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The Process Classification Scheme

A wide selection of fundamental $2 \to 1$ and $2 \to 2$ tree processes of the Standard Model (electroweak and strong) has been included in PYTHIA, and slots are provided for some more, not (yet) implemented. In addition, `minimum-bias'-type processes (like elastic scattering), loop graphs, box graphs, $2 \to 3$ tree graphs and many non-Standard Model processes are included. The classification is not always unique. A process that proceeds only via an $s$-channel state is classified as a $2 \to 1$ process (e.g. $\mathrm{q}\overline{\mathrm{q}}\to \gamma^* / \mathrm{Z}^0\to \mathrm{e}^+\mathrm{e}^-$). A generic $2 \to 2$ process may have contributions from $s$-, $t-$ and $u$-channel diagrams. Also, in the program, $2 \to 1$ and $2 \to 2$ graphs may sometimes be convoluted with two $1 \to 2$ splittings to form effective $2 \to 3$ or $2 \to 4$ processes ( $\mathrm{W}^+ \mathrm{W}^- \to \mathrm{h}^0$ is folded with $\mathrm{q}\to \mathrm{q}'' \mathrm{W}^+$ and $\mathrm{q}' \to \mathrm{q}''' \mathrm{W}^-$ to give $\mathrm{q}\mathrm{q}' \to \mathrm{q}'' \mathrm{q}''' \mathrm{h}^0$).

The original classification and numbering scheme is less relevant today than when originally conceived. The calculation of $2 \to 3$ or $2 \to 4$ matrix elements by hand is sufficiently complicated that approximation schemes were employed, such as the effective $\mathrm{W}$-approximation which factored $\mathrm{W}$ bosons into an effective parton density. Today, improvements in computational techniques and increases in computing power make the exact calculation manageable. Given the large top mass and large Higgs boson mass limits, there is also a natural subdivision, such that the $\b $ quark is the heaviest object for which the parton-distribution concept makes sense at current or near-future colliders. Therefore most of the prepared but empty slots are likely to remain empty, or be reclaimed for other processes.

It is possible to select a combination of subprocesses and also to know which subprocess was actually selected in each event. For this purpose, all subprocesses are numbered according to an ISUB code. The list of possible codes is given in Tables [*] through [*], and summarized in Appendix A. Only processes marked with a `+' sign in the first column have been implemented in the program to date. Although ISUB codes were originally designed in a logical fashion, subsequent developments of the program have obscured the structure. For instance, the process numbers for Higgs production are spread out, in part as a consequence of the original classification, in part because further production mechanisms have been added one at a time, in whatever free slots could be found. In the thematic descriptions that follow the main tables, the processes of interest are repeated in a more logical order. If you want to look for a specific process, it will be easier to find it there.

In the following, $\mathrm{f}_i$ represents a fundamental fermion of flavour $i$, i.e. $\d $, $\u $, $\mathrm{s}$, $\c $, $\b $, $\t $, $\b '$, $\t '$, $\mathrm{e}^-$, $\nu_{\mathrm{e}}$, $\mu^-$, $\nu_{\mu}$, $\tau^-$, $\nu_{\tau}$, ${\tau'}^-$ or ${\nu'}_{\tau}$. A corresponding antifermion is denoted by $\overline{\mathrm{f}}_i$. In several cases, some classes of fermions are explicitly excluded, since they do not couple to the $\mathrm{g}$ or $\gamma$ (no $\mathrm{e}^+\mathrm{e}^-\to \mathrm{g}\mathrm{g}$, e.g.). When processes have only been included for quarks, while leptons might also have been possible, the notation $\mathrm{q}_i$ is used. A lepton is denoted by $\ell$; in a few cases neutrinos are also lumped under this heading. In processes where fermion masses are explicitly included in the matrix elements, an $\mathrm{F}$ or $\mathrm{Q}$ is used to denote an arbitrary fermion or quark. Flavours appearing already in the initial state are denoted by indices $i$ and $j$, whereas new flavours in the final state are denoted by $k$ and $l$.

In supersymmetric processes, antiparticles of sfermions are denoted by $^*$, i.e. $\tilde{\mathrm t}^*$.

Charge-conjugate channels are always assumed included as well (where separate), and processes involving a $\mathrm{W}^+$ also imply those involving a $\mathrm{W}^-$. Wherever $\mathrm{Z}^0$ is written, it is understood that $\gamma^*$ and $\gamma^* / \mathrm{Z}^0$ interference should be included as well (with possibilities to switch off either, if so desired). In practice, this means that fermion pairs produced from $\gamma^* / \mathrm{Z}^0$ decay will have invariant masses as small as the program cutoff, and not regulated by the large $\mathrm{Z}$ mass. The cutoff is set by an appropriate $\texttt{CKIN}$ variable. In some cases, $\gamma^* / \mathrm{Z}^0$ interference is not implemented; see further below. Correspondingly, $\mathrm{Z}'^0$ denotes the complete set $\gamma^*/\mathrm{Z}^0/\mathrm{Z}'^0$ (or some subset of it). Thus the notation $\gamma$ is only used for a photon on the mass shell.

In the last column of the tables below, references are given to works from which formulae have been taken. Sometimes these references are to the original works on the subject, sometimes only to the place where the formulae are given in the most convenient or accessible form, or where chance lead us. Apologies to all matrix-element calculators who are not mentioned. However, remember that this is not a review article on physics processes, but only a way for readers to know what is actually found in the program, for better or worse. In several instances, errata have been obtained from the authors. Often the formulae given in the literature have been generalized to include trivial radiative corrections, Breit-Wigner line shapes with $\hat{s}$-dependent widths (see section [*]), etc.

The following sections contain some useful comments on the processes included in the program, grouped by physics interest rather than sequentially by ISUB or MSEL code (see [*] for further information on the MSEL code). The different ISUB and MSEL codes that can be used to simulate the different groups are given. ISUB codes within brackets indicate the kind of processes that indirectly involve the given physics topic, although only as part of a larger whole. Some obvious examples, such as the possibility to produce jets in just about any process, are not spelled out in detail.

The text at times contains information on which special switches or parameters are of particular interest to a given process. All these switches are described in detail in sections [*] [*] and [*], but are alluded to here so as to provide a more complete picture of the possibilities available for the different subprocesses. However, the list of possibilities is certainly not exhausted by the text below.

next up previous contents
Next: QCD Processes Up: Physics Processes Previous: Physics Processes   Contents
Stephen Mrenna 2007-10-30