PYTHIA 6.4 Physics and Manual

1 IntroductionMultiparticle production is the most characteristic feature of current high-energy physics.Today, observed particle multiplicities are typically between ten and a hundred, and withfuture machines this range will be extended upward. The bulk of the multiplicity is foundin jets, i.e. in collimated bunches of hadrons (or decay products of hadrons) producedby the hadronization of partons, i.e. quarks and gluons. (For some applications it willbe convenient to extend the parton concept also to some non-coloured but showeringparticles, such as electrons and photons.)1.1 The Complexity of High-Energy ProcessesTo first approximation, all processes have a simple structure at the level of interactionsbetween the fundamental objects of nature, i.e. quarks, leptons and gauge bosons. Forinstance, a lot can be understood about the structure of hadronic events at LEP just fromthe ‘skeleton’ process e + e − → Z 0 → qq. Corrections to this picture can be subdivided,arbitrarily but conveniently, into three main classes.Firstly, there are bremsstrahlung-type modifications, i.e. the emission of additionalfinal-state particles by branchings such as e → eγ or q → qg. Because of the largenessof the strong coupling constant α s , and because of the presence of the triple gluonvertex, QCD emission off quarks and gluons is especially prolific. We therefore speakabout ‘parton showers’, wherein a single initial parton may give rise to a whole bunch ofpartons in the final state. Also photon emission may give sizable effects in e + e − and epprocesses. The bulk of the bremsstrahlung corrections are universal, i.e. do not dependon the details of the process studied, but only on one or a few key numbers, such as themomentum transfer scale of the process. Such universal corrections may be included toarbitrarily high orders, using a probabilistic language. Alternatively, exact calculationsof bremsstrahlung corrections may be carried out order by order in perturbation theory,but rapidly the calculations then become prohibitively complicated and the answerscorrespondingly lengthy.Secondly, we have ‘true’ higher-order corrections, which involve a combination of loopgraphs and the soft parts of the bremsstrahlung graphs above, a combination needed tocancel some divergences. In a complete description it is therefore not possible to considerbremsstrahlung separately, as assumed here. The necessary perturbative calculations areusually very difficult; only rarely have results been presented that include more than onenon-‘trivial’ order, i.e. more than one loop. As above, answers are usually very lengthy,but some results are sufficiently simple to be generally known and used, such as therunning of α s , or the correction factor 1 + α s /π + · · · in the partial widths of Z 0 → qqdecay channels. For high-precision studies it is imperative to take into account the resultsof loop calculations, but usually effects are minor for the qualitative aspects of high-energyprocesses.Thirdly, quarks and gluons are confined. In the two points above, we have used aperturbative language to describe the short-distance interactions of quarks, leptons andgauge bosons. For leptons and colourless bosons this language is sufficient. However, forquarks and gluons it must be complemented with the structure of incoming hadrons, anda picture for the hadronization process, wherein the coloured partons are transformedinto jets of colourless hadrons, photons and leptons. The hadronization can be furthersubdivided into fragmentation and decays, where the former describes the way the creationof new quark-antiquark pairs can break up a high-mass system into lower-mass ones,ultimately hadrons. (The word ‘fragmentation’ is also sometimes used in a broader sense,but we will here use it with this specific meaning.) This process is still not yet understoodfrom first principles, but has to be based on models. In one sense, hadronization effectsare overwhelmingly large, since this is where the bulk of the multiplicity comes from. In1