Volume 256, number 1 PHYSICS LETTERS B 28 February 1991

Five jet p r o d u c t i o n in e + e - ann ih i la t ion above the W + W - thresho ld

N . B r o w n Rutherford Appleton Laboratory, Chilton, Didcot, Oxon 0Xl l OQX, UK

Received 7 November 1990

Above the W+W- threshold, gluon bremsstrahlung from the decay of W bosons into quark pairs gives rise to five jet configu- rations. At lowest QCD order, this dominates over the point-like five jet production, and allows the hadronic decays of the W to be tested with QCD. Some results for integrated cross-sections and jet distributions are given.

The product ion o f jets is a well known feature of e+e - annih i la t ion at high energies, and is well de- scr ibed by the predic t ions of QCD. In part icular , the radia t ion o f gluons leads to final states with a mult i - je t structure. Below the W + W - pair product ion threshold these je t events arise through the annihila- t ion o f the electron and posi t ron into a qua rk -an t i - quark pair, via a vir tual photon or Z boson. This pro- cess, and those related to it by gluon radiat ion we shall refer to as "point - l ike" . There is some small back- ground from z+x- events and from two photon phys- ics, but these are largely removed by demanding that there be no missing energy. The x+x - events are also ident i f ied by their relat ively low mult ipl ici ty. Thus je t physics in e+e - annih i la t ion is a relat ively clean env i ronment in which to test Q C D [ 1 ].

All this changes as we go to energies above the W + W - threshold, as is scheduled for LEP200. The W boson has a relatively large branching fraction into q¢l pairs [B(W--,q~I) ~ ] ], and so W + W - events are a copious source o f jets. When both the W bosons de- cay into qcl, we have the possibi l i ty of four je t config- urations. At a centre o f mass energy x / ~ = 2 0 0 GeV, these will have a product ion cross-section before acceptance cuts o f approx imate ly

a ( W + W - ) ( ~ ) 2 ~ 8 . 6 p b . (1)

The point- l ike four je t process will depend strongly on the cri teria used to define the jets. A commonly used method is based on an invar iant mass cut y. At

the pat ton level we form the invariant masses squared s;j = (p; +pj)2 of all pairs of final state partons, where Pi is the momen tum o fpa r ton i. The lowest order four je t configurations arise at O ( a 2 ) , where as is the strong coupling constant, and involve four patrons in the final state. We then demand that sij>ys for all par ton pairs to define a four je t event.

At y = 0 . 0 2 , for example, the point- l ike four je t cross-section will be roughly 1 pb. It is clear then, that W + W - events will be the dominan t source of multi- je t events. The four je t final state has been well stud- ied theoretically, see for example ref. [ 2 ].

It is also possible, however, for the q~l pair from the decay o f W bosons to radiate a gluon, leading to a possible five je t configuration. Just as above, we will expect this process to domina te over the point- l ike five je t rate. This allows the possibi l i ty of investigat- ing the QCD correct ions to the hadronic W decays. Although it would be very surprising i f these had- ronic decays were not in accord with QCD, it will be o f interest to test this, i f possible.

To investigate this, we have calculated the com- plete matr ix element for e+e - ~ qqq~lg via the W + W - in termedia te state. The details o f the calculat ion are somewhat lengthy and are presented elsewhere [3]. There are twelve contr ibut ing Feynman diagrams. Three o f these are shown in fig. 1. The remaining dia- grams are obta ined by at taching the gluon to differ- ent quarks.

Note that there is vir tual ly no interference between

0370-2693/91/$ 03.50 © 1991 - Elsevier Science Publishers B.V. ( North-Holland ) 87

Volume 256, number 1 PHYSICS LETTERS B 28 February 1991

e_/ ' q

e + ~ g

+ e

e

q

• g

Fig. 1. Three of the Feynman diagrams contributing to the pro- cess e+e-~lqdlqg via a W+W - intermediate state. The other diagrams are obtained by attaching the gluon to different quark legs.

the W+W - and point-like processes. This is mainly because of the different kinematics and quark fla- vour content of the two processes. The point cross- section is also dominated by the q~lggg final state, the qclqclg state being somewhat suppressed.

