PYTHIA 6.4 Physics and Manual

a colour triplet quark and a colour antitriplet diquark, each of which are colour-connectedto the hard interaction. The energy sharing between these two remnant objects, and theirrelative transverse momentum, introduces additional degrees of freedom, which are notunderstood from first principles.Naïvely, one would expect an ep event to have only one beam remnant, and an e + e −event none. This is not always correct, e.g. a γγ → qq interaction in an e + e − event wouldleave behind the e + and e − as beam remnants, and a qq → gg interaction in resolvedphotoproduction in an e + e − event would leave behind one e ± and one q or q in eachremnant. Corresponding complications occur for photoproduction in ep events.There is another source of beam remnants. If parton distributions are used to resolvean electron inside an electron, some of the original energy is not used in the hard interaction,but is rather associated with initial-state photon radiation. The initial-stateshower is in principle intended to trace this evolution and reconstruct the original electronbefore any radiation at all took place. However, because of cut-off procedures, somesmall amount may be left unaccounted for. Alternatively, you may have chosen to switchoff initial-state radiation altogether, but still preserved the resolved electron parton distributions.In either case the remaining energy is given to a single photon of vanishingtransverse momentum, which is then considered in the same spirit as ‘true’ beam remnants.So far we have assumed that each event only contains one hard interaction, i.e. thateach incoming particle has only one parton which takes part in hard processes, and thatall other constituents sail through unaffected. This is appropriate in e + e − or ep events,but not necessarily so in hadron–hadron collisions (where a resolved photon counts as ahadron). Here each of the beam particles contains a multitude of partons, and so theprobability for several interactions in one and the same event need not be negligible.In principle these additional interactions could arise because one single parton from onebeam scatters against several different partons from the other beam, or because severalpartons from each beam take part in separate 2 → 2 scatterings. Both are expected, butcombinatorics should favour the latter, which is the mechanism considered in Pythia.The dominant 2 → 2 QCD cross sections are divergent for p ⊥ → 0, and drop rapidlyfor larger p ⊥ . Probably the lowest-order perturbative cross sections will be regularizedat small p ⊥ by colour coherence effects: an exchanged gluon of small p ⊥ has a largetransverse wave function and can therefore not resolve the individual colour charges ofthe two incoming hadrons; it will only couple to an average colour charge that vanishesin the limit p ⊥ → 0. In the program, some effective p ⊥min scale is therefore introduced,below which the perturbative cross section is either assumed completely vanishing or atleast strongly damped. Phenomenologically, p ⊥min comes out to be a number of the orderof 1.5–2.5 GeV, with some energy dependence.In a typical ‘minimum-bias’ event one therefore expects to find one or a few scatteringsat scales around or a bit above p ⊥min , while a high-p ⊥ event also may have additionalscatterings at the p ⊥min scale. The probability to have several high-p ⊥ scatterings in thesame event is small, since the cross section drops so rapidly with p ⊥ .The understanding of multiple interaction is still very primitive. Pythia thereforecontains several different options. These differ e.g. on the issue of the ‘pedestal’ effect: isthere an increased probability or not for additional interactions in an event which is knownto contain a hard scattering, compared with one that contains no hard interactions? Otherdifferences concern the level of detail in the generation of scatterings after the first one,and the model that describes how the scatterings are intercorrelated in flavour, colour,and momentum space.The default underlying-event scenario obtained in a call to PYEVNT corresponds to theso-called ’Tune A’ [Fie02] (although with a slightly different energy dependence), whichreproduces many aspects of Tevatron data correctly. Starting from Pythia version 6.3,a more advanced model for the underlying event is also available. This model is obtained18