A U B E R T d, C. B A C C I e, J.R. B A T L E Y f, G. B A U E R g, A. B E T T I N I h, A. B E Z A G U E T i, R.K. B O C K i, K. BOS J, E. B U C K L E Y r, j. B U N N a, G. B U S E T T O h, p. C A T Z d, p. C E N N I N I i, S. C E N T R O h, F. C E R A D I N I e , G. C I A P E T T I e, S. CITTOLIN'Ti, D. C L A R K E f, D. C L I N E k, C. C O C H E T l, J. C O L A S d, p. C O L A S l, M. C O R D E N m, G. C O X m, D. D A L L M A N n, D. D A U b, M. D E B E E R l, J.P. D E B R I O N l, M. D E G I O R G I h, M. D E L L A N E G R A d.i, M. D E M O U L I N i, B. D E N B Y a, D. D E N E G R I ¢, A. D I C I A C C I O e, L. D O B R Z Y N S K I o, j. D O R E N B O S C H J, J.D. D O W E L L m, E. D U C H O V N I i, R. E D G E C O C K m, K. E G G E R T P, E. E I S E N H A N D L E R f, N. E L L I S m, P. E R H A R D P, H. F A I S S N E R P, M. F I N C K E K E E L E R c, P. F L Y N N a, G. F O N T A I N E o R. F R E Y q, R. FRI21HWIRTH n, J. G A R V E Y m, D. G E E q, S. G E E R g, C. G H E S Q U I F ; R E o, P. G H E Z d F. G H I O e p. G I A C O M E L L I i W.R. G I B S O N r, y . G I R A U D - H E R A U D ° A. G I V E R N A U D t, A. G O N I D E C d, M. G O O D M A N g, H. G R A S S M A N N P, G. G R A Y E R a, W. G U R Y N q, T. H A N S L - K O Z A N E C K A p,l W. H A Y N E S a, S.J. H A Y W O O D m H. H O F F M A N N i D.J. H O L T H U I Z E N J, R.J. H O M E R m A. H O N M A f W. J A N K i M. J I M A C K m, G. J O R A T i P.I.P. K A L M U S f V. K A R I M A K I r R. K E E L E R C , I. K E N Y O N m A. K E R N A N q, W. K I E N Z L E i, R. K I N N U N E N r, W. K O Z A N E C K I q.1 j. K R O L L g D. K R Y N o, p. K Y B E R D f, F. L A C A V A e, j.p. L A U G I E R t, j.p. LEES d R. L E U C H S b S. L E V E G R U N b, A. L E V E Q U E i j M. LEVI i D. L I N G L I N d E. L O C C I / K. L O N G i T. M A R K I E W I C Z k, M. M A R K Y T A N ", T. M A R T I N °, G. M A U R I N i, T. M c M A H O N m, j._ P. M E N D I B U R U o, A. M E N E G U Z Z O h, O. M E Y E R i, T. MEYER i M.-N. M I N A R D d M. M O H A M M A D I k, K. M O R G A N q, M. M O R I C C A ix, H. M O S E R P, B. M O U R S d, Th. M U L L E R i, A. N A N D I f, L. N A U M A N N i, A. N O R T O N i, L. P A O L U Z I ~, D. P A S C O L I h, F. PAUSS i, C. P E R A U L T d, G. P I A N O M O R T A R I e, E. P I E T A R I N E N r, C. P I G O T / M. P I M I A ~, D. P I T M A N q, A. P L A C C I i, j._p. P O R T E i, E. R A D E R M A C H E R P, J. R A N S D E L L q, T. R E D E L B E R G E R P, H. R E I T H L E R P, J.P. R E V O L ~, J. R I C H M A N i M. R I J S S E N B E E K i, j. R O H L F g, P. ROSSI b, C. R O B E R T S a, W. R U H M i, C. R U B B I A i, G. S A J O T o, G. S A L V I N I ~, J. SASS id, B. S A D O U L E T i D. S A M Y N i A. S A V O Y - N A V A R R O / D. S C H I N Z E L i A. S C H W A R T Z g W. SCOTI" a, T.P. S H A H ~ I. S H E E R q, I. S I O T I S t D. S M I T H q, R. SOBIE ~, P. S P H I C A S ~, J. S T R A U S S n, j. S T R E E T S m, C. S T U B E N R A U C H t, D. S U M M E R S k, K. S U M O R O K g, F. S Z O N C Z O n, C. T A O °, I. T E N H A V E J, G. T H O M P S O N f, E. T S C H E S L O G P, J. T U O M I N I E M I r, B. V A N E I J K J, P. V E R E C C H I A t J.P. V I A L L E d, T.S. V I R D E E t, H. V O N D E R S C H M I T T i, W. V O N S C H L I P P E r j. V R A N A o, V. V U I L L E M I N i, H.D. W A H L ~, P. W A T K I N S m, R. W I L K E i, j. W I L S O N m, I. W I N G E R T E R d S.J. W I M P E N N Y i C.-E. W U L Z n T. W Y A T T i M. Y V E R T d.i I. Z A C H A R O V Jr N. Z A G A N I D I S ~, L. Z A N E L L O e and P. Z O T T O h
0370-2093/86[$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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Volume 172, number 3,4
PHYSICS LETTERS B
22 May 1986
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OXI10QX, UK b Institut far Reine und Angewandte Kernphysik, Christian Albrechts Universiti~t, Olshausenstrasse 40-60, D-2300 Kiel, Fed. Rep. Germany c University of Victoria, P.O. Box 1700, Victoria, B.C., Canada V 8 W 2 Y 2 d LAPP, Chemin de Bellevue, B.P. 909, F-74019 Annecy le Vieux Cedex, France e Dipartimento di Fisica, Universith "La Sapienza". Piazzale Aldo Moro 2, 1-00185 Rome, Italy ! Department of Physics, Queen Mary College, Mile End Road, London E1 4NS, UK s High Energy Physics Laboratory, Harvard University, 42 Oxford Street, Cambridge, MA 02138, USA h Universith degli Studi, Via 8 Febbraio 9, 1-35100 Padua, Italy ' CERN, CH-1211 Geneva 23, Switzerland J NIKHEF-H, Kruislaan 409, Postbus 41882, NL-IO09 DB Amsterdam, The Netherlands k Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, WI 53706, USA l CEN Saclay, D P H P E / S E C B , B.P. 2, F-91190 Gif-sur-Yvette, France " Department of Physics, University of Birmingham, P.O. Box 363, Birmingham B15 2TT, UK Institut fi~r Hochenergiephysik, Osterreichische Akademie der Wissenschaften, Nikolsdorfergasse 18, A-1050 Vienna, Austria o Laboratoire Physique Corpusculaire, Collbge de France, 11, Place Marcelin Berthelot, F-75231 Paris Cedex 05, France P IlL Physikalische Institut A, R W T H , Physikzentrum, ArnoM SommerfeM Strasse, D-5100 Aachen, Fed. Rep. Germany q Physics Department, University of California, Riverside, CA 92502, USA r Department of Physics, Helsinki University, Siltavuorenpenger 20C, SF-O0170 Helsinki 17, Finland s MIT, Cambridge, MA 02139, USA t Imperial College, London S W 7 2 A Z , UK
Received 27 February 1986
The inclusive jet cross section has been measured in the UA1 experiment at the CERN p~ Collider at centre-of-mass energies V~ = 546 GeV and V~-= 630 GeV. The cross sections are found to be consistent with QCD predictions. The observed change in the cross section with the centre-of-mass energy V;S is accounted for in terms of x-r scaling.
