Final-State Showers

Final-state showers are time-like, i.e. all virtualities $m^2 = E^2 - \mathbf{p}^2 \geq 0$. The maximum allowed virtuality scale $Q^2_{\mathrm{max}}$ is set by the hard-scattering process, and thereafter the virtuality is decreased in each subsequent branching, down to the cut-off scale $Q_0^2$. This cut-off scale is used to regulate both soft and collinear divergences in the emission probabilities.

Many different approaches can be chosen for the parton-shower algorithm, e.g. in terms of evolution variables, kinematics reconstruction and matrix-element corrections. The traditional approach in PYTHIA is the mass-ordered PYSHOW algorithm. As an alternative, a $p_{\perp}$-ordered PYPTFS algorithm has recently been introduced. It is not yet fully tried out, and is described only briefly at the end of this section.

The main points of the PYSHOW showering algorithm are as follows.

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It is a leading-log algorithm, of the improved, coherent kind, i.e. with angular ordering.

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It can be used for an arbitrary initial pair of partons or, in fact, for any number between one and eighty given entities (including hadrons and gauge bosons) although only quarks, gluons, leptons, squarks and gluinos can initiate a shower.

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The pair of showering partons may be given in any frame, but the evolution is carried out in the c.m. frame of the showering partons.

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Energy and momentum are conserved exactly at each step of the showering process.

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If the initial pair comes from the decay of a known resonance, an additional rejection technique is used in the gluon emission off a parton of the pair, so as to reproduce the lowest-order differential 3-jet cross section.

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In subsequent branchings, angular ordering (coherence effects) is imposed.

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Gluon helicity effects, i.e. correlations between the production plane and the decay plane of a gluon, can be included.

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The first-order $\alpha_{\mathrm{s}}$ expression is used, with the $Q^2$ scale given by (an approximation to) the squared transverse momentum of a branching. The default $\Lambda_{\mathrm{QCD}}$, which should not be regarded as a proper $\Lambda_{\overline{\mathrm{MS}}}$, is 0.29 GeV.

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The parton shower is by default cut off at a mass scale of 1 GeV.

Let us now proceed with a more detailed description.