Supersymmetry

MSEL = 39-45
ISUB = 201-296 (see tables at the beginning of the chapter)

PYTHIA simulates the Minimal Supersymmetric extension of the Standard Model (MSSM), based on an effective Lagrangian of softly-broken SUSY with parameters defined at the weak scale, which is typically between $m_{\mathrm{Z}}$ and 1 TeV. In the MSSM, the particle spectrum of the Standard Model is expanded to include spin-partners of the fermions and gauge bosons. Moreover, to generate masses for up- and down-type fermions while preserving SUSY and gauge invariance, the Higgs sector must be enlarged to two doublets and their spin-partners. After Electroweak symmetry breaking, there is a quintet of physical Higgs boson states: two CP-even scalars $h$ (code 25) and $H$ (code 35), one CP-odd pseudoscalar $A$ (code 36), and a pair of charged $H^\pm$ Higgs bosons (code 37). All the Higgs bosons and other SM particles have superpartners with the same quantum numbers under the SM gauge groups $SU(3)_C \times SU(2)_L \times U(1)_Y$, but with different spin. The spin-1/2 partners of the $U(1)_Y$ and $SU(2)_L$ gauge bosons (gauginos) are the Bino $\widetilde B$, the unmixed neutral Wino $\w3$, and the unmixed charged Winos $\widetilde W_1$ and $\widetilde W_2$, while the partner of the gluon is the gluino $\tilde \mathrm{g}$ (code 1000021). (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 are normally not mass eigenstates.) The spin-1/2 partners of the Higgs bosons (Higgsinos) are $\widetilde H_1, \widetilde H_2$ and $\widetilde H^\pm$. After Electroweak symmetry breaking, the Higgsinos and $SU(2)_L \times U(1)_Y$ gauginos mix to give physical mass eigenstates consisting of two Dirac fermions of electric charge one, the charginos $\widetilde \chi^\pm _{1,2}$ (codes 1000024 and 1000037), and four neutral Majorana fermions, the neutralinos $\widetilde \chi^0_{1-4}$ (codes 1000022, 1000023, 1000025, and 1000035). The spin-0 partners of the fermions (sfermions) are squarks $\tilde \mathrm{q}$, sleptons $\tilde\ell$ and sneutrinos $\tilde \nu$. Each charged lepton or quark has two scalar partners, one associated with each chirality. These are named left-handed squarks such as $\tilde \u _L$ (code 1000002) and $\tilde \d _L$ (code 1000001) and left-handed sleptons such as $\tilde \mathrm{e}_L$ (code 1000011) and sneutrinos such as ${\tilde \nu }_e$ (code 1000012), which belong to $SU(2)_L$ doublets, and right-handed squarks such as $\tilde \u _R$ (code 2000002) and $\tilde \d _R$ (code 2000001) and right-handed sleptons such as $\tilde \mathrm{e}_R$ (code 2000011), which are $SU(2)_L$ singlets. Similar codes exist for the second generation sfermions. For the third generation, there are good reasons to believe that the mass eigenstates are not accurately labeled by interaction quantum numbers, and thus they are labeled by integers 1 or 2 to denote the lightest and heaviest, e.g. $M_{\tilde \t _1} < M_{\tilde \t _2}$. The gluino $\tilde \mathrm{g}$ and squarks $\tilde \mathrm{q}$ carry color indices and are $SU(3)_C$ octets and triplets, respectively.

The particle partners and KF codes are listed 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, fixed by SUSY. There are also a number of soft SUSY-breaking mass parameters. ``Soft'' means that they break the mass degeneracy between SM particles and their SUSY partners without reintroducing quadratic divergences or destroying the gauge invariance of the theory. The soft SUSY-breaking parameters are extra mass terms for gauginos and scalar fermions, and trilinear scalar couplings. The exact number of independent parameters depends on the detailed mechanism of SUSY breaking. In general, the 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 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.