1. I n t r o d u c t i o n . The emergence o f jets with large transverse energy was one of the first results from the CERN p~ Collider [ 1 ]. At the energies o f the Collider (x/s--= 546 and 630 GeV), jets are clearly distinguished from the background. Thus jet production properties can be studied with little dependence on the fragmentation, as the emitted jets can be associated directly with the scattered partons. Recently, jet production properties have been investigated by measurements of the inclusive cross section [2,3] and of the two-jet angular distribution [4]. These results have been shown to strongly support the QCD description of the hard scattering o f partons in p~ collisions. In this letter, we present the inclusive jet cross sections recently measured at x F = 546 and 630 GeV with the UA1 detector. The energy dependence of the inclusive cross section is examined, and comparisons with current theoretical predictions are made. I Present address: SLAC, Stanford, CA, USA.
462
2. A p p a r a t u s a n d data taking. T h e UA1 detector and the data-taking conditions are essentially unchanged from those reported in our previous publications, and we refer the reader to ref. [3] for more detafls. The data sample is comprised o f all jet triggers from the 1983 Collider run at x/~-= 546 GeV and from the 1984 CoUider run at V~ -= 630 GeV. At the trigger level, a jet is defined as a localized transverse energy E T deposition anywhere in the central calorimetry (pseudorapidity Ir/I < 3). F o r the 1983 run, the data were based on an inclusive single-jet trigger, while for the 1984 run, the data were based partially on a low-E T threshold, two-jet trigger, but primarily on a high-E T inclusive single-jet trigger. The luminosities and relevant thresholds o f the various data samples are presented in table 1. A jet is defined by the UA1 jet algorithm [3], which combines calorimeter hits within a cone of radius 1 unit in 7, q~space around the highest transverse-
22 May 1986
PHYSICS LETTERS B
Volume 172, number 3,4 Table 1 Summary of data sets.
Run
,,/7
Integrated luminosity (nb -1 )
Trigger
Off-line threshold
Jet detection efficiency ~ 90%
1983
546 GeV
6 106
I jet E T/> 15 GeV I jet E T ~ 25 or 30 GeV
None 1 jet PT ~ 30 GeV
PT ~ 24 GeV PT ~ 40 GeV
1984
630 GeV
18 ~8
2jetsE T ~ 15 GeV each 1 jet E T ~ 25 or 30 GeV
None I jet PT ) 40 GeV
PT ~ 32 GeV PT ~>48 GeV
energy hits (¢ is the azimuthal angle in radians). The energy and momentum of each jet are computed by taking the respective scalar and vector sums over the associated calorimeter cells. Charged-track information is not used for finding jets or for defining their energy. Corrections have to be applied off-line to the data for the effect o f radiation damage to the calorimetry. The light yield coming from the electromagnetic calorimeter cells decreased by 6% during the 1983 run and 11% during the 1984 run periods. We have corrected this ageing by a factor proportional to the integrated luminosity received; however, we cannot exclude the possibility that ageing has partially occurred at one, or several, discrete times during the running periods. The data were found to contain a small fraction o f background events from b e a m - g a s interactions and events involving two interactions in the same SPS bunch crossing. These are removed from the sample by imposing requirements on the total energy (Eto t < 600 GeV for the 1983 data and Eto t < 700 GeV for the 1984 data), and on the magnitude of the missing energy vector (E~ross < 2.50, where o = 0.7 X/~-~-T I). An additional veto against beam halo overlapping with real events was applied by rejecting jets where more than 80% of the energy is deposited in the hadronic part o f the calorimeter. A correction was applied to the measured energy and momentum of each jet, as a function of the pseudorapidity and azimuth of the jet, on the basis o f a Monte Carlo analysis, to account for the effect o f uninstrumented material and containment losses [4,5]. Finally, a fiducial cut in azimuthal angle ¢ was used to exclude jets within 30 ° o f the vertical direction, where there is a low trigger efficiency and a large uncertainty in the reconstructed jet energy.
