Multijet production in W, Z events at pp colliders

VoLume 224, number 1,2

PHYSICS LETTERS B

22 June 1989

M U L T I J E T P R O D U C T I O N I N W, Z E V E N T S AT p~ C O L L I D E R S F.A. BERENDS, W.T. G I E L E 1, H. K U I J F Instituut-Lorentz, University of Leiden, POB 9506, 2300 RA Leiden, The Netherlands

R. KLEISS CERN, CH-1211 Geneva 23, Switzerland

and W.J. S T I R L I N G Department of Physics, University of Durham, Durham DH1 3LE, UK

Received 28 March 1989

We calculate cross sections for the production of 0, 1, 2 and 3 jets in W, Z events at p!bcollider energies. Full leptonic decays of the weak bosons are included. We analyse in particular the relative rate of multijet production, the contribution of the different subprocesses and some overall properties of the events.

1. Introduction One o f the most i m p o r t a n t s t a n d a r d m o d e l physics processes at high energy h a d r o n - h a d r o n colliders is the p r o d u c t i o n o f a W or Z with a c c o m p a n y i n g hadronic (quark or gluon) jets. The i m p o r t a n c e o f such processes has already been established at the C E R N p~ collider [ 1 ]. Essentially a n y " n e w physics" process (heavy quarks, SUSY .... ) can be m i m i c k e d by W, Z + j e t s production, and it is therefore vitally important to be able to estimate these b a c k g r o u n d processes accurately. At the same time, quantitative tests o f the s t a n d a r d model are possible - the UA2 Collaboration has recently reported a m e a s u r e m e n t o f the strong coupling as from the relative rate o f W + I jet production [ 2 ]. In the last few years, some o f us have been involved in detailed studies o f the p r o d u c t i o n o f W, Z + 0 , 1, 2 jets. This work involved first calculating the a p p r o p r i a t e matrix elements [ 3 ] - using " s p i n o r techniques" - and then c o m b i n i n g these with phase space and p a t t o n distribution integrations to calcuWork supported by the Stichting FOM. 0 3 7 0 - 2 6 9 3 / 8 9 / $ 03.50 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division )

late physical cross sections [4]. Recently, the calculational techniques have been extended to allow the matrix elements for W, Z + 5 { q , g} to be evaluated [5,6]. A complete analysis o f up to 3 jet p r o d u c t i o n with W or Z is therefore now possible. In this letter we s u m m a r i s e the i m p o r t a n t features o f 0, l, 2 and 3 j e t production in W, Z events at the CERN (~=630 G e V ) and F N A L Tevatron ( x / s = 1.8 TeV) pl~ colliders. Our analysis is not intended to be exhaustive - we concentrate rather on the overall properties o f the cross sections such as relative total rates, subprocess contributions, etc. Detailed phenomenology requires a proper simulation o f the events in a given detector situation ~1 In section 2 a s u m m a r y o f how the various elements o f the calculation are o b t a i n e d and incorporated in the c o m p u t e r program is presented. Section 3 describes some o f the phenomenological results, Finally, we should mention that a similar and independent analysis of multijet production with W and ¢tl The computer programs used to generate the cross sections reported here are available and can be obtained via electronic mail by contacting the authors. 237

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Z - based on the matrix element calculation of ref. [ 5 ] - has recently been reported [ 7 ]. We believe that the importance of an accurate calculation of these processes warrants a complementary analysis. In fact we focus, in general, on different properties of the cross sections and present results at both C E R N and F N A L collider energies ~2.