The matrix element was calculated using the spi- nor technique of Kleiss and Stirling [ 4 ]. The calcu- lation was checked by showing that in the narrow width limit the cross-section factorizes as

aww(5 jet) F W ~ 0

a (WW) 2B(W~q¢I) B(W--*q(tg). (2)

To give an idea of the number of expected events, we integrated the matrix element with the following acceptance cuts on the final state partons to define the jets:

I cos0 i l<0 .9 , E i > 1 0 G e V , cos00<0 .9 ,

where 0i is the polar angle of parton i, E~ is its energy in the centre of mass system, and O~j is the opening

angle between each parton. With this set of cuts we obtain a cross-section of

aww(5 jet) = 1.83 pb . (3)

If instead we use cos 0 o < 0.707 the cross-section falls to

aww(5 jet) =0.65 pb . (4)

These integrations were performed using a Monte Carlo generation of events, with an error on the in- tegrals of less than 1%. All the results are given at a centre of mass energy x/~= 200 GeV, using the fol- lowing values of standard model parameters: Mz = 91.1 GeV, Mw=80.6 GeV, Fz=2.5 GeV, Fw=2.05 GeV, sin20w = 0.23, a = ~28, as = 0.11. We have treated the five lighter quarks and the electrons as massless,

O

i t t l

10

0.1

0.01

0-001

ww .......... OCD

I o.oi 0.02 Y

I i I 0.03 0.04 0-05

Fig. 2. Five jet rate from e+e - ~qqf]qg via the W+W - interme- diate state (full line ) and the point like process (dashed line ), as a function of an invariant mass cut y. The five jet rate is defined to be the five jet cross section divided by the point-like Born cross section pp.

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Volume 256, number 1 PHYSICS LETTERS B 28 February 1991

10 0

10-'

bl-- ~ 1 ~ lO- 2

- l e

10-3

- - W W

. . . . . . . . . . . . QCD

r -J L_~ r J L_,

i r_.l

r-J

r i l

I i

o'-~ 0.6 o'.7 T

I

0.4 1.0

I i I

0 - 8 0"9

Fig. 3. Thrust distribution from five jet events satisfying an in- variant mass cut so> ys. The W + W - contribution is shown with the full line, the point-l ike process with the dashed line.

10-1

lO'Z

b < ~ 1 ~ 10-3

10 -4

L

r- i..~ r " j L~ I

"J I L 1

_J L~

L] i L~

L G i L- I

= I L~

I L]

- - W W

. . . . . . . . . . QCD

I p ~7

i

i i i i i I

0'5 1 0 - ~ I I

0"0 0!1 0-2 0"3 01"4 0-6 0!7 A

Fig. 4. Acoplanarity distribution from five jet events satisfying an invariant mass cut so> ys. The W + W - contribution is shown with the full line, the point-like process with the dashed line.

and have assumed that the top quark is too heavy for the W to decay into.

For the "canonical" integrated luminosity of 500 pb-1, these cross-sections would correspond to 915 and 325 events respectively. This is obviously a large enough event sample to test the QCD corrections to hadronic W decays.

In fig. 2 we show the five jet rate for both the W+W - and point-like process as a function of y, where we have demanded that all parton-parton in- variant masses are larger than ys. Here we have de-

f i n e d the five jet rate to be the five jet cross-section divided by the Born point-like cross-section ao (e +e- -~qq) which at x /~=200 GeV, with the values of standard model parameters above is ao= 18.194 pb. Multiplying by this number allows five jet cross-sec- tions to be determined. The point-like cross-sections

are taken from Falck et al. [ 5 ] where we have taken into account the different value of as used there. In figs. 3 and 4 we show the thrust (T) and acoplanarity (A) distributions for those events of the five jet sam- ple satisfying the constraint s o > ys, for y-- 0.02, again comparing with the point-like process. It is clear that at energies above the W+W - threshold, that the five jet final state will allow us to test the QCD correc- tions to the hadronic decay of the W with good precision.

Finally we note that by demanding that the five jet sample approximately reconstructs two W bosons in invariant mass, we would reduce the point-like pro- cess much further. Here we have shown that even without this improvement a sufficiently large and relatively clean sample of WW events is obtained. Of course, for a full analysis, electroweak radiative cor-

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Volume 256, number 1 PHYSICS LETTERS B 28 February 1991

rections will have to be taken into account, as well as a full Monte Carlo simulation of the hadronization and the detectors. Once again, it is apparent that LEP200 will indeed be a unique environment in which to study the decays and properties of the W boson in detail.

References

[ 1 ] G. Altarelli, R. Kleiss and C. Verzegnassi, eds., Z. Physics at LEP1, Vol. 1, CERN report 89-08 (1989).

[2] A. B6hm, ed., ECFA Workshop on LEP200, Vol. 1, CERN 87-08, ECFA 87/108 ( 1987 ).

[3] N. Brown, Rutherford report RAL-90-080 (1990). [4] R. Kleiss and W.J. Stirling, Nucl. Phys. B 262 (1985) 235. [5] N.K. Falck, D. Graudenz and G. Kramer, Phys. Lett. B 220

(1989) 299; Nucl. Phys. B 328 (1989) 317.

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