3. Results. The inclusive jet cross section do/dPT drl averaged over the pseudorapidity interval Ir/I < 0.7 has been calculated from the observed number of jets and normalized to the integrated luminosity. As the raw event rate has to be corrected for the effects of detector resolution, Monte Carlo studies of the detector were made to determine the jet resolution. By folding the Monte Carlo jet PT resolution with a steeply failing PT spectrum from a QCD calculation (described later), a smearing correction factor was obtained. Typical multiplicative corrections range from 0.8 at low PT .(30 GeV) to 0.7 at high PT (130 GeV). The correction factors are quite similar at ~ = 546 and 630 GeV. The luminosity was calculated from the rate observed in a pair of scintillator hodoscopes covering the range 1 2 - 5 6 mrad. The results for the inclusive jet cross section are presented in table 2 and shown in fig. 1. The errors shown include statistical errors and an energy-dependent uncertainty on the smearing correction. The overall systematic uncertainty in the cross section is estimated to be -+70%. This includes an error of -+50% due to the uncertainty in acceptance functions and jet energy corrections. In addition, there is a -+40% error in the cross section due to the uncertainty in the calorimeter calibration. The error on the correction o f the ageing effects on the calorimeter is estimated to be -+10% and the uncertainty in the luminosity is approximately -+15%. The differential cross section at X/~-= 546 GeV is slightly higher than that obtained in the 1982 Collider run [3]. We attribute the difference to our improved calculations of jet-energy resolution and jet-energy corrections. The present data are in good agreement with similar results at x/~-= 546 and 630 GeV from the UA2 Collaboration [2]. Fig. 1 clearly shows the increase in the single-jet 463
Volume 172, number 3,4
PHYSICS LETTERS B
22 May 1986
Table 2 Inclusive jet cross sections.
PT
da/dp T dn ( n b / G e V ) , l n l < 0.7
UAI INCLUSIVE
102
(GeV) Vc~-=546 GeV 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 78 82 86 92 100 112 130 150
274 192 119 75 49 30.5 21.5 11.8 9.8 7.5 5.62 4.57 3.44 2.49 2.01 1.36 1.12 0.82 0.60 0.404 0.342 0.300 0.173 0.138 0.114 0.091 0.062 0.032 0.0224 0.0120 0.0063 0.0039 0.00032 0.00032
-+ 57 ± 40 ± 25 -+ 15 ± 10 ± 6.4 ± 4.6 ± 2.1 ± 1.4 -+ 1.1 ± 0.81 ± 0.66 ± 0.50 ± 0.37 ± 0.30 ± 0.21 +- 0.17 ± 0.13 ± 0.10 ± 0.069 -+ 0.061 ± 0.054 ± 0.035 ± 0.030 ± 0.026 ± 0.023 ± 0.014 ± 0.009 -+ 0.0072 ± 0.0037 ± 0.0025 ± 0.0014 ± 0.00032 ± 0.00032
x/~-= 630 GeV
o C-s: 546 5eV • C-s: 630 GeV
47 35.9 27.9 19.6 15.2 11.7 8.7 7.1 5.52 4.53 3.45 2.70 1.96 1.47 1.14 0.87 0.625 0.556 0.403 0.348 0.284 0.264 0.142 0.106 0.070 0.0351' 0.0196 0.0055 0.00158 0.00040
± 11 +- 8.1 ± 4.0 ± 2.9 _+ 2.2 ± 1.7 ± 1.3 ± 1.1 ± 0.79 ± 0.65 ± 0.49 ± 0.28 ± 0.20 ± 0.16 +- 0.12 ± 0.09 ± 0.070 ± 0.063 ± 0.047 ± 0.042 ± 0.036 ± 0.033 -+ 0.018 ± 0.014 ± 0.010 ± 0.0051 ± 0.0034 ± 0.0012 ± 0.00050 ± 0.00023
inclusive cross section as X/s--increases f r o m V~--= 5 4 6 t o 6 3 0 G e V . Qualitatively, we observe t h a t the differe n c e b e t w e e n t h e t w o cross sections appears t o increase w i t h t h e PT o f the jets. We can c o m p a r e t h e inclusive j e t cross s e c t i o n w i t h Q C D calculations evalua t e d at r / = 0 [6]. T h e curves s h o w n in fig. 1 were calculated f r o m a leading o r d e r in as, t w o - p a r t o n scattering Q C D c a l c u l a t i o n using t h e s t r u c t u r e f u n c t i o n s o f E i c h t e n et al. [7]. The scale is d e f i n e d t o b e Q2 = p 2 a n d the A p a r a m e t e r in t h e s t r o n g c o u p l i n g c o n s t a n t a s ( Q 2) is A = 0.2 G e V . The Q C D c a l c u l a t i o n gives a g o o d d e s c r i p t i o n o f t h e PT d e p e n d e n c e o f t h e data. 464
JET CROSS SECTION
1°'I
0.CO - - - ~ --¢~
r~
= 546 5eV : 630OeV
10°
,7
10-~
\ "o
10.2
x__
\\
10-3
X \
10-~ 0
20
40
60
80
100
120
140
160
PT (GeV)
Fig. 1. The inclusive jet cross section for the pseudorapidity interval Inl < 0 . 7 , as a f u n c t i o n o f the jet transverse m o m e n t u m . The open dots correspond to the data at x/~-= 546 GeV and the solid dots to those at x/s-= 630 GeV. The systematic errors on both cross sections is +70%. The curves are QCD calculations and are renormalized upward by 50%.