2. Caleulational details In this section we briefly discuss the method used to calculate the matrix element and the implementation in a computer program. For the calculation of the matrix elements we use the results of ref. [ 6 ]. All the matrix elements for a vector boson V (7", W or Z) and up to five partons are presented there. Through appropriate crossing all the relevant subprocesses can readily be obtained. In addition, the decay of the vector boson into leptons is very easy to implement in this scheme. The calculation makes use o f a recursive method [8], to obtain compact expressions for the matrix elements. The usual method of calculating the helicity amplitudes by choosing special polarization directions for the gluons in order to reduce the number of contributing Feynman diagrams [ 9 ] is not used here. This latter method gives, in the case of the qClggg amplitudes, insufficient simplification to obtain compact expressions. Therefore a more powerful method, based on the recursion relation, is used. This relation allows a rearrangement of the matrix element in such a way that the gluon polarization vector e, only appears in the following combination with its corresponding m o m e n t u m Ku: ). 2 -K.e~,. ,;~ F~,.=K¢,e.

(2.1)

This "abelian" field strength F is gauge invariant. The expression for the amplitude is written entirely in terms of these field strengths and no explicit helicity vectors are present. The resulting expressions are very compact and systematic. If one specifies the helicity of the gluons, the matrix element directly reduces, without much calculational effort, to a short expression involving spinorial inner products, which can be

evaluated numerically. All the expressions are extensively tested for the correct collinear and soft behavtour [ 10 ]. The abelian limit of qdlq' q' g is also compared with known QED amplitudes [ 11 ] by replacing the vector boson by an on-shell photon. The matrix elements with five partons have also been checked with those of refs. [ 5,12 ], the latter concerning the decay ofT* into five partons. The matrix elements thus obtained are incorporated in a computer program which calculates the cross section for a W + or Z and up to 3 jets. The W decays into ev and the Z into e+e - or vg. In both cases we take four quark flavours in the initial state and add to that set the bottom quark for the final state. As discussed in the next section, rapidity, transverse m o m e n t u m and separation cuts are applied to the final state leptons, quarks and gluons. There are a number of relevant process statistics, shown in tables 1-3. In table 1 the number ofsubprocesses for each process is presented. In the W -+ case we have also counted the number of subprocesses when the KM matrix is set to unity. This approximation has been used in the cross section calculations of ref. [7 ]. We have checked that using this approximation gives an O (2%) overestimate of the 0 jet cross section, and that this overestimate becomes smaller for higher numbers of jets as initial state gluons become more important. The time needed to calculate the various matrix elements at the parton level is presented in table 2. There is no difference in time when V is a Z or a W, except in the four quark case. In this case we make explicit use of the fact that the W has only a lefthanded coupling to fermions. We also give the number of times that we have to call a particular matrix element for each accepted event. This represents the number of different kinematic situations which we have to calculate before we are able to compute all Table 1 Number of subprocesses for p + 15-, V + n jets, with 4 flavours incoming and 5 flavours outgoing (W is W + or W - ). #jets

Z

W full KM

W diagonal KM

0

8 24 125 205

8 24 236 412

4 12 94 158

1

~2 A comparison of the W matrix elements used in the present calculation with those of ref. [ 7 ] yields complete agreement. We thank Dieter Zeppenfeld for performing the comparisons.

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2 3

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Table 2 CPU timing for subprocess calls and number of calls per event. Timing in seconds on a VAX 750. Process

One call

qCl qqg q~lgg qClq'0'

