General Introduction

In any ($N=1$) supersymmetric version of the SM there exists a partner to each SM state with the same gauge quantum numbers but whose spin differs by one half unit. Additionally, the dual requirements of generating masses for up- and down-type fermions while preserving SUSY and gauge invariance, require that the SM Higgs sector be enlarged to two scalar doublets, with corresponding spin-partners.

After Electroweak symmetry breaking (EWSB), the bosonic Higgs sector contains a quintet of physical states: two CP-even scalars, $h^0$ and $H^0$, one CP-odd pseudoscalar, $A^0$, and a pair of charged scalar Higgs bosons, $H^\pm$ (naturally, this classification is only correct when CP violation is absent in the Higgs sector. Non-trivial phases between certain soft-breaking parameters will induce mixing between the CP eigenstates). The fermionic Higgs (called ``Higgsino'') sector is constituted by the superpartners of these fields, but these are not normally exact mass eigenstates, so we temporarily postpone the discussion of them.

In the gauge sector, the spin-1/2 partners of the $\bf U(1)_Y$ and $\bf SU(2)_L$ gauge bosons (called ``gauginos'') are the Bino, $\widetilde B$, the neutral Wino, $\w3$, and the charged Winos, $\widetilde W_1$ and $\widetilde W_2$, while the partner of the gluon is the gluino, $\tilde \mathrm{g}$. After EWSB, the $\widetilde B$ and $\w3$ mix with the neutral Higgsinos, $\widetilde H_1, \widetilde H_2$, to form four neutral Majorana fermion mass-eigenstates, the neutralinos, $\widetilde \chi^0_{1-4}$. In addition, the charged Higgsinos, $\widetilde H^\pm$, mix with the charged Winos, $\widetilde W_1$ and $\widetilde W_2$, resulting in two charged Dirac fermion mass eigenstates, the charginos, $\widetilde \chi^\pm _{1,2}$. Note that the $\tilde{\gamma}$ and $\tilde{\mathrm{Z}}$, which sometimes occur in the literature, are linear combinations of the $\widetilde B$ and $\w3$, by exact analogy with the mixing giving the $\gamma$ and $\mathrm{Z}^0$, but these are not normally mass eigenstates after EWSB, due to the enlarged mixing caused by the presence of the Higgsinos.

The spin-0 partners of the SM fermions (so-called ``scalar fermions'', or ``sfermions'') are the squarks $\tilde \mathrm{q}$, sleptons $\tilde\ell$, and sneutrinos $\tilde \nu$. Each fermion (except the neutrinos) has two scalar partners, one associated with each of its chirality states. These are named left-handed and right-handed sfermions, respectively. Due to their scalar nature, it is of course impossible for these particles to possess any intrinsic ``handedness'' themselves, but they inherit their couplings to the gauge sector from their SM partners, so that e.g. a $\tilde \d _R$ does not couple to $\bf SU(2)_L$ while a $\tilde \d _L$ does.

Generically, the KF code numbering scheme used in PYTHIA reflects the relationship between particle and sparticle, so that e.g. for sfermions, the left-handed (right-handed) superpartners have codes 1000000 (2000000) plus the code of the corresponding SM fermion. A complete list of the particle partners and their KF codes is given in Table . Note that, at times, antiparticles of scalar particles are denoted by $^*$, i.e. $\tilde{\mathrm t}^*$ rather than the more correct but cumbersome $\overline{\tilde{\mathrm t}}$ or $\tilde{\overline{\mathrm{t}}}$.

The MSSM Lagrangian contains interactions between particles and sparticles, with couplings fixed by SUSY. There are also a number of soft SUSY-breaking mass parameters. ``Soft'' here means that they break the mass degeneracy between SM particles and their SUSY partners without reintroducing quadratic divergences in the theory or destroying its gauge invariance. In the MSSM, the soft SUSY-breaking parameters are extra mass terms for gauginos and sfermions and trilinear scalar couplings. Further soft terms may arise, for instance in models with broken $R$-parity, but we here restrict our attention to the minimal case.

The exact number of independent parameters depends on the detailed mechanism of SUSY breaking. The general MSSM model in PYTHIA assumes only a few relations between these parameters which seem theoretically difficult to avoid. Thus, the first two generations of sfermions with otherwise similar quantum numbers, e.g. $\tilde \d _L$ and $\tilde \mathrm{s}_L$, have the same masses. Despite such simplifications, there are a fairly large number of parameters that appear in the SUSY Lagrangian and determine the physical masses and interactions with Standard Model particles, though far less than the $>100$ which are allowed in all generality. The Lagrangian (and, hence, Feynman rules) follows the conventions set down by Kane and Haber in their Physics Report article [Hab85] and the papers of Gunion and Haber [Gun86a]. Once the parameters of the softly-broken SUSY Lagrangian are specified, the interactions are fixed, and the sparticle masses can be calculated.