The best fit t o the d a t a requires t h a t t h e t h e o r e t i c a l curves be m u l t i p l i e d b y a f a c t o r o f 1.5, w h i c h is w i t h in t h e s y s t e m a t i c errors a n d the a c c u r a c y o f the calculation. In fig. I , b o t h curves have b e e n scaled u p w a r d b y a f a c t o r o f 1.5. U n c e r t a i n t i e s in the Q2 scale, the QCD scale p a r a m e t e r , t h e choice o f t h e s t r u c t u r e funct i o n s , a n d h i g h e r - o r d e r c o r r e c t i o n s , d o n o t allow a greater a c c u r a c y t h a n a f a c t o r o f 2 in t h e Q C D calculations [8]. The ratio o f the cross s e c t i o n s at x/S-= 5 4 6 a n d
Volume 172, number 3,4 I
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RATIO=
I
PHYSICS LETTERS B I
I
I
I
22 May 1986
I
106
da/dp~dq Iq=0Ivrs=630 OeV) do/dp~dq Iq=o(C's:5(,6 GeV)
/
/
O,C D - /+.0
SCALED JET CROSS SECTION
. ~ = 546 GeV O's = 630 5eV
I0s
•
/ 3.0
&CD - - ¢ - ~ = 630 6eV - - - ~ = 2000 fieV
\\\
/ 10~'
S 2.0_
103
~J
\ \\
10-
\
\
-
\ \\
107 I
I
t
t
I
I
20
t~O
60
80
100
120
L
140
L
160
PT (CieV)
Fig. 2. The ratio of the inclusive cross section at x/~-= 630 GeV to the c~oss section at x/~-= 546 GeV. The systematic error on the ratio is approximately -+15%. The curve is a ratio of the QCD calculations at x/~-= 630 and 546 GeV.
630 GeV is shown in fig. 2. Although most systematic errors cancel in the ratio, the uncertainty in the ageing correction in each o f the 1983 and 1984 data-taking periods yields a systematic error of-+15%. The curve presented is the ratio of the QCD calculations shown in fig. 1 which, within the systematic error, gives a satisfactory description of the data. The increase in the cross section between the two centre-of-mass energies can be accounted for in terms o f x T scaling. Fig. 3 shows the dimensionless quantity pT4 E do/dp 3- plotted ve r su s x T = 2PT/V~-for the two different beam energies. On this plot the two sets o f data overlap, demonstrating that the observed increase in the cross section with x/~-is entirely consistent with perfect scaling. A much larger lever-arm in energy, e.g. x / s = 2000 GeV (broken curve), would be needed to be sensitive to non-scaling QCD effects, although such effects have been observed previously in ISR experiments [9].
Io, I
t
01
I
0.2
1
03
i 04
I
05
I
06
X T = 2pr/~s
Fig. 3. The scaled jet cross section as a function of the scaling variable x T = 2pT/x/~. The curves are QCD predictions at = 630 GeV (solid curve) and x R = 2000 GeV (dashed curve). The predicted cross section at x/)-= 546 GeV is very similar to that at x/~-= 630 GeV.
Recently there have been theoretical speculations that quarks and leptons have composite structures, and that they are bound states o f more fundamental constituents called preons. Following the model of Eichten et al. [7], the energy scale o f compositeness is defined as A c. In this model, values of A c different from infinity (i.e. consistent with ordinary QCD), produce an excess o f events in the high-pT regions of the inclusive jet cross section. To determine the value o f Ac, we have renormalized the QCD calculations to the low-PT region. In all instances, the A c = oo solution gave a good fit to the data. Taking into account theoretical and experimental uncertainties, the lower limit becomes A c > 400 GeV at the 95% confidence level. This result compares well with the recent limit published b y the UA2 Collaboration o f A c > 370 GeV 465
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22 May 1986
Science and Engineering Research Council, United Kingdom. Stichting Voor Fundamenteel Onderzoek der Materie, The Netherlands. Department of Energy, USA. The Natural Sciences and Engineering Council of Canada. Thanks are also due to F. Bernasconi and L. Dumps, who have worked with the Collaboration in the preparations for and data collection on the runs described here.
[2]. Recently, limits for the scale of compositeness have been determined from the two-jet angular distribution [10]. The results of that analysis are similar to the limits from the inclusive jet cross section. In conclusion, we have presented the inclusive jet cross section for p~ collisions at x/~-= 546 and 630 GeV. The cross sections are found to be well described by QCD calculations. The observed energy dependence of the cross section is consistent with QCD, and no significant scaling violations are found in the scaled cross section. The lower limit on Ac, the energy scale of quark compositeness, is found to be A c > 400 GeV (95% CL).
References
We thank W.J. Stifling for the informative discussions we have had with him. We are grateful to the management and staff of CERN and of all participating Institutes for their vigorous support of the experiment. The following funding agencies have contributed to this programme: Fonds zur F6rderung der Wissenschaftlichen Forschung, Austria. Valtion luonnontieteellinen toimikunta Suomen Akatemia, Finland. Institut National de Physique Nucl~aire et de Physique des Particules and Institut de Recherche Fondamentale (CEA), France. Bundesministerium fiir Forschung und Technologie, Fed. Rep. Germany. Istituto Nazionale di Fisica Nucleare, Italy.
[1] UA2 Collab., M. Banner et aL, Phys. Lett. B 118 (1982) 203; UA1 Collab., G. Arnison et aL, Phys. Lett. B 123 (1983) 115. [2] UA2 CoUab., P. Bagnaia et al., Phys. Lett. B 138 (1984) 430; UA2 Collab., J. Appel et al., Phys. Lett. B 160 (1985) 349. [3] UA1 Co/dab., G. Arnison et aL, Phys. Lett. B 132 (1983) 214. [4] UA1 Collab., G. Arnison et al., Phys. Lett. B 136 (1984) 294. [5] EJ. Buckley and W. Kozanecki, UA1 Technical Note, TN-85-08 (1985). [6] J. Stifling, private communication. [7] E. Eichten et al., Rev. Mod. Phys. 56 (1984) 579. [8] G. Altaxelli, pxeprint CERN TH-3733 (1983). [9] AFS Collab., T. Akesson et aL, Phys. Lett. B 123 (1983) 133. [10] UA1 Collab., G. Arnison et aL, to be published.
