Triple-jet structures in proton-proton interactions

Volume 105B, number 2,3

PHYSICS LETTERS

1 October 1981

TRIPLE-JET STRUCTURES IN P R O T O N - P R O T O N INTERACTIONS C E R N - C o l u m b i a - O x f o r d - R o c k e f e l l e r (CCOR) Collaboration A.L.S. ANGELIS c, H.-J. BESCH a, B.J. BLUMENFELD b, a, 1, L. CAMILLERI a, T.J. CHAPIN a, R.L. COOL d, C. del PAPA a, 2, L. Di LELLA a, Z. DIM~OVSKI d, 3, R.J. HOLLEBEEK b,4, L.M. LEDERMAN b,s , D.A. LEVINTHAL b, J.T. LINNEMANN d, C.B. NEWMAN a, 6, N. PHINNEY a'c, B.G. POPE a, 6, S.H. PORDES a, d, s, A.F. ROTHENBERG d,a, R.W. RUSACK b, A.M. SEGAR c, J. SINGH-SIDHU a, 7, A.M. SMITH a, M.J. TANNENBAUM d, 8, R.A. VIDAL b, 4, J.S. WALLACE-HADRILL c, a, J.M. YELTON c and K.K. YOUNG a, 9 a CERN, Geneva, Switzerland b Columbia University 10, New York, NY, USA c University o f Oxford, Oxford, UK d RockefeUer University 11, New York, NY, USA

Received 11 May 1981

A search for triple jets produced in proton-proton collisions at x/'~= 62 GeV has been performed at the CERN ISR. For 42 000 events obtained with an average trigger no transverse momentum of 6 GeV/c, 782 triple-jet events are identified using a clustering method. The two jets opposite the trigger show a correlation in their polar angle distributions. The triple-jet production rate is much higher than expected by scaling the rate from e÷e- processes.

At ISR energies, two-jet structures have been studied for many years ,1. By this is meant events where two jets o f high transverse m o m e n t u m approximately balance each other, while the remainder o f the particles o f the event, sometimes called the spectator jets, follow the beam directions. Two-jet structures, attributed to q u a r k - a n t i q u a r k pair production, have also been studied in e+e - interactions. Recently, three-jet structures have been observed to occur in addition to the two-jet hadronic events in e+e - annihilations [ 2 - 5 ] . These events are 1 Present address: Physics Department, Johns Hopkins University, Baltimore, MA, USA. 2 Present address: Physics Department, University of Washington, Seattle, WA, USA. 3 Present address: University of Skopje, Macedonia, Yugoslavia. 4 Present address: SLAC, Stanford, CA, USA. 5 Present address: FNAL, Batavia, IL, USA. 6 Present address: Physics Department, Princeton University, Princeton, NJ, USA.. 7 Present address: Physics Deparment, University of Manchester, Manchester, UK. 8 Present address: Brookhaven National Laboratory, Upton, NY, USA. 0 0 3 1 - 9 1 6 3 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 02.75 © 1981 North-Holland

thought to be due to gluon jets accompanying the quark and antiquarkjets, the gluons being produced b y bremsstrahlung. This mechanism for producing a third jet should evidently be expected to occur in p r o t o n - p r o t o n interactions, but there are many other sub-processes which can contribute to multijet production in the p r o t o n - p r o t o n case, and these have been estimated in QCD calculations [ 6 - 8 ] . Although expected to occur in relatively large numbers, triple-jet events are very difficult to extract experimentally as the third jet is usually hidden within the part i d e s o f the second. At the highest jet energies, however, some third jets are sufficiently separated in angle to be identified. In this letter we show that our data are consistent with QCD expectations, some triple-jet structures being observed at large separation angles. 9 Permanent address: Physics Department, University of Washington, Seattle, WA, USA. lo Research supported in part by the National Science Foundation. 11 Research supported in part by the US Department of Energy. * 1 Darriulat [ 1] gives a list of experiments and references. 233