0.0084 0.016 0.044 0.098 0.044 0.40 1.51 0.83

qClggg qCtq'q'g

Per Z event

Per Wevent

2 6 7 7

1 3 4 6 4

7 13

10

Table 3 CPU timing per accepted event. Timing in seconds on a VAX 750. ~jets

Z

W

0 l 2 3

0.039 0.12 1.04 22.8

0.031 0.071 0.49 10.2

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p r o d u c t i o n in W and Z events at the C E R N and F N A L Tevatron Pl~ colliders. D e t a i l e d p h e n o m e n o logical tests can only be p e r f o r m e d in the context o f a particular detector, allowing for parton fragmentation, detector response, experimental cuts, etc. In what follows, therefore, we will a t t e m p t to present an overall picture o f multijet production, concentrating on some general properties o f the p r o d u c t i o n processes and o f the final states. In o r d e r to get a feeling for the multijet cross sections we define a set o f " s t a n d a r d " cuts and p a r a m e ters, designed to typify the U A and C D F detectors. We i m p o s e transverse m o m e n t u m and r a p i d i t y cuts on the final state partons and charged leptons, and a cut on "missing energy" (i.e. neutrino transverse m o m e n t u m ) for W events. In addition, the jets and charged leptons are required to have a m i n i m u m separation in phase space. At x ~ = 630 G e V the cuts are p T ( j ) > 10 G e V , A R ( j ~ , j 2 ) > 1.0, p v ( ~ ) > 15 G e V ,

the subprocesses. F o r example, to be able to calculate all 205 subprocesses for the Z + 3 jets cross section, we have to call the qClq' Cl'g a m p l i t u d e 13 times and qClggg a m p l i t u d e 7 times. F o r the W it makes no difference whether we only want the W +, or both the W + and the W - . They are calculated at the same time. Because o f the left-handed coupling o f the W to ferm i o n s the process a d ~ W - follows from a u ~ w + by means o f complex conjugation. F o r this reason fewer matrix elements have to be evaluated for the W processes than for the Z processes. In table 3 we present the times needed to calculate one accepted event. It is evident from tables 2 and 3 that almost all the c o m p u t e r time is used to calculate the p a r t o n matrix elements. In this respect, the number of subprocesses is not important. F u r t h e r m o r e , the time needed to p e r f o r m the phase-space integration and to call the p a r t o n distributions is essentially negligible in the 2 a n d 3 jet case.

[r/(j) I < 2 . 5 ,

Iq(£)l < 2 . 5 ,

p v ( v ) > 15 G e V ,

an(~,j)> 1.0,

(3.1)

and at x / ~ = 1.8 TeV we choose p T ( j ) > 15 G e V ,

Iq(j)l <2.5,

AR(jl,j2) >0.7, p v ( ~ ) > 15 G e V ,

Iq(~)l < 2 . 5 ,

p v ( v ) > 15 G e V , AR(~,j) >0.7.

(3.2)

Here AR is the usual separation in ~/, ~ space. Other relevant p a r a m e t e r values are Mw = 81 GeV, M z = 92 GeV, sin20w=0.23, m t > M w and, unless otherwise stated, we use the latest MRSB parton distributions [ 13] (A~s = 2 0 0 M e V ) with the Q C D scale Q=Mv

(v=w, z). Perhaps the most fundamental quantity to consider is the fraction o f events with a given n u m b e r o f jets:

3. Phenomenology f~(V)= It is neither practical nor meaningful to a t t e m p t here a complete phenomenological analysis o f j e t

a(V+njets) ~ma(V+m jets) "

(3.3)

In fact the UA1 Collaboration have recently pre239

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sented measurements of f, from the sample of W events collected up to 1987 [14]. Fig. 1 shows the UA 1 data and the theoretical expectations for n ~<3. We have chosen a slightly different set of cuts from eq. (3.1) to try to mimic the actual experimental measurements. For example, we have used PT (j) > 5 GeV to try to model the actual jet E~ m of 7 GeV. This should not therefore be considered a precise comparison: we are calculating at the parton level taking no account of fragmentation, smearing, resolution etc. We show fig. 1 simply to illustrate that the theory and the data are in broad agreement and to show the effect of the theoretical uncertainty coming from the choice of parton distributions and scale. The dashed lines are calculated using the MRSE distributions [13] ( A ~ s = 100 MeV) with a larger scale Q = x/~. Notice that, as expected, the difference increases with the number of jets and is about 30% for ~. Although the above comparison is rather crude, a more detailed analysis combining the exact matrix elements for nje, ~<2 with a fragmentation model and T