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PHYSICS LETTERS B
22 May 1986
M E A S U R E M E N T OF THE INCLUSIVE JET CROSS SECTION AT THE CERN p~ COLLIDER UA1 Collaboration, C E R N , Geneva, Switzerland Aachen-Amsterdam (NIKHEF)-Annecy (LAPP)-Birmingham-CERN-HarvardH e l s i n k i - K i e l - I m p e r i a l College, L o n d o n - Q u e e n M a r y College, L o n d o n - M I T P a d u a - P a r i s (Coll6ge de F r a n c e ) - R i v e r s i d e - R o m e - R u t h e r f o r d Appleton L a b o r a t o r y Saclay ( C E N ) - V i c t o r i a - V i e n n a - W i s c o n s i n G. A R N I S O N a, M.G. A L B R O W a, O.C. A L L K O F E R b, A. A S T B U R Y c, B. A U B E R T d, C. B A C C I e, J.R. B A T L E Y f, G. B A U E R g, A. B E T T I N I h, A. B E Z A G U E T i, R.K. B O C K i, K. BOS J, E. B U C K L E Y r, j. B U N N a, G. B U S E T T O h, p. C A T Z d, p. C E N N I N I i, S. C E N T R O h, F. C E R A D I N I e , G. C I A P E T T I e, S. CITTOLIN'Ti, D. C L A R K E f, D. C L I N E k, C. C O C H E T l, J. C O L A S d, p. C O L A S l, M. C O R D E N m, G. C O X m, D. D A L L M A N n, D. D A U b, M. D E B E E R l, J.P. D E B R I O N l, M. D E G I O R G I h, M. D E L L A N E G R A d.i, M. D E M O U L I N i, B. D E N B Y a, D. D E N E G R I ¢, A. D I C I A C C I O e, L. D O B R Z Y N S K I o, j. D O R E N B O S C H J, J.D. D O W E L L m, E. D U C H O V N I i, R. E D G E C O C K m, K. E G G E R T P, E. E I S E N H A N D L E R f, N. E L L I S m, P. E R H A R D P, H. F A I S S N E R P, M. F I N C K E K E E L E R c, P. F L Y N N a, G. F O N T A I N E o R. F R E Y q, R. FRI21HWIRTH n, J. G A R V E Y m, D. G E E q, S. G E E R g, C. G H E S Q U I F ; R E o, P. G H E Z d F. G H I O e p. G I A C O M E L L I i W.R. G I B S O N r, y . G I R A U D - H E R A U D ° A. G I V E R N A U D t, A. G O N I D E C d, M. G O O D M A N g, H. G R A S S M A N N P, G. G R A Y E R a, W. G U R Y N q, T. H A N S L - K O Z A N E C K A p,l W. H A Y N E S a, S.J. H A Y W O O D m H. H O F F M A N N i D.J. H O L T H U I Z E N J, R.J. H O M E R m A. H O N M A f W. J A N K i M. J I M A C K m, G. J O R A T i P.I.P. K A L M U S f V. K A R I M A K I r R. K E E L E R C , I. K E N Y O N m A. K E R N A N q, W. K I E N Z L E i, R. K I N N U N E N r, W. K O Z A N E C K I q.1 j. K R O L L g D. K R Y N o, p. K Y B E R D f, F. L A C A V A e, j.p. L A U G I E R t, j.p. LEES d R. L E U C H S b S. L E V E G R U N b, A. L E V E Q U E i j M. LEVI i D. L I N G L I N d E. L O C C I / K. L O N G i T. M A R K I E W I C Z k, M. M A R K Y T A N ", T. M A R T I N °, G. M A U R I N i, T. M c M A H O N m, j._ P. M E N D I B U R U o, A. M E N E G U Z Z O h, O. M E Y E R i, T. MEYER i M.-N. M I N A R D d M. M O H A M M A D I k, K. M O R G A N q, M. M O R I C C A ix, H. M O S E R P, B. M O U R S d, Th. M U L L E R i, A. N A N D I f, L. N A U M A N N i, A. N O R T O N i, L. P A O L U Z I ~, D. P A S C O L I h, F. PAUSS i, C. P E R A U L T d, G. P I A N O M O R T A R I e, E. P I E T A R I N E N r, C. P I G O T / M. P I M I A ~, D. P I T M A N q, A. P L A C C I i, j._p. P O R T E i, E. R A D E R M A C H E R P, J. R A N S D E L L q, T. R E D E L B E R G E R P, H. R E I T H L E R P, J.P. R E V O L ~, J. R I C H M A N i M. R I J S S E N B E E K i, j. R O H L F g, P. ROSSI b, C. R O B E R T S a, W. R U H M i, C. R U B B I A i, G. S A J O T o, G. S A L V I N I ~, J. SASS id, B. S A D O U L E T i D. S A M Y N i A. S A V O Y - N A V A R R O / D. S C H I N Z E L i A. S C H W A R T Z g W. SCOTI" a, T.P. S H A H ~ I. S H E E R q, I. S I O T I S t D. S M I T H q, R. SOBIE ~, P. S P H I C A S ~, J. S T R A U S S n, j. S T R E E T S m, C. S T U B E N R A U C H t, D. S U M M E R S k, K. S U M O R O K g, F. S Z O N C Z O n, C. T A O °, I. T E N H A V E J, G. T H O M P S O N f, E. T S C H E S L O G P, J. T U O M I N I E M I r, B. V A N E I J K J, P. V E R E C C H I A t J.P. V I A L L E d, T.S. V I R D E E t, H. V O N D E R S C H M I T T i, W. V O N S C H L I P P E r j. V R A N A o, V. V U I L L E M I N i, H.D. W A H L ~, P. W A T K I N S m, R. W I L K E i, j. W I L S O N m, I. W I N G E R T E R d S.J. W I M P E N N Y i C.-E. W U L Z n T. W Y A T T i M. Y V E R T d.i I. Z A C H A R O V Jr N. Z A G A N I D I S ~, L. Z A N E L L O e and P. Z O T T O h
0370-2093/86[$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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Volume 172, number 3,4
PHYSICS LETTERS B
22 May 1986
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OXI10QX, UK b Institut far Reine und Angewandte Kernphysik, Christian Albrechts Universiti~t, Olshausenstrasse 40-60, D-2300 Kiel, Fed. Rep. Germany c University of Victoria, P.O. Box 1700, Victoria, B.C., Canada V 8 W 2 Y 2 d LAPP, Chemin de Bellevue, B.P. 909, F-74019 Annecy le Vieux Cedex, France e Dipartimento di Fisica, Universith "La Sapienza". Piazzale Aldo Moro 2, 1-00185 Rome, Italy ! Department of Physics, Queen Mary College, Mile End Road, London E1 4NS, UK s High Energy Physics Laboratory, Harvard University, 42 Oxford Street, Cambridge, MA 02138, USA h Universith degli Studi, Via 8 Febbraio 9, 1-35100 Padua, Italy ' CERN, CH-1211 Geneva 23, Switzerland J NIKHEF-H, Kruislaan 409, Postbus 41882, NL-IO09 DB Amsterdam, The Netherlands k Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, WI 53706, USA l CEN Saclay, D P H P E / S E C B , B.P. 2, F-91190 Gif-sur-Yvette, France " Department of Physics, University of Birmingham, P.O. Box 363, Birmingham B15 2TT, UK Institut fi~r Hochenergiephysik, Osterreichische Akademie der Wissenschaften, Nikolsdorfergasse 18, A-1050 Vienna, Austria o Laboratoire Physique Corpusculaire, Collbge de France, 11, Place Marcelin Berthelot, F-75231 Paris Cedex 05, France P IlL Physikalische Institut A, R W T H , Physikzentrum, ArnoM SommerfeM Strasse, D-5100 Aachen, Fed. Rep. Germany q Physics Department, University of California, Riverside, CA 92502, USA r Department of Physics, Helsinki University, Siltavuorenpenger 20C, SF-O0170 Helsinki 17, Finland s MIT, Cambridge, MA 02139, USA t Imperial College, London S W 7 2 A Z , UK