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The apparatus has been described elsewhere [9-13]. Charged particles were detected by drift chambers inside a solenoidal magnetic field, and rr0's in two arrays of lead-glass total absorption ~erenkov counters, on either side of the interaction region. The crucial feature of the apparatus for this analysis was its 27r acceptance in azimuth angle ~b for charged particles, essential in picking up three jets at large angles to each other. The polar angle range for charged particles was A0 ~ +40 ° about the plane normal to the beams. (All angles measured in the pp centre of mass.) The apparatus was triggered by an electromagnetic shower, with transverse momentum PTt > 5 GeV/c, detected in the lead-glass counters, acceptance A¢ ~ _+25°, A0 ~ _+30 ° on the inside of the ISR ring, A0 ~ + 30 °, A0 ~ -+38 ° on the outside. Particles other than 7r0 contribute to the trigger, but this is not significant in this analysis since the triggers are still component particles of jets, excepting the small direct photon component [14,15]. Neutral and charged particles are required to have transverse momenta > 300 MeV/c to be accepted, and the analysis was restricted to events with/> 5 particles. To find three-jet events among a large sample of twojet events, a duster analysis was used ,2 [17]. The trajectory of each particle is initially identified as an individual cluster, represented as a point at (0, q~) on a unit sphere. The number of clusters is then systematically reduced by finding the closest pair of dusters on the sphere, and merging them to one new duster in the position of the vector sum of the momenta. This is repeated until there are just two clusters left. At each stage with n clusters a quantity Wn can be calculated to represent the quality of the clustering at that level: n

where (JT)i is the mean squared transverse m o m e n t u m of particles in cluster i, relative to the vector sum. Small Wn corresponds to a particularly good clustering combination, and a small ratio W3/W 2 corresponds to an event with better three-jet than two-jet clustering. This particular choice of W function, and of the procedure for reduction of the number of dusters, follows one of the standard methods of cluster analysis *2. The method was applied to three-jet Monte Carlo events, *2 The "k-means" method of cluster analysis, see ref. [ 16 ]. 234

1 October 1981

and with the cut chosen in all this analysis, W3/W2 < 0.5, the three-jet events were identified with full efficiency at large separations, the efficiency dropping to 79% for angles 423 between jets 2 and 3 of 1.2 rad. The efficiency dropped still further at small angles, and a distortion effect was seen due to incorrect allocation of tracks to clusters. Closely similar effects were seen with the real events, as discussed and corrected below, see fig. 2. In spite of these deficiencies, when applied to the Monte Carlo events, the cluster method proved more sensitive than the triplicity method [ 2 - 5 ] . A total of 105 lr0 trigger events was analysed in this way, yielding the total shown in table 1 as "real" events. Cluster 1 (or jet 1) refers to the cluster containing the trigger n 0 ; cluster 2 (or jet 2) is the one with the largest momentum away-side particle; cluster 3 (or jet 3) is then the one remaining. Of the 105 events, 42 000 satisfied the initial requirement of ~>5 particles. Of these 1203 satisfied the further requirements for a triple-jet event, i.e. W3/W 2 • 0.5, and/> 3 particles in duster 3. Events with cluster 3 containing < 3 particles were not accepted since the real/ random ratio of these events (see later) was not large enough to give a useful contribution to the signal. Fluctuations of particle distributions in two-jet events are capable of simulating third jets, by random groupings of particles to form third dusters. To assess this effect, in as model-independent a way as possible, use was made of the expectation that particles in twojet events are uniformly distributed in azimuth about the jet axis. In each of the 42 000 events, each particle assigned to clusters 2 and 3 was rotated through a randomly-chosen azimuth angle about the centre of momentum of those particles, i.e. about the vector sum of all their momenta. However, to preserve the same number of particles, the random angles were chosen to lie within the acceptance. The whole data sample was then reanalysed, to obtain a different sample of triple-jet events labelled "random" in table 1 and on the figures. The randornised events analysed in this way retain on average all their original two-jet properties,/'T distribution etc., but lose any real spatial correlations of particles in the tails of the second jets, so it can be assumed that the triple-jet sample obtained from them gives an accurate assessment of background from random correlations. The final triple-jet signal is obtained by subtracting these random events from the real events above. A correlation effect which would be lost in the ran-

