Models

When IMSS(1)=1, it is assumed that the user will specify all of the soft SUSY-breaking parameters at the weak scale. Simplifications have already been made to greatly reduce the number of parameters from over 100. At present, the exact mechanism of SUSY breaking is unknown. It is generally assumed that the breaking occurs spontaneously in a set of fields that are almost entirely disconnected from the fields of the MSSM; if SUSY is broken explicitly in the MSSM, then some superpartners must be lighter than the corresponding Standard Model particle, a phenomenological disaster. The breaking of SUSY in this ``hidden sector'' is then communicated to the MSSM fields through one or several mechanisms: gravitational interactions, gauge interactions, anomalies, etc. While any one of these may dominate, it is also possible that all contribute at once.

Several models exist which predict the rich set of directly measurable mass and mixing parameters from the assumed soft SUSY breaking scenario with a much smaller set of free parameters. One example is Supergravity (SUGRA) inspired models, where the number of free parameters is reduced by imposing universality and exploiting the apparent unification of gauge couplings. Five parameters fixed at the gauge coupling unification scale, $\tan\beta, M_0, m_{1/2}, A_0,$ and sign($\mu$), are then related to the mass parameters at the scale of Electroweak symmetry breaking by renormalization group equations (see e.g. [Pie97]).

The user who wants to study this and other models in detail can use the ISASUSY [Bae93] and SUSYGEN [Kat98] programs, which numerically solve these equations to determine the mass parameters, to generate the correct PYTHIA input parameters.

An interface to ISASUSY can be accessed by the option IMSS(1)=12, in which case the SUGRA routine of ISASUSY is called by PYINIT. This routine then calculates the mSUGRA spectrum of SUSY masses and mixings (CP conservation is assumed), and all of PYTHIA's own internal mSUGRA machinery is switched off. This means that none of the other IMSS switches can be used, except for IMSS(51:53) ($R$-parity violation), IMSS(10) (force $\tilde{\chi}_2\to\tilde{\chi_1}\gamma$), and IMSS(11) (gravitino on/off). Note that, although they have no effect, values in IMSS will not be overwritten, save for IMSS(4) which is forced equal to 2. Also note that the dependence of the $b$ and $t$ quark Yukawa couplings on $\tan\beta$ and the gluino mass is ignored when using IMSS(1)=12. The mSUGRA model input parameters should be given in RMSS as usual, i.e.: RMSS(1)$= M_{1/2}$, RMSS(4)= sign($\mu$), RMSS(5)$= \tan\beta$, RMSS(8)$= M_0$, and RMSS(16)$= A_0$. The routine PYSUGI handles the conversion between the conventions of PYTHIA and ISASUSY, so that conventions are self-consistent inside PYTHIA. Cross sections and decay widths are then calculated by PYTHIA. Since PYTHIA cannot always be expected to be linked with ISAJET, a dummy routine and a dummy function have been added to the PYTHIA source. These are SUBROUTINE SUGRA and FUNCTION VISAJE. These must first be given other names and PYTHIA recompiled before proper linking with ISAJET can be achieved.

As a cross check, the option IMSS(1)=2 uses approximate analytical solutions of the renormalization group equations [Dre95], which reproduce the output of ISASUSY within $\simeq 10\%$ (based on comparisons of masses, decay widths, production cross sections, etc.). In the near future, the interface to ISASUSY will be extended to handle also the non-mSUGRA SUSY breaking models included in ISASUSY.

In SUGRA, the spin-3/2 superpartner of the graviton, the gravitino $\widetilde G$ (code 1000039), has a mass of order $M_\mathrm{W}$ and interacts only gravitationally. In models of gauge-mediated SUSY breaking [Din96], however, the gravitino can play a crucial role in the phenomenology, and can be the lightest superpartner (LSP). Typically, sfermions decay to fermions and gravitinos, and neutralinos, chargino, and gauginos decay to gauge or Higgs bosons and gravitinos. Depending on the gravitino mass, the decay lengths can be substantial on the scale of colliders. PYTHIA correctly handles finite decay lengths for all sparticles.

In the production of superpartners, R-parity conservation is assumed (at least on the time and distance scale of a typical collider experiment), and only lowest order, sparticle pair production processes are included. Only those processes with $\mathrm{e}^+\mathrm{e}^-, \mu^+\mu^-$, or quark and gluon initial states are simulated. Tables , and list available SUSY processes. In processes 210 and 213, $\tilde{\ell}$ refers to both $\tilde{\mathrm e}$ and $\tilde{\mu}$. For ease of readability, we have removed the subscript $L$ on $\tilde{\nu}$. $\tilde{\mathrm t}_i\tilde{\mathrm t}^*_i, \tilde\tau _i\tilde\tau _j^*$ and $\tilde\tau _i\tilde{\nu}_{\tau}^*$ production correctly account for sfermion mixing. Several processes are conspicuously absent from the table. For example, processes 255 and 257 would simulate the associated production of right handed squarks with charginos. Since the right handed squark only couples to the higgsino component of the chargino, the interaction strength is proportional to the quark mass, so these processes can be ignored.

By default, only R-parity conserving decays are allowed, so that one sparticle is stable, either the lightest neutralino, the gravitino, or a sneutrino. SUSY decays of the top quark are included, but all other SM particle decays are unaltered.

Generally, the decays of superpartners are calculated using the formulae of refs. [Gun88,Bar86a,Bar86b,Bar95]. All decays are spin averaged. Decays involving $\tilde{\mathrm b}$ and $\tilde{\mathrm t}$ use the formulae of [Bar95], so they are valid for large values of $\tan\beta$. The one loop decays $\tilde{\chi}_j\to\tilde{\chi}_i\gamma$ and $\tilde{\mathrm t}\to \c\tilde{\chi}_1$ are also included, but only with approximate formula. Typically, these decays are only important when other decays are not allowed because of mixing effects or phase space considerations.

One difference between the SUSY simulation and the other parts of the program is that it is not beforehand known which sparticles may be stable. Normally this would mean either the $\tilde{\chi}^0_1$ or the gravitino $\tilde{\mathrm G}$, but in principle also other sparticles could be stable. The ones found to be stable have their MWID(KC) and MDCY(KC,1) values set zero at initialization. If several PYINIT calls are made in the same run, with different SUSY parameters, the ones set zero above are not necessarily set back to nonzero values, since most original values are not saved anywhere. As an exception to this rule, the PYMSIN SUSY initialization routine, called by PYINIT, does save and restore the MWID(KC) and MDCY(KC,1) values of the lightest SUSY particle. It is therefore possible to combine several PYINIT calls in a single run, provided that only the lightest SUSY particle is stable. If this is not the case, MWID(KC) and MDCY(KC,1) values may have to be reset by hand, or else some particles that ought to decay will not do that.