Received 27 February 1986
The inclusive jet cross section has been measured in the UA1 experiment at the CERN p~ Collider at centre-of-mass energies V~ = 546 GeV and V~-= 630 GeV. The cross sections are found to be consistent with QCD predictions. The observed change in the cross section with the centre-of-mass energy V;S is accounted for in terms of x-r scaling.
1. I n t r o d u c t i o n . The emergence o f jets with large transverse energy was one of the first results from the CERN p~ Collider [ 1 ]. At the energies o f the Collider (x/s--= 546 and 630 GeV), jets are clearly distinguished from the background. Thus jet production properties can be studied with little dependence on the fragmentation, as the emitted jets can be associated directly with the scattered partons. Recently, jet production properties have been investigated by measurements of the inclusive cross section [2,3] and of the two-jet angular distribution [4]. These results have been shown to strongly support the QCD description of the hard scattering o f partons in p~ collisions. In this letter, we present the inclusive jet cross sections recently measured at x F = 546 and 630 GeV with the UA1 detector. The energy dependence of the inclusive cross section is examined, and comparisons with current theoretical predictions are made. I Present address: SLAC, Stanford, CA, USA.
462
2. A p p a r a t u s a n d data taking. T h e UA1 detector and the data-taking conditions are essentially unchanged from those reported in our previous publications, and we refer the reader to ref. [3] for more detafls. The data sample is comprised o f all jet triggers from the 1983 Collider run at x/~-= 546 GeV and from the 1984 CoUider run at V~ -= 630 GeV. At the trigger level, a jet is defined as a localized transverse energy E T deposition anywhere in the central calorimetry (pseudorapidity Ir/I < 3). F o r the 1983 run, the data were based on an inclusive single-jet trigger, while for the 1984 run, the data were based partially on a low-E T threshold, two-jet trigger, but primarily on a high-E T inclusive single-jet trigger. The luminosities and relevant thresholds o f the various data samples are presented in table 1. A jet is defined by the UA1 jet algorithm [3], which combines calorimeter hits within a cone of radius 1 unit in 7, q~space around the highest transverse-
22 May 1986
PHYSICS LETTERS B
Volume 172, number 3,4 Table 1 Summary of data sets.
Run
,,/7
Integrated luminosity (nb -1 )
Trigger
Off-line threshold
Jet detection efficiency ~ 90%
1983
546 GeV
6 106
I jet E T/> 15 GeV I jet E T ~ 25 or 30 GeV
None 1 jet PT ~ 30 GeV
PT ~ 24 GeV PT ~ 40 GeV
1984
630 GeV
18 ~8
2jetsE T ~ 15 GeV each 1 jet E T ~ 25 or 30 GeV
None I jet PT ) 40 GeV
PT ~ 32 GeV PT ~>48 GeV
energy hits (¢ is the azimuthal angle in radians). The energy and momentum of each jet are computed by taking the respective scalar and vector sums over the associated calorimeter cells. Charged-track information is not used for finding jets or for defining their energy. Corrections have to be applied off-line to the data for the effect o f radiation damage to the calorimetry. The light yield coming from the electromagnetic calorimeter cells decreased by 6% during the 1983 run and 11% during the 1984 run periods. We have corrected this ageing by a factor proportional to the integrated luminosity received; however, we cannot exclude the possibility that ageing has partially occurred at one, or several, discrete times during the running periods. The data were found to contain a small fraction o f background events from b e a m - g a s interactions and events involving two interactions in the same SPS bunch crossing. These are removed from the sample by imposing requirements on the total energy (Eto t < 600 GeV for the 1983 data and Eto t < 700 GeV for the 1984 data), and on the magnitude of the missing energy vector (E~ross < 2.50, where o = 0.7 X/~-~-T I). An additional veto against beam halo overlapping with real events was applied by rejecting jets where more than 80% of the energy is deposited in the hadronic part o f the calorimeter. A correction was applied to the measured energy and momentum of each jet, as a function of the pseudorapidity and azimuth of the jet, on the basis o f a Monte Carlo analysis, to account for the effect o f uninstrumented material and containment losses [4,5]. Finally, a fiducial cut in azimuthal angle ¢ was used to exclude jets within 30 ° o f the vertical direction, where there is a low trigger efficiency and a large uncertainty in the reconstructed jet energy.