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1 October 1981

normal to either proton direction. The triple-jet events, obtained by the above procedure, have a distribution in polar angle 0 o f jet 3 shown in fig. la. Both real and random distributions drop at the extremes o f acceptance 101 > 0.7 rad, and the random distribution is rather uniform, characteristic o f the fiat rapidity distribution of all the two-jet and background contributions. But the real signal is peaked toward the maximum 101 which lies within the acceptance. Jet 2 shows a similar peaking in the opposite sense. In fig. lb, the jet 3 " 0 " distributions for selected bins of jet 2 " 0 " positions are presented. The random events show no particular correlation, but the real events tend to maximise the modulus Of0re 1 = 02 - 03. Thus, if events are excluded where 02 and 03 are of the same sign, 0re1 being therefore small, mainly background is eliminated and the remaining events have a real/random o f 802 to 231, or 3.47 to 1. To explain this property o f the 0 distributions, we note that the triple jets are formed in a plane in the centre o f mass o f the colliding partons. In QCD, the angular distribution o f the triple-jet plane with respect to the colliding parton direction can be expected to be fairly uniform. Thus, in e+e - annihilation, the distribution in 0a, the polar angle between the colliding direction and the hormal to the triple-jet plane has been calculated to be [18] :

dora event construction as described, would be that due to clustering corresponding to decays of resonances. However, there are not large numbers of high-momentum particles observed at large angles to the away-jet momentum sum vector, about 200 with momenta > 2 GeV/c and at angles > 1 rad in our data sample. So, it is considered unlikely that there could be such a large proportion o f resonances among these particles that they could contribute significantly to the third jet signal. Random groupings o f spectator particles could also contribute to a background of third jets, but these will be correctly subtracted by the above technique. In any case, we note that the third clusters have such a high transverse momentum, 2.2 GeV/c on average, that they must be involved in the high-p T part of the interaction and the random third cluster transverse momentum is appreciably less, about 1.5 GeV/c. The results for real and random events are presented in table 1. The ratio real/random is 2.86 overall, higher for the higher multiplicity events. Note the basic asymmetry o f the trigger - the trigger jet tends to be of higher momentum, so the third-jet usually is on the second-jet ("away") side, helping to balance momentum. We are left with a "true" triple jet signal o f 782 events, after subtracting 421 random events. We find that the triple-jet events are distributed uniformly according to the acceptance o f the apparatus, except that an interesting effect is seen in the polar angle distribution. We define the polar angle 0 with respect to the colliding protons, 0 = 0 corresponding to jets in the plane

dn/dg2 = dn/27r sin 0ad0 a ~ 1 + ½Sin20a • Consequently, the distribution in 0a, dn/d0 a, is proportional to sin 0 a, and has a zero at 0 a = 0. This distri-

Table 1 Number of particles in cluster 3

3

4

5

>5

Total

real events, cluster 3 on the away side

690

239

62

31

1022

real events, cluster 3 on the toward side

137

37

7

-

181

real event total

827

276

69

31

1203

random events, cluster 3 on the away side

291

52

19

5

367

random events, cluster 3 on the toward side

45

7

1

1

54

336

59

20

6

421

random event total

235

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PHYSICS LETTERS

1 October 1981 Angle shift and jet toss corrections from Monte [aria using repositioned jet

listribution of cluster 3 in 0 i

(a)

1.8

I

I

!

I

f~'

i

I

100

-1.0

0

1.0 >

0 (rndians)

8 1.0 Distributions of cl.uster 3 in 0, for bonds of duster 2 in O as indicated by arrows

J f

0.6

(b)

1.0

1.8

1 t,

Generated angle 423 (re.dian)

I

p_~

I

I

I

!

