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$\mathrm{e}^+\mathrm{e}^-$ collisions

The main annihilation process is number 1, $\mathrm{e}^+\mathrm{e}^-\to \mathrm{Z}^0$, where in fact the full $\gamma^* / \mathrm{Z}^0$ interference structure is included. This process can be used, with some confidence, for c.m. energies from about 4 GeV upwards, i.e. at DORIS/CESR/PEP-II/KEKB, PETRA/PEP, TRISTAN, LEP, and any future linear colliders. (To get below 10 GeV, you have to change PARP(2), however.) This is the default process obtained when MSEL = 1, i.e. when you do not change anything yourself.

Process 141 contains a $\mathrm{Z}'^0$, including full interference with the standard $\gamma^* / \mathrm{Z}^0$. With the value MSTP(44) = 4 in fact one is back at the standard $\gamma^* / \mathrm{Z}^0$ structure, i.e. the $\mathrm{Z}'^0$ piece has been switched off. Even so, this process may be useful, since it can simulate e.g. $\mathrm{e}^+\mathrm{e}^-\to \mathrm{h}^0 \mathrm{A}^0$. Since the $\mathrm{h}^0$ may in its turn decay to $\mathrm{Z}^0 \mathrm{Z}^0$, a decay channel of the ordinary $\mathrm{Z}^0$ to $\mathrm{h}^0 \mathrm{A}^0$, although physically correct, would be technically confusing. In particular, it would be messy to set the original $\mathrm{Z}^0$ to decay one way and the subsequent ones another. So, in this sense, the $\mathrm{Z}'^0$ could be used as a copy of the ordinary $\mathrm{Z}^0$, but with a distinguishable label.

The process $\mathrm{e}^+\mathrm{e}^-\to \Upsilon$ does not exist as a separate process in PYTHIA, but can be simulated by using PYONIA, see section [*].

At LEP 2 and even higher energy machines, the simple $s$-channel process 1 loses out to other processes, such as $\mathrm{e}^+\mathrm{e}^-\to \mathrm{Z}^0 \mathrm{Z}^0$ and $\mathrm{e}^+ \mathrm{e}^- \to \mathrm{W}^+ \mathrm{W}^-$, i.e. processes 22 and 25. The former process in fact includes the structure $\mathrm{e}^+\mathrm{e}^-\to (\gamma^* / \mathrm{Z}^0)(\gamma^* / \mathrm{Z}^0)$, which means that the cross section is singular if either of the two $\gamma^* / \mathrm{Z}^0$ masses is allowed to vanish. A mass cut therefore needs to be introduced, and is actually also used in other processes, such as $\mathrm{e}^+ \mathrm{e}^- \to \mathrm{W}^+ \mathrm{W}^-$.

For practical applications, both with respect to cross sections and to event shapes, it is imperative to include initial-state radiation effects. Therefore MSTP(11) = 1 is the default, wherein exponentiated electron-inside-electron distributions are used to give the momentum of the actually interacting electron. By radiative corrections to process 1, such processes as $\mathrm{e}^+\mathrm{e}^-\to \gamma \mathrm{Z}^0$ are therefore automatically generated. If process 19 were to be used at the same time, this would mean that radiation were to be double-counted. In the alternative MSTP(11) = 0, electrons are assumed to deposit their full energy in the hard process, i.e. initial-state QED radiation is not included. This option is very useful, since it often corresponds to the `ideal' events that one wants to correct back to.

Resolved electrons also means that one may have interactions between photons. This opens up the whole field of $\gamma\gamma$ processes, which is described in section [*]. In particular, with 'gamma/e+','gamma/e-' as beam and target particles in a PYINIT call, a flux of photons of different virtualities is convoluted with a description of direct and resolved photon interaction processes, including both low-$p_{\perp}$ and high-$p_{\perp}$ processes. This machinery is directed to the description of the QCD processes, and does e.g. not address the production of gauge bosons or other such particles by the interactions of resolved photons. For the latter kind of applications, a simpler description of partons inside photons inside electrons may be obtained with the MSTP(12) = 1 options and $\mathrm{e}^{\pm}$ as beam and target particles.

The thrust of the PYTHIA programs is towards processes that involve hadron production, one way or another. Because of generalizations from other areas, also a few completely non-hadronic processes are available. These include Bhabha scattering, $\mathrm{e}^+\mathrm{e}^-\to \mathrm{e}^+\mathrm{e}^-$ in process 10, and photon pair production, $\mathrm{e}^+\mathrm{e}^-\to \gamma \gamma$ in process 18. However, note that the precision that could be expected in a PYTHIA simulation of those processes is certainly far less than that of dedicated programs. For one thing, electroweak loop effects are not included. For another, nowhere is the electron mass taken into account, which means that explicit cut-offs at some minimum $p_{\perp}$ are always necessary.


next up previous contents
Next: Lepton-hadron collisions Up: Main Processes by Machine Previous: Main Processes by Machine   Contents
Stephen Mrenna 2007-10-30