3. Results. The inclusive jet cross section do/dPT drl averaged over the pseudorapidity interval Ir/I < 0.7 has been calculated from the observed number of jets and normalized to the integrated luminosity. As the raw event rate has to be corrected for the effects of detector resolution, Monte Carlo studies of the detector were made to determine the jet resolution. By folding the Monte Carlo jet PT resolution with a steeply failing PT spectrum from a QCD calculation (described later), a smearing correction factor was obtained. Typical multiplicative corrections range from 0.8 at low PT .(30 GeV) to 0.7 at high PT (130 GeV). The correction factors are quite similar at ~ = 546 and 630 GeV. The luminosity was calculated from the rate observed in a pair of scintillator hodoscopes covering the range 1 2 - 5 6 mrad. The results for the inclusive jet cross section are presented in table 2 and shown in fig. 1. The errors shown include statistical errors and an energy-dependent uncertainty on the smearing correction. The overall systematic uncertainty in the cross section is estimated to be -+70%. This includes an error of -+50% due to the uncertainty in acceptance functions and jet energy corrections. In addition, there is a -+40% error in the cross section due to the uncertainty in the calorimeter calibration. The error on the correction o f the ageing effects on the calorimeter is estimated to be -+10% and the uncertainty in the luminosity is approximately -+15%. The differential cross section at X/~-= 546 GeV is slightly higher than that obtained in the 1982 Collider run [3]. We attribute the difference to our improved calculations of jet-energy resolution and jet-energy corrections. The present data are in good agreement with similar results at x/~-= 546 and 630 GeV from the UA2 Collaboration [2]. Fig. 1 clearly shows the increase in the single-jet 463
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PHYSICS LETTERS B
22 May 1986
Table 2 Inclusive jet cross sections.
PT
da/dp T dn ( n b / G e V ) , l n l < 0.7
UAI INCLUSIVE
102
(GeV) Vc~-=546 GeV 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 78 82 86 92 100 112 130 150
274 192 119 75 49 30.5 21.5 11.8 9.8 7.5 5.62 4.57 3.44 2.49 2.01 1.36 1.12 0.82 0.60 0.404 0.342 0.300 0.173 0.138 0.114 0.091 0.062 0.032 0.0224 0.0120 0.0063 0.0039 0.00032 0.00032
-+ 57 ± 40 ± 25 -+ 15 ± 10 ± 6.4 ± 4.6 ± 2.1 ± 1.4 -+ 1.1 ± 0.81 ± 0.66 ± 0.50 ± 0.37 ± 0.30 ± 0.21 +- 0.17 ± 0.13 ± 0.10 ± 0.069 -+ 0.061 ± 0.054 ± 0.035 ± 0.030 ± 0.026 ± 0.023 ± 0.014 ± 0.009 -+ 0.0072 ± 0.0037 ± 0.0025 ± 0.0014 ± 0.00032 ± 0.00032
x/~-= 630 GeV
o C-s: 546 5eV • C-s: 630 GeV
47 35.9 27.9 19.6 15.2 11.7 8.7 7.1 5.52 4.53 3.45 2.70 1.96 1.47 1.14 0.87 0.625 0.556 0.403 0.348 0.284 0.264 0.142 0.106 0.070 0.0351' 0.0196 0.0055 0.00158 0.00040
± 11 +- 8.1 ± 4.0 ± 2.9 _+ 2.2 ± 1.7 ± 1.3 ± 1.1 ± 0.79 ± 0.65 ± 0.49 ± 0.28 ± 0.20 ± 0.16 +- 0.12 ± 0.09 ± 0.070 ± 0.063 ± 0.047 ± 0.042 ± 0.036 ± 0.033 -+ 0.018 ± 0.014 ± 0.010 ± 0.0051 ± 0.0034 ± 0.0012 ± 0.00050 ± 0.00023
inclusive cross section as X/s--increases f r o m V~--= 5 4 6 t o 6 3 0 G e V . Qualitatively, we observe t h a t the differe n c e b e t w e e n t h e t w o cross sections appears t o increase w i t h t h e PT o f the jets. We can c o m p a r e t h e inclusive j e t cross s e c t i o n w i t h Q C D calculations evalua t e d at r / = 0 [6]. T h e curves s h o w n in fig. 1 were calculated f r o m a leading o r d e r in as, t w o - p a r t o n scattering Q C D c a l c u l a t i o n using t h e s t r u c t u r e f u n c t i o n s o f E i c h t e n et al. [7]. The scale is d e f i n e d t o b e Q2 = p 2 a n d the A p a r a m e t e r in t h e s t r o n g c o u p l i n g c o n s t a n t a s ( Q 2) is A = 0.2 G e V . The Q C D c a l c u l a t i o n gives a g o o d d e s c r i p t i o n o f t h e PT d e p e n d e n c e o f t h e data. 464
JET CROSS SECTION
1°'I
0.CO - - - ~ --¢~
r~
= 546 5eV : 630OeV
10°
,7
10-~
\ "o
10.2
x__
\\
10-3
X \
10-~ 0
20
40
60
80
100
120
140
160
PT (GeV)
Fig. 1. The inclusive jet cross section for the pseudorapidity interval Inl < 0 . 7 , as a f u n c t i o n o f the jet transverse m o m e n t u m . The open dots correspond to the data at x/~-= 546 GeV and the solid dots to those at x/s-= 630 GeV. The systematic errors on both cross sections is +70%. The curves are QCD calculations and are renormalized upward by 50%.