10

g

8

6

c I

10

-1.0

0 8 (radie.ns)

1.0

Fig. t. (a) The distribution in polar angte O of jet 3 relative to the plane normal to the dkection of the colliding protons. (b) The distribution of cluster 3 in 0, for bands in 0 of cluster 2 as indicated by arrows.

bution will be distorted in the Lorentz transformation to the system of the colliding protons, nevertheless the zero at 0 a = 0 will correspond to a minimum at 0re1 = 0. Notice that jets 2 and 3 always have a large separation in azimuth ~, ~b>~ 1 rad, in order to be identified as separate jets, separation in 0 alone not having sufficient range, so 0re1 gives an approximate measure of 0 a, and 0re1 = 0 still corresponds to the original plane beingnorreal to the partons. This favours configurations where jets 2 and 3 are at the limits of our acceptance, 0re1 as 236

I

I

I

1.t,.

I

1.8

Observed ongte ~b'23 (r~dians)

Fig. 2. Angle shift and jet loss corrections, estimated using repositioned jets.

large as possible, as is observed. This feature of the triplejet events, which follows naturally from their QCD origin, is quite unlike the behaviour of background events and lends strong support to their interpretation in QCD. It was noted in the Monte Carlo study that the efficiency of finding triple jets dropped rapidly as jets 2 and 3 merged. To estimate this efficiency in a modelindependent way, real events with dearly separated jets, events with the observed angle between jets 2 and 3 ~23 > 1.5 rad, were used. All the tracks of the third clusters were bodily moved toward the second cluster

Volume 105B, number 2,3

PHYSICS LETTERS

axis to a given separation ~23, and the events re-analysed. The results are shown in fig. 2. There were two effects, firstly the drop in efficiency r/, which was 100% at large angles but dropped away for angles xP23 < 1.2

Ctusfer Angle Separation distributions I

i

I

200

I

I

i

I

|

I

I, I

100 t.a,.,I

0

0

1.0 Observed Separation d?'23 (radians}

2.0

!

I

(b)

~- 0.1 t.Lty3

0.01

11o

21o

rad. The plot shows this as the acceptance correction factor 1/7. Secondly the position of the centre of cluster 3 was distorted by confusion of tracks between dusters 2 and 3, so the observed separation had to be reduced to give the correct angle xi,23. Empirical fits were made to the points, shown as solid lines in fig. 2. In fig. 3a the distribution in ~23, the observed angle, is given for real and randomised data. The real data cut off sharply for angles ~23 < 1.5 rad, as expected from the estimated efficiency as a function of opening angle, and they are qualitatively quite different from randomised data in their xI'~3 distribution. This experimental distribution must be corrected for: (a) Inefficiency and distortion as a function of ~23, correction functions as shown in fig. 2. (b) Acceptance in both 0 and ~bfor both charged and neutral particles. The distribution in 0 a is taken to be either of the forms 1 or 1 + ~sm 2 0a, these two cases giving a range of the possible "model" dependent correction. The resulting corrected distribution is given in fig. 3b where the result has been normalised to the total data sample of 42 000 events, and plotted for ~23 > 0.7 rad, the extrapolation not being considered reliable for opening angles smaller than this. Integrating the distribution, we obtain the results o f table 2. According to QCD ideas, jets 2 and 3 arise from the fragmentation o f both quarks and gluons. However, jet 2 was chosen to have the highest momentum particle on the away side, so when the jets differ, jet 3 is more likely to be the gluon jet. Its transverse momentum (]T) and fractional longitudinal momentum (z) distributions might be expected to show distinctive properties of gluon jets. We find the rms fT of jet 3 has been strongly constricted by apparatus acceptance, so it does not give a useful test. The distribution in z is not so sensitive to acceptance, and we find it to be relatively steep for third 1

Differenfiat distribution of tripte jet fraction with separation ~23 I,G

1 October 1981

30

q~23 (radions) Fig. 3. (a) Angular distribution in "~'23,the observed angle between clusters 2 and 3 for real events, and for randomised events (shaded). This is raw data, uncorrected. (b) Corrected angular distribution in ~t,23 for "true" triple-jet events. The plot is normalised to the number of two-jet events in the sample, 42 000 events, dFa/dq,2a = N -1 dna/dq%3.