22 June 1989

detector simulation has shown that there is in fact excellent quantitative agreement between theory and experiment [ 2 ]. Fig. 2a shows the predictions f o r f , ( W ) at the two collider energies using the standard cuts listed above. The enhanced rate of multijet events at the higher energy is due to the fact that the jets can be relatively softer, i.e. the dimensionless ratio p~"/x~ss is smaller at the higher energy. This effect, then, is simply an artefact of the cuts chosen. The corresponding predictions for f , ( Z ) are shown in fig. 2b. Comparing figs. 2a and 2b we see that the differences between W and Z events are very small, and due largely to the different effects of the separation cuts on multijet events with one or two charged leptons in the final state. We stress again that all these theoretical predictions are afflicted with the usual uncertainties from the choice of parton distributions and scale. The size of this uncertainty can be judged from the predictions given in fig. 1. The bulk of W and Z events arise from quark-antiquark annihilation. However, initial state gluons

UAI

ppLwI-e+njets ! --

1 8TeV -

p ~-Zl-e" e-)+ n jets

630GeV

- - I 8TeV

.... 630GeV

fn (W)

1

___

10-I

10-1

I

....

I0-I fn(Z)

fn(W)

.....

V

I

0

J

I

I

2

4

n

Fig. 1. Multiplicity of jets f, as a function of n. Data from the UA 1 Collaboration [ 14 ] on p15~ W ( ~ ~v) + jets are compared with the theoretical predictions. The upper edge of the bands corresponds to the MRSB parton distributions [13] with Q=Mw and the lower edge to the MRSE distributions with Q=x/~. In accordance with ref. [ 14] there are no lepton cuts. The jet minimum transverse momentum, rapidity and separation cuts are 5, 2.5 and 1.0 GeV, respectively.

240

I

I

3

10-2

I0-~

i0 -3

- -- I

[ 16~

t

I

I

I

0

1

2

3

1

0

I

2

3

I(#~

n Fig. 2. Jet multiplicities at ,,/:s= 630 G e V (dashed lines) and 1.8

TeV (solid lines) for (a) W--*ev and (b) Z ~ e + e -, with the full set of lepton and jet cuts defined in eqs. (3.1), (3.2).

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gg EZ23 qg ES2J qq

630GeV

The results are largely as expected, with the gg processes making a small contribution to the (nje, >/2) cross sections. The gluon-induced contributions are significantly more i m p o r t a n t at the higher energy, as smaller x values are sampled. F o r Z production, the results are very similar except that the gluon contributions are slightly reduced. It is interesting to note that "switching off" the four quark processes reduces the 2 and 3 jet cross sections (for W p r o d u c t i o n at x / s = 1.8 TeV) by approximately 15% and 25%, respectively. It follows that the final state jets are p r e d o m i n a n t l y gluonjets. The cross sections calculated above are o f course sensitive to the cuts on the final state particles, especially where these serve to regulate collinear and soft singularities. As an illustration o f this we show in fig. 4 the cross sections for up to 3 jet p r o d u c t i o n at ( a ) x / s = 630 GeV and ( b ) x / s = 1.8 TeV, as a function of the jet m i n i m u m transverse m o m e n t u m , p ~ " . All other cuts are as defined in eqs. (3.1), (3.2). The b r e a k d o w n o f low order p e r t u r b a t i o n theory becomes a p p a r e n t a s p ~ m ~ 0 . Fig. 4 can also be used to test the hypothesis - first suggested in ref. [ 4 ] - that the multijet cross sections decrease a p p r o x i m a t e l y

1B TeV

1.0

~7 \~\

\ \

~, \

'

//

//'1 //1

'\,\

0.5

\\ \\ \\

\\

\\ \ \

\\ \\ \,\ \\

0

1

2

]

1

R jets

\\

i\\ \\ \\

\\ \\ \\

2

3

n jets

Fig. 3. Relative contributions of the qq, qg and gg subprocesses to the pp--*W+jets cross sections at x/s= 630 GeV and 1.8 TeV. contribute at O ( a s ) . To see the relative i m p o r t a n c e o f gluon-induced contributions to multijet production, we show in fig. 3 the relative c o n t r i b u t i o n o f q q , qg and gg induced processes to W p r o d u c t i o n at the two collider energies. ( N o t e that here qq stands for all possible c o m b i n a t i o n s o f quarks and antiquarks. )