The best fit t o the d a t a requires t h a t t h e t h e o r e t i c a l curves be m u l t i p l i e d b y a f a c t o r o f 1.5, w h i c h is w i t h in t h e s y s t e m a t i c errors a n d the a c c u r a c y o f the calculation. In fig. I , b o t h curves have b e e n scaled u p w a r d b y a f a c t o r o f 1.5. U n c e r t a i n t i e s in the Q2 scale, the QCD scale p a r a m e t e r , t h e choice o f t h e s t r u c t u r e funct i o n s , a n d h i g h e r - o r d e r c o r r e c t i o n s , d o n o t allow a greater a c c u r a c y t h a n a f a c t o r o f 2 in t h e Q C D calculations [8]. The ratio o f the cross s e c t i o n s at x/S-= 5 4 6 a n d
Volume 172, number 3,4 I
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RATIO=
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PHYSICS LETTERS B I
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I
I
22 May 1986
I
106
da/dp~dq Iq=0Ivrs=630 OeV) do/dp~dq Iq=o(C's:5(,6 GeV)
/
/
O,C D - /+.0
SCALED JET CROSS SECTION
. ~ = 546 GeV O's = 630 5eV
I0s
•
/ 3.0
&CD - - ¢ - ~ = 630 6eV - - - ~ = 2000 fieV
\\\
/ 10~'
S 2.0_
103
~J
\ \\
10-
\
\
-
\ \\
107 I
I
t
t
I
I
20
t~O
60
80
100
120
L
140
L
160
PT (CieV)
Fig. 2. The ratio of the inclusive cross section at x/~-= 630 GeV to the c~oss section at x/~-= 546 GeV. The systematic error on the ratio is approximately -+15%. The curve is a ratio of the QCD calculations at x/~-= 630 and 546 GeV.
630 GeV is shown in fig. 2. Although most systematic errors cancel in the ratio, the uncertainty in the ageing correction in each o f the 1983 and 1984 data-taking periods yields a systematic error of-+15%. The curve presented is the ratio of the QCD calculations shown in fig. 1 which, within the systematic error, gives a satisfactory description of the data. The increase in the cross section between the two centre-of-mass energies can be accounted for in terms o f x T scaling. Fig. 3 shows the dimensionless quantity pT4 E do/dp 3- plotted ve r su s x T = 2PT/V~-for the two different beam energies. On this plot the two sets o f data overlap, demonstrating that the observed increase in the cross section with x/~-is entirely consistent with perfect scaling. A much larger lever-arm in energy, e.g. x / s = 2000 GeV (broken curve), would be needed to be sensitive to non-scaling QCD effects, although such effects have been observed previously in ISR experiments [9].
Io, I
t
01
I
0.2
1
03
i 04
I
05
I
06
X T = 2pr/~s
Fig. 3. The scaled jet cross section as a function of the scaling variable x T = 2pT/x/~. The curves are QCD predictions at = 630 GeV (solid curve) and x R = 2000 GeV (dashed curve). The predicted cross section at x/)-= 546 GeV is very similar to that at x/~-= 630 GeV.
Recently there have been theoretical speculations that quarks and leptons have composite structures, and that they are bound states o f more fundamental constituents called preons. Following the model of Eichten et al. [7], the energy scale o f compositeness is defined as A c. In this model, values of A c different from infinity (i.e. consistent with ordinary QCD), produce an excess o f events in the high-pT regions of the inclusive jet cross section. To determine the value o f Ac, we have renormalized the QCD calculations to the low-PT region. In all instances, the A c = oo solution gave a good fit to the data. Taking into account theoretical and experimental uncertainties, the lower limit becomes A c > 400 GeV at the 95% confidence level. This result compares well with the recent limit published b y the UA2 Collaboration o f A c > 370 GeV 465
Volume 172, number 3,4
PHYSICS LETTERS B
22 May 1986
Science and Engineering Research Council, United Kingdom. Stichting Voor Fundamenteel Onderzoek der Materie, The Netherlands. Department of Energy, USA. The Natural Sciences and Engineering Council of Canada. Thanks are also due to F. Bernasconi and L. Dumps, who have worked with the Collaboration in the preparations for and data collection on the runs described here.
[2]. Recently, limits for the scale of compositeness have been determined from the two-jet angular distribution [10]. The results of that analysis are similar to the limits from the inclusive jet cross section. In conclusion, we have presented the inclusive jet cross section for p~ collisions at x/~-= 546 and 630 GeV. The cross sections are found to be well described by QCD calculations. The observed energy dependence of the cross section is consistent with QCD, and no significant scaling violations are found in the scaled cross section. The lower limit on Ac, the energy scale of quark compositeness, is found to be A c > 400 GeV (95% CL).
References
We thank W.J. Stifling for the informative discussions we have had with him. We are grateful to the management and staff of CERN and of all participating Institutes for their vigorous support of the experiment. The following funding agencies have contributed to this programme: Fonds zur F6rderung der Wissenschaftlichen Forschung, Austria. Valtion luonnontieteellinen toimikunta Suomen Akatemia, Finland. Institut National de Physique Nucl~aire et de Physique des Particules and Institut de Recherche Fondamentale (CEA), France. Bundesministerium fiir Forschung und Technologie, Fed. Rep. Germany. Istituto Nazionale di Fisica Nucleare, Italy.
[1] UA2 Collab., M. Banner et aL, Phys. Lett. B 118 (1982) 203; UA1 Collab., G. Arnison et aL, Phys. Lett. B 123 (1983) 115. [2] UA2 CoUab., P. Bagnaia et al., Phys. Lett. B 138 (1984) 430; UA2 Collab., J. Appel et al., Phys. Lett. B 160 (1985) 349. [3] UA1 Co/dab., G. Arnison et aL, Phys. Lett. B 132 (1983) 214. [4] UA1 Collab., G. Arnison et al., Phys. Lett. B 136 (1984) 294. [5] EJ. Buckley and W. Kozanecki, UA1 Technical Note, TN-85-08 (1985). [6] J. Stifling, private communication. [7] E. Eichten et al., Rev. Mod. Phys. 56 (1984) 579. [8] G. Altaxelli, pxeprint CERN TH-3733 (1983). [9] AFS Collab., T. Akesson et aL, Phys. Lett. B 123 (1983) 133. [10] UA1 Collab., G. Arnison et aL, to be published.
466