I report results from a next-to-leading order event generator of purely
gluonic jet production. This calculation, is the first step in the construction
of a full next-to-leading order calculation of three jet production at hadron
colliders.Comment: 4 pages, 2 figures, LaTeX, uses sprocl.sty and epsf.st

Kilgore, William B.

English

arXiv

I report results from a next-to-leading order event generator of purely gluonic jet production. This calculation, performed in collaboration with Walter Giele, is the first step in the construction of a full next-to-leading order calculation of three jet production at hadron colliders

Kilgore, W.B.

UNT Digital Library

arXiv:hep-ph/9609367 v1   16 Sep 1996hep-ph/9609367Fermilab-Conf-96/315-TAugust 1996Gluonic Three Jet Production atNext to Leading Order aWilliam B. Kilgore bFermi National Accelerator LaboratoryP.O. Box 500Batavia, IL 60510, USAABSTRACTI report results from a next-to-leading order event generator ofpurely gluonic jet production. This calculation, performed in col-laboration with Walter Giele, is the first step in the constructionof a full next-to-leading order calculation of three jet productionat hadron colliders.aTalk presented at the 1996 Divisional Meeting of the Division of Particles and Fields of theAmerican Physical Society, 10-15 August, Minneapolis, Minnesota.bkilgore@fnal.govTHREE JET PRODUCTION AT NEXT TO LEADING ORDERWILLIAM B. KILGOREFermi National Accelerator LaboratoryP.O. Box 500Batavia, IL 60510, USAI report results from a next-to-leading order event generator of purely gluonic jetproduction. This calculation, performed in collaboration with Walter Giele, is thefirst step in the construction of a full next-to-leading order calculation of three jetproduction at hadron colliders.IntroductionIn this talk I will discuss some results of a next-to-leading order event generatorfor hadronic three jet production. I will begin by briefly outlining the procedurefor performing next-to-leading order jet calculations. I will then present astatus report on the progress of this calculation.Next-to-Leading Order Jet CalculationsThe calculation of three jet production at next-to-leading order combines two-to-three parton scattering to one loop with Born level two-to-four parton scat-tering. Both of these contributions are singular. Only the sum of the twocontributions is finite and physically meaningful. The one loop two-to-threeparton amplitudes contain infrared singularities arising from the presence ofnearly on-shell massless partons in the loops. The Born level two-to-four par-ton amplitudes are also infrared singular, diverging when one of the partons isvery soft or when two partons are highly collinear.The origin of the singularities concerns parton resolvability. If a partonbecomes very soft, or if two partons are highly collinear, it becomes impos-sible to resolve all final state partons from one another. The four partonfinal state looks instead like a three parton final state. (In fact, of course,individual partons can never be resolved, and are only observed as jets ofhadrons.) By imposing a resolvabilty criterion one can define an infrared re-gion of phase space. By using asymptotic approximations of soft or collinearmatrix elements1 within that region, one can integrate out the unresolved par-ton and obtain effective three body matrix elements with poles that exactlycancel those of the one loop matrix elements.This is known as the phase space slicing method.2,3 The infrared region isdefined by the arbitrary resolution parameter smin. If the invariant mass sij1of two partons labelled i and j is larger than smin, the partons are said to beresolved from one another (although they may yet be clustered into the samejet), otherwise partons i and j are said to be unresolved from one another. Ifthere is only one pair of unresolved partons i and j, then those partons aresaid to be collinear. If there is some parton i which in unresolvable from twoor more partons j, k, . . ., then parton i is said to be soft.Using phase space slicing, the singularities are removed from the two-to-four parton scattering process and added to the one-loop two-to-three process,cancelling the singularities. However, since the boundary of the infrared regionwas defined by the arbitrary parameter smin, the slicing procedure induceslogarithmic smin dependence in both sub-processes. The cancellation of thesmin dependence in the sum of the two processes provides an important crosscheck on the calculation.The resolution parameter smin is completely arbitrary and is independentof the jet clustering algorithm. This allows us to use a variety of jet algorithmsand facilitates comparison with experiment. In principle, smin can take anyvalue, but in practice must lie within a finite range. If smin is too large, itforces partons to be clustered that the jet algorithm would otherwise leaveunclustered. If smin is too small, the logarithms of smin become large. Themagnitude of the cancellation between the two sub-processes grows, requir-ing increased computer time to obtain the cancellation to a given statisticalaccuracy.Progress ReportAt this time, we have developed a working event generator for pure gluonscattering. We thus combine the one-loop virtual cross section for gg → gggscattering4 with the Born level cross section for gg → gggg. This developmentis a significant step towards completing an event generator for the full three jetcross section at next to leading order, since all essential components such asphase space generators, jet clustering algorithms, phase space slicing, etc., mustbe working properly. In principle, the completion of the project simply involvesadding the remaining matrix elements to the existing program structure.In Figure 1, I show the smin dependence of the total cross section and ofthe two component subprocesses. Clearly, the calculation is well behaved forany value of smin below approximately 30 GeV2. Above that value, the reso-lution parameter interferes with the jet algorithm and forces excessive partonclustering. As expected, good statistical accuracy is more difficult to obtainat small values of smin.2100 101 102smin (GeV)2-5000500σ (nb)100 101 102smin (GeV)268707274σ (nb)Figure 1: a) smin dependence of the total cross section (center), gg → gggg sub-process(top) and gg → ggg sub-process (bottom). b) Expanded view of the smin dependence of thetotal cross section.AcknowledgmentsFermilab is operated by Universities Research Association, Inc., under contractDE-AC02-76CH03000 with the U.S. Department of Energy.References1. F.A. Berends, W.T. Giele, Nuclear Physics B 306 (1988) 759.2. W.T. Giele, E.W.N Glover, Physical Review D 46 (1992) 1980.3. W.T. Giele, E.W.N Glover, D.A. Kosower, Nuc. Phys. B 403 (1993) 633.4. Z. Bern, L. Dixon, D.A. Kosower, Phys. Rev. Lett. 70 (1993) 2677.3

Gluonic Three Jet Production at Next to Leading Order

Abstract

Similar works

Full text

Available Versions

UNT Digital Library