-

Table 2 F3(~c) is fraction of the event sample with a third jet of ~ 3 tracks, and separation xt,23 > "t,c. ~c 0.7 1.0 1.5 2.0

Fa(,t,c) 0.325 0.202 0.115 0.043

Statistical error

Model

0.043 0.013 0.010 0.007

0.040 0.023 0.014 0.006

error

237

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jets, exPonential fits giving slopes o f - 7 . 8 + 0.5 for the z distribution o f real jets 3 as compared with - 5.8 -+0.8 for random jets 3. So there is perhaps some indication here o f the anticipated softer fragmentation of gluon jets. It is interesting to compare the fraction o f triple jets seen here with those seen in e + e - annihilation at PETRA. The PLUTO collaboration [4,19] has given a detailed analysis o f their three-jet events, and they obtain a fraction 0.093 o f separated three-jets events for opening angles ~23 exceeding 0.8 rad. This compares with 0.28 for the present data, for the same opening angle cut. But the PLUTO data asked for only/> 2 tracks in jet 3, and refer to a X/S7 value o f 30 GeV rather than the 12 GeV average total energy o f the 3 jets in the present data. We correct for the x/s dependence by using a factor In - 1 v ~ / A with A = 0.5 GeV for the variation o f the coupling. To correct for the different cuts on numbers o f tracks, we increase the p - p result by a factor 2.2 + 0.3, the error reflecting our uncertainty as to the track multiplicities. Our final result for the ratio of hadronic to e+e - triple-jet production is 5.3 -+ 0.9 (statistical) -+ 0.9 (systematic). Gottschalk et al. [8] give calculations for the processes qq ~ qqg and gg -+ ggg and compare the fraction o f triple jets produced by these processes to that produced by the quark bremsstrahlung of e+e - production. They deduce that triple-jet production is 2 - 4 times greater in the hadronic processes. Kunszt and Pietarinen [6] give calculations for triplejet processes in p - p collisions. It is not possible to exactly reproduce the cuts that they apply to their calculations, because they require jet tracks to have at least 1.5 GeV/c, but with comparable cuts and for opening

238

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angles > 0 . 8 rad, they give ~ 0 . 2 5 as the fraction triple jet/(double jet + triple jet) at x/~ = 52 GeV. If we correct the calculated fraction for the m o m e n t u m cut, and extrapolate to our multiplicity, we obtain ~ 0 . 3 9 as the expected triple-jet fraction, in approximate agreement with our result of 0.28, and confirming the relatively large hadronic triple-jet production.

References [ 1] P. Darriulat, Large transverse momentum hadronic processes, CERN EP/80-16. [2] TASSO CoUab., R. Brandelik et al., Phys. Lett. 86B (1979) 243. [3] MARK J CoUab., D.P. Barber et al., Phys. Rev. Lett. 43 (1979) 830. [4] PLUTO Collab., Ch. Berger et al., Phys. Lett. 86B (1979) 418. [5] JADE CoUab., W. Bartel et al., DESY 79/80. [6] Z. Kunszt and E. Pietarinen, Nucl. Phys. B164 (1980) 45. [7] J. Kripfganz and A. Schiller, Phys. Lett. 79B (1978) 317. [8] T. Gottschalk, E. Monsay and D. Sivers, Phys. Rev. D21 (1980) 1799. [9] A.L.S. Angelis et al., Phys. Lett. 94B (1980) 106. [10] A.L.S. Angelis et al., Phys. Lett. 79B (1978) 505. [11] A.L.S. Angelis et al., Phys. Lett. 87B (1979) 398. [12] L. Camilleri et at., Nucl. Instrum. Methods 156 (1978) 275. [13] M. Morpurgo, Cryogenics 17 (1977) 89. [14] A.L.S. Angelis et al., Phys. Lett. 98B (1981) 115. [15] M. Diakonou et al., Phys. Lett. 91B (1980) 301. {16] E.g., J.A. Hartigan, Clustering algorithms (Wiley, New York). [ 17] J.S. WaUace-Hadrill,D. Phil. Thesis, Univ. of Oxford. [18] J. Ellis, M.K. Gaillard and G.G. Ross, Nucl. Phys. B l l l (1976) 253; B130 (1977) 516. [19] Ch. Berger et al., Phys. Lett. 97B (1980) 459.