10

(a)

t

10 t~Tb~

,

~ - = 630EeV

22 June 1989

--p~-~

W(--ev)+ n jets

. . . . pp ~

Z (-e+e)÷n]efs

~" ~ : 1

--

8TeV

p~W{--ev]+

n jets

. . . . pp ~ Z (~e+e)+ n jefs

I

1

1

I

°

1~~ o-,B

(nb) 102

i~ ~

lo-~f

~o-~

1¢b 5

10

15

mqn

PT (QeV)

20

25

30

-.

1'0

1'5 2'0 p~'~ (GeV)

25

30

Fig. 4. Cross sections for p0~W(~ev) +jets and p0~Z(-~e +e- ) +jets as a function of the minimum jet transverse momentum, p~"", at (a) ~ = 630 GeV and (b) x/s = 1.8 TeV. All other cuts are as specified in eqs. (3.1), (3.2). 241

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Table 4 Average values of event parameters (in GeV) for plb--,W+ n jets at x/~ = 630 GeV with cuts as defined in eq. ( 3.1 ). #jets

(p~)

(M(W +jets) )

(M(jets))

1

21 27 30

118 152 194

44 80

2

3

-

geometrically, i.e. ( an/ao) ~- ( aj/ao) ~. E v i d e n t l y this v e r y c r u d e a p p r o x i m a t i o n works surprisingly well. F o r e x a m p l e , at x / s = 1.8 T e V a n d for p~lin v a l u e s in the 10-15 G e V region, it gives 2 a n d 3 j e t cross sections w i t h i n 20% o f their correct values. Finally, we c o n s i d e r the p r o p e r t i e s o f the m u l t i j e t events. Because any d i s t r i b u t i o n we m i g h t c o n s i d e r (e.g. t r a n s v e r s e m o m e n t u m or r a p i d i t y d i s t r i b u t i o n s o f the final state leptons and j e t s ) w o u l d be strongly affected by f r a g m e n t a t i o n and smearing, we prefer to list only the average v a l u e s o f s o m e i m p o r t a n t e v e n t p a r a m e t e r s . Tables 4 a n d 5 s h o w the results for W p r o d u c t i o n at the two c o l l i d e r energies. ( T h e results for Z p r o d u c t i o n are v e r y similar and are not displayed. ) N o t e that ( a ) the average W t r a n s v e r s e m o m e n t u m increases with increasing jet multiplicity and is larger at the higher collider energy, ( b ) the overall final state mass is significantly larger for m u l t i j e t e v e n t s at the higher energy, a n d ( c ) the overall in-

Table 5 Average values of event parameters (in GeV ) for pO-, W + n jets at x/~= 1.8 TeV with cuts as defined in eq. (3.2). ~jets

(p~)

(M(W +jets) )

1

31 44 55

140 235 310

2

3

242

(M(jets)) -

80 157

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v a r i a n t mass o f the j e t s can be large. T h i s has i m p o r tant c o n s e q u e n c e s w h e n c o n s i d e r i n g b a c k g r o u n d s to n e w physics processes [ 7 ]. F o r e x a m p l e , we see f r o m table 5 that at x / s = 1.8 T e V the average j e t - j e t m a s s in a two j e t e v e n t is close to Mw. T h e j e t p a i r can t h e r e f o r e easily m i m i c a second W - , q O ' . L i k e w i s e a triplet o f j e t s can m i m i c the decay o f a h e a v y quark: Q ~ qqq. T h e multi jet cross sections c o n s i d e r e d in this letter are, therefore, a vitally i m p o r t a n t c o m p o n e n t o f any search for n e w h e a v y states.

References

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