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Models

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.

We may parametrize our ignorance of the exact mechanism of SUSY breaking by simply setting each of the soft SUSY breaking parameters in the Lagrangian by hand. In PYTHIA this approach can be effected by setting IMSS(1) = 1, although some simplifications have already been made to greatly reduce the number of parameters from the initial more than 100.

As to specific models, several exist which predict the rich set of 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 at some high scale, motivated by 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 spectrum calculation programs (e.g. ISASUSY [Bae93], SOFTSUSY [All02], SPHENO [Por03], or SUSPECT [Djo02]), which numerically solve the renormalization group equations (RGE) to determine the mass and mixing parameters at the weak scale. These may then be input to PYTHIA via a SLHA spectrum file [Ska03] using IMSS(1) = 11 and IMSS(21) equal to the unit number where the spectrum file has been opened. All of PYTHIA's own internal mSUGRA machinery (see below) is then 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 is the LSP). Note that the dependence of the $\b $ and $\t $ quark Yukawa couplings on $\tan\beta$ and the gluino mass is at present ignored when using IMSS(1) = 11.

As an alternative, a run-time interface to ISASUSY can be accessed by the options IMSS(1) = 12 and IMSS(1) = 13, in which case the SUGRA routine of ISASUSY is called by PYINIT. This routine then calculates the spectrum of SUSY masses and mixings (CP conservation, i.e. real-valued parameters, is assumed) and passes the information run-time rather than in a file.

For IMSS(1) = 12, only the mSUGRA model of ISASUSY can be accessed. The mSUGRA model input parameters should then be given in RMSS as for IMSS(1) = 2, i.e.: RMSS(1)$= M_{1/2}$, RMSS(4) = sign($\mu$), RMSS(5)$ = \tan\beta$, RMSS(8)$ = M_0$, and RMSS(16)$= A_0$.

For IMSS(1) = 13, the full range of ISASUSY models can be interfaced, but the input parameters must then be given in the form of an ISAJET input file which PYTHIA reads during initialization and passes to ISASUSY. The contents of the input file should be identical to what would normally be typed when using the ISAJET RGE executable stand-alone (normally isasugra.x). The input file should be opened by the user in his/her main program and the Logical Unit Number should be stored in IMSS(20), where PYTHIA will look for it during initialization.

The routine PYSUGI handles the conversion between the conventions of PYTHIA and ISASUSY, so that conventions are self-consistent inside PYTHIA. In the call to PYSUGI, the RMSS array is filled with the values produced by ISASUSY as for IMSS(1) = 1. In particular, this means that when using the IMSS(1) = 12 option, the mSUGRA input parameters mentioned above will be overwritten during initialization. Cross sections and decay widths are then calculated by PYTHIA. Note that, since PYTHIA cannot always be expected to be linked with ISAJET, two dummy routines and a dummy function have been added to the PYTHIA source. These are SUBROUTINE SUGRA, SUBROUTINE SSMSSM and FUNCTION VISAJE. These must first be given other names and PYTHIA recompiled before proper linking with ISAJET can be achieved.

A problem is that the size of some ISASUSY common blocks has been expanded in more recent versions. Corresponding changes have been implemented in the PYSUGI interface routine. Currently PYTHIA is matched to ISAJET 7.71, and thus assumes the SSPAR, SUGPAS, SUGMG and SUGXIN common blocks to have the forms:

