Event Generators Conveners Leif Lonnblad Mike Seymour Working group Edouard Boudinov Jon Butterworth Ralph Engel Alex Finch Suen Hou Maria KienzleFo cacci Mark Lehto Ed McKigney David Miller Denis PerretGallix Johannes Ranft Gerhard Schuler Torb jorn Sjostrand Ro d Walker Alison Wright Contents Intro duction General Features Comparisons Description of programs Other generators Conclusions Intro duction At LEP twophoton collisions make up by far the largest class of events These are pro cesses in which the incoming electrons each radiate a photon which collide to pro duce a hadronic or leptonic nal state A photon can obviously interact electromagnetically with any charged ob ject However since it has the same quantum numb ers as a vector meson it can uctuate into one and can therefore also b e considered as an incoming hadron interacting strongly through its partonic constituents The interplay b etween these two ways of interacting is unique to the photon and provides much of the interest in physics The twophoton invariant mass sp ectrum is p eaked at low mass so the bulk of events only pro duce a few particles and resonances and exclusive nal states can b e studied The total crosssection is so large however that there are enough events to study deep inelastic e scattering and highp jets and heavy quark pro duction in collisions ? LEP is the highest energy and luminosity e and collider available and many of the same studies as at electronhadron and hadronhadron colliders can b e made here However one essential dierence is that since the b eam remnants the electrons and p ositrons typically leave the detectors undetected the energies of the incoming photons are not known and must b e reconstructed from the prop erties of the nal state In events in which most of the nalstate particles are visible in the detector this is easily done However at high energies the nalstate distribution b ecomes increasingly forwardp eaked and much of the energy go es into the very forward parts of the detector or is even missed in the b eam pip e It is therefore essential that as much of the nal state as p ossible is measured in particular to detect hadrons in the forward detectors that have hitherto only b een used for electron tagging It is also essential that we are able to understand the details of the multiparticle nal states in these interactions which puts very high demands on the event generators used in the analysis During the course of this workshop some of the standard general purp ose event generator programs on the market have b een develop ed to also handle e and collisions This means that we can use our exp erience from ep and pp collisions to give a more complete description of the hadronic nal state of twophoton collisions These mo dels can now b e tested at LEP and should give reliable extrap olations to LEP energy In section of this rep ort we will describ e briey the mo dels of the generators we have studied during the workshop Then in section some comparisons b etween the programs are presented for dierent classes of events In section the main programs are presented in some detail followed by section where some other generators are presented more briey Finally in section we present our conclusions Related work is presented in the rep orts of the Physics and QCD Event Generator working groups General Features The event generators used for physics can b e divided into two main groups One deals with low multiplicity nal states like resonances exclusive channels and leptonic channels and the other with high mass multiparticle nal states When there are few particles in the nal state the fully dierential crosssection for a given pro cess can usually b e derived directly from a mo del of that pro cess Event generators can then b e viewed as a particularly convenient numerical implementation of that crosssection in which arbitrarily complicated phasespace cuts and detector simulation can b e incorp orated In this group are fourfermion generators which incorp orate the full set of QED matrix elements for e e e e f f and more general programs that use a luminosity function to separate the pro cess e e e e X into two stages e e e e and X The other group of generators describ e multiparticle pro duction for which crosssections cannot b e directly calculated in quantum mechanics They use semiclassical probabilistic mo dels to separate the pro cess into several phases First photons are radiated from the incoming electrons to give b eams of quasireal photons Then a hard subpro cess is generated using partonic matrix elements folded with the parton densities of the photon The emission of additional partons from the incoming partons is generated by evolving them backwards in an initialstate parton shower and from outgoing partons by generating a nalstate parton shower Finally the partons are converted to hadrons which are then allowed to decay Photon generation A twophoton reaction can b e factorized into photon uxes of radiation from incoming e and the nal state of twophoton collisions The decomp osed dierential crosssection for 0 0 0 0 Xq q e p q q e p e p e p e p e p is q q q q d j j cos TT TT q p p m q m 0 0 d p d p j cos j TL LL LT TL 0 0 E E where the s and s are linear combinations of the crosssections for X of transverseT ab and longitudina lL photons the ux factor has photon helicities lab elled by Some i dedicated generators such as Twogam use the full form of Eq while most mo dels simplify further by taking the q approximation At q the photons are quasireal and transversely p olarized and after integration over the angle b etween lepton scattering planes the only remaining term is Expressed in terms of a luminosity function we have TT d L e e e e X TT d d d d 0 where w E E is the photon energy in the lab frame The luminosity function can b e i b i decomp osed as the pro duct of a factor for each of the photons d L d L d L d d d d d d d d where apart from a trivial kinematic factor d L is the Equivalent Photon Approximation EPA ux factor d L p f x P t d d with x the lightcone momentum fraction and P the photon virtuality P jq j As discussed in Ref there are two imp ortant corrections to the usual EPA formula The rst is to include P the subleading term of relative order m e x x f x P m e e xP P which can give corrections of order for untagged and antitagged crosssections At present of the QCD event generators only Phojet includes this correction The second imp ortant correction is to include the correct pro cessdep endent dynamic upp er limit on P However this is only imp ortant for untagged crosssections and when an antitag condition is imp osed as it is throughout this rep ort this corrections b ecome small Photon distribution functions In resolvedphoton pro cesses we need parametrizations of the distribution functions for partons inside the photon These ob ey an inhomogeneous form of the usual evolution equations As discussed in more detail in the rep ort of the Physics working group their solution can b e written as the sum of a hadronic or VMD part which evolves according the usual homogeneous equation and a p ointlike or anomalous part There are a numb er of parametrizations available for the parton distribution functions of on shell photons Most of them are contained in a single package PDFLIB to which most of the event generators are interfaced At present none use the recent mo dels of the structure of virtual photons although HERWIG do es implement a simple P suppression mo del In the following when comparing dierent generators we use the fairly similar SaS D or GRV LO sets direct qq single resolved q qg g qq 0 0 double resolved qq qq gg qq DIS eq eq Table The standard hard subprocesses used by event generators for dierent event classes Hard subpro cesses Having dened the structure functions and parton densities we can now use the same ma chinery as for pp or ep collisions to generate hard subpro cesses with the exception that we here have additional pro cesses where the photon couples directly in the hard interaction In collisions we therefore talk ab out three kinds of events direct singleresolved and double resolved dep ending on whether the photons couple directly or not In Table the standard hard subpro cesses are listed for dierent event classes Some programs like Pythia make a further distinction b etween the anomalous and VMDlike part of the resolved photon and therefore have six dierent event classes In deep inelastic e scattering the exchanged photon is usually more virtual than the struck quark so the EPA is no longer a go o d approximation in other words the pro cessdep endent dynamic upp er limit on P mentioned in Section is exceeded One therefore needs in principle to use the full pro cesses eq eqg eg eqq and e eqq However when the quark line is much less virtual than the photon it can b e approximated by the DGLAP probability distribution to nd the quark inside a higherx quark q qg gluon g qq or photon qq and hence can b e absorb ed into the evolution of the photon distribution functions Thus we are again left with a pro cess eq eq for which one uses the lowestorder matrix element Other pro cesses that are usually treated separately are the ones involving heavy quarks where the