Compositeness and anomalous couplings

ISUB =

11	$\mathrm{f}_i \mathrm{f}_j \to \mathrm{f}_i \mathrm{f}_j$ (QCD)
12	$\mathrm{f}_i \overline{\mathrm{f}}_i \to \mathrm{f}_k \overline{\mathrm{f}}_k$
20	$\mathrm{f}_i \overline{\mathrm{f}}_j \to \gamma \mathrm{W}^+$
165	$\mathrm{f}_i \overline{\mathrm{f}}_i \to \mathrm{f}_k \overline{\mathrm{f}}_k$ (via $\gamma^* / \mathrm{Z}^0$)
166	$\mathrm{f}_i \overline{\mathrm{f}}_j \to \mathrm{f}_k \overline{\mathrm{f}}_l$ (via $\mathrm{W}^{\pm}$)

Some processes have been set up to allow anomalous coupling to be introduced, in addition to the Standard Model ones. These can be switched on by MSTP(5)$\geq 1$; the default MSTP(5)=0 corresponds to the Standard Model behaviour.

In processes 11 and 12, the quark substructure is included in the left-left isoscalar model [Eic84,Chi90] for MSTP(5)=1, with compositeness scale $\Lambda$ given in PARU(155) (default 1000 GeV) and sign $\eta$ of interference term in PARU(156) (default $+1$; only other alternative $-1$). The above model assumes that only $\u$ and $\d$ quarks are composite (at least at the scale studied); with MSTP(5)=2 compositeness terms are included in the interactions between all quarks.

The processes 165 and 166 are basically equivalent to 1 and 2, i.e. $\gamma^* / \mathrm{Z}^0$ and $\mathrm{W}^{\pm}$ exchange, respectively, but a bit less fancy (no mass-dependent width etc.). The reason for this duplication is that the resonance treatment formalism of processes 1 and 2 could not easily be extended to include other than $s$-channel graphs. In processes 165 and 166, only one final-state flavour is generated at the time; this flavour should be set in KFPR(165,1) and KFPR(166,1), respectively. For process 166 one gives the down-type flavour, and the program will associate the up-type flavour of the same generation. Defaults are 11 in both cases, i.e. $\mathrm{e}^+\mathrm{e}^-$ and $\mathrm{e}^+ \nu_{\mathrm{e}}$ ( $\mathrm{e}^- \overline{\nu}_{\mathrm{e}}$) final states. While MSTP(5)=0 gives the Standard Model results, MSTP(5)=1 contains the left-left isoscalar model (which does not affect process 166), and MSTP(5)=3 the helicity-non-conserving model (which affects both) [Eic84,Lan91]. Both models above assume that only $\u$ and $\d$ quarks are composite; with MSTP(5)= 2 or 4, respectively, contact terms are included for all quarks in the initial state. Parameters are PARU(155) and PARU(156), as above.

Note that processes 165 and 166 are book-kept as $2 \to 2$ processes, while 1 and 2 are $2 \to 1$ ones. This means that the default $\mathrm{Q}^2$ scale in parton distributions is $p_{\perp}^2$ for the former and $\hat{s}$ for the latter. To make contact between the two, it is recommended to set MSTP(32)=4, so as to use $\hat{s}$ as scale also for processes 165 and 166.

In process 20, for $\mathrm{W}\gamma$ pair production, it is possible to set an anomalous magnetic moment for the $\mathrm{W}$ in PARU(153) ( $= \eta = \kappa-1$; where $\kappa = 1$ is the Standard Model value). The production process is affected according to the formulae of [Sam91], while $\mathrm{W}$ decay currently remains unaffected. It is necessary to set MSTP(5)=1 to enable this extension.