      COMMON/SSPAR/AMGLSS,AMULSS,AMURSS,AMDLSS,AMDRSS,AMSLSS
     &,AMSRSS,AMCLSS,AMCRSS,AMBLSS,AMBRSS,AMB1SS,AMB2SS
     &,AMTLSS,AMTRSS,AMT1SS,AMT2SS,AMELSS,AMERSS,AMMLSS,AMMRSS
     &,AMLLSS,AMLRSS,AML1SS,AML2SS,AMN1SS,AMN2SS,AMN3SS
     &,TWOM1,RV2V1,AMZ1SS,AMZ2SS,AMZ3SS,AMZ4SS,ZMIXSS(4,4)
     &,AMW1SS,AMW2SS
     &,GAMMAL,GAMMAR,AMHL,AMHH,AMHA,AMHC,ALFAH,AAT,THETAT
     &,AAB,THETAB,AAL,THETAL,AMGVSS,MTQ,MBQ,MLQ,FBMA,
     &VUQ,VDQ
      REAL AMGLSS,AMULSS,AMURSS,AMDLSS,AMDRSS,AMSLSS
     &,AMSRSS,AMCLSS,AMCRSS,AMBLSS,AMBRSS,AMB1SS,AMB2SS
     &,AMTLSS,AMTRSS,AMT1SS,AMT2SS,AMELSS,AMERSS,AMMLSS,AMMRSS
     &,AMLLSS,AMLRSS,AML1SS,AML2SS,AMN1SS,AMN2SS,AMN3SS
     &,TWOM1,RV2V1,AMZ1SS,AMZ2SS,AMZ3SS,AMZ4SS,ZMIXSS
     &,AMW1SS,AMW2SS
     &,GAMMAL,GAMMAR,AMHL,AMHH,AMHA,AMHC,ALFAH,AAT,THETAT
     &,AAB,THETAB,AAL,THETAL,AMGVSS,MTQ,MBQ,MLQ,FBMA,VUQ,VDQ
      COMMON /SUGPAS/ XTANB,MSUSY,AMT,MGUT,MU,G2,GP,V,VP,XW,
     &A1MZ,A2MZ,ASMZ,FTAMZ,FBMZ,B,SIN2B,FTMT,G3MT,VEV,HIGFRZ,
     &FNMZ,AMNRMJ,NOGOOD,IAL3UN,ITACHY,MHPNEG,ASM3,
     &VUMT,VDMT,ASMTP,ASMSS,M3Q
      REAL XTANB,MSUSY,AMT,MGUT,MU,G2,GP,V,VP,XW,
     &A1MZ,A2MZ,ASMZ,FTAMZ,FBMZ,B,SIN2B,FTMT,G3MT,VEV,HIGFRZ,
     &FNMZ,AMNRMJ,ASM3,VUMT,VDMT,ASMTP,ASMSS,M3Q
      INTEGER NOGOOD,IAL3UN,ITACHY,MHPNEG
      COMMON /SUGMG/ MSS(32),GSS(31),MGUTSS,GGUTSS,AGUTSS,FTGUT,
     &FBGUT,FTAGUT,FNGUT
      REAL MSS,GSS,MGUTSS,GGUTSS,AGUTSS,FTGUT,FBGUT,FTAGUT,FNGUT
      COMMON /SUGXIN/ XISAIN(24),XSUGIN(7),XGMIN(14),XNRIN(4),
     &XAMIN(7)
      REAL XISAIN,XSUGIN,XGMIN,XNRIN,XAMIN
ISASUSY users are warned to check that no incompatibilities arise between the versions actually used. Unfortunately there is no universal solution to this problem: the Fortran standard does not allow you dynamically to vary the size of a (named) common block. So if you use an earlier ISASUSY version, you have to shrink the size accordingly, and for a later you may have to check that the above common blocks have not been expanded further.

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.). This option is intended for debugging only, and does not represent the state-of-the-art.

In SUGRA and in other models with the SUSY breaking scale of order $M_{\mathrm{GUT}}$, the spin-3/2 superpartner of the graviton, the gravitino $\widetilde\mathrm{G}$ (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.

$R$-parity is a possible symmetry of the SUSY Lagrangian that prevents problems of rapid proton decay and allows for a viable dark matter candidate. However, it is also possible to allow a restricted amount of $R$-parity violation. At present, there is no theoretical consensus that $R$-parity should be conserved, even in string models. In the production of superpartners, PYTHIA assumes $R$-parity conservation (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 the 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.


next up previous contents
Next: SUSY examples Up: Supersymmetry Previous: Superpartners of Standard Model   Contents
Stephen Mrenna 2007-10-30