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2 | \section{ISASUSY: Decay Modes in the Minimal Supersymmetric | |

3 | Model\label{SUSY}} | |

4 | ||

5 | The code in patch ISASUSY of ISAJET calculates decay modes of | |

6 | supersymmetric particles based on the work of H. Baer, M. Bisset, M. | |

7 | Drees, D. Dzialo (Karatas), X. Tata, J. Woodside, and their | |

8 | collaborators. The calculations assume the minimal supersymmetric | |

9 | extension of the standard model. The user specifies the gluino mass, | |

10 | the pseudoscalar Higgs mass, the Higgsino mass parameter $\mu$, | |

11 | $\tan\beta$, the soft breaking masses for the first and third | |

12 | generation left-handed squark and slepton doublets and right-handed | |

13 | singlets, and the third generation mixing parameters $A_t$, $A_b$, and | |

14 | $A_\tau$. Supersymmetric grand unification is assumed by default in | |

15 | the chargino and neutralino mass matrices, although the user can | |

16 | optionally specify arbitrary $U(1)$ and $SU(2)$ gaugino masses at the | |

17 | weak scale. The first and second generations are assumed by default to | |

18 | be degenerate, but the user can optionally specify different values. | |

19 | These inputs are then used to calculate the mass eigenstates, mixings, | |

20 | and decay modes. | |

21 | ||

22 | Most calculations are done at the tree level, but one-loop | |

23 | results for gluino loop decays, $H \to \gamma\gamma$ and $H \to gg$, loop | |

24 | corrections to the Higgs mass spectrum and couplings, and leading-log | |

25 | QCD corrections to $H \to q \bar q$ are included. The Higgs masses have | |

26 | been calculated using the effective potential approximation including | |

27 | both top and bottom Yukawa and mixing effects. Mike Bisset and Xerxes | |

28 | Tata have contributed the Higgs mass, couplings, and decay routines. | |

29 | Manuel Drees has calculated several of the three-body decays including | |

30 | the full Yukawa contribution, which is important for large tan(beta). | |

31 | Note that e+e- annihilation to SUSY particles and SUSY Higgs bosons | |

32 | have been included in ISAJET versions $>7.11$. ISAJET versions $>7.22$ | |

33 | include the large $\tan\beta$ solution as well as non-degenerate | |

34 | sfermion masses. | |

35 | ||

36 | Other processes may be added in future versions as the physics | |

37 | interest warrants. Note that | |

38 | the details of the masses and the decay modes can be quite sensitive | |

39 | to choices of standard model parameters such as the QCD coupling ALFA3 | |

40 | and the quark masses. To change these, you must modify subroutine | |

41 | SSMSSM. By default, ALFA3=.12. | |

42 | ||

43 | All the mass spectrum and branching ratio calculations in ISASUSY | |

44 | are performed by a call to subroutine SSMSSM. Effective with version 7.23, | |

45 | the calling sequence is | |

46 | \begin{verbatim} | |

47 | SUBROUTINE SSMSSM(XMG,XMU,XMHA,XTANB,XMQ1,XMDR,XMUR, | |

48 | $XML1,XMER,XMQ2,XMSR,XMCR,XML2,XMMR,XMQ3,XMBR,XMTR, | |

49 | $XML3,XMLR,XAT,XAB,XAL,XM1,XM2,XMT,IALLOW) | |

50 | \end{verbatim} | |

51 | where the following are taken to be independent parameters: | |

52 | ||

53 | \smallskip\noindent | |

54 | \begin{tabular}{lcl} | |

55 | XMG &=& gluino mass\\ | |

56 | XMU &=& $\mu$ = SUSY Higgs mass\\ | |

57 | &=& $-2*m_1$ of Baer et al.\\ | |

58 | XMHA &=& pseudo-scalar Higgs mass\\ | |

59 | XTANB &=& $\tan\beta$, ratio of vev's\\ | |

60 | &=& $1/R$ (of old Baer-Tata notation).\\ | |

61 | \end{tabular} | |

62 | ||

63 | \noindent | |

64 | \begin{tabular}{lcl} | |

65 | XMQ1 &=& $\tilde q_l$ soft mass, 1st generation\\ | |

66 | XMDR &=& $\tilde d_r$ mass, 1st generation\\ | |

67 | XMUR &=& $\tilde u_r$ mass, 1st generation\\ | |

68 | XML1 &=& $\tilde \ell_l$ mass, 1st generation\\ | |

69 | XMER &=& $\tilde e_r$ mass, 1st generation\\ | |

70 | \\ | |

71 | XMQ2 &=& $\tilde q_l$ soft mass, 2nd generation\\ | |

72 | XMSR &=& $\tilde s_r$ mass, 2nd generation\\ | |

73 | XMCR &=& $\tilde c_r$ mass, 2nd generation\\ | |

74 | XML2 &=& $\tilde \ell_l$ mass, 2nd generation\\ | |

75 | XMMR &=& $\tilde\mu_r$ mass, 2nd generation\\ | |

76 | \\ | |

77 | XMQ3 &=& $\tilde q_l$ soft mass, 3rd generation\\ | |

78 | XMBR &=& $\tilde b_r$ mass, 3rd generation\\ | |

79 | XMTR &=& $\tilde t_r$ mass, 3rd generation\\ | |

80 | XML3 &=& $\tilde \ell_l$ mass, 3rd generation\\ | |

81 | XMTR &=& $\tilde \tau_r$ mass, 3rd generation\\ | |

82 | XAT &=& stop trilinear term $A_t$\\ | |

83 | XAB &=& sbottom trilinear term $A_b$\\ | |

84 | XAL &=& stau trilinear term $A_\tau$\\ | |

85 | \\ | |

86 | XM1 &=& U(1) gaugino mass\\ | |

87 | &=& computed from XMG if > 1E19\\ | |

88 | XM2 &=& SU(2) gaugino mass\\ | |

89 | &=& computed from XMG if > 1E19\\ | |

90 | \\ | |

91 | XMT &=& top quark mass\\ | |

92 | \end{tabular} | |

93 | \smallskip | |

94 | ||

95 | \noindent The variable IALLOW is returned: | |

96 | ||

97 | \smallskip\noindent | |

98 | \begin{tabular}{lcl} | |

99 | IALLOW &=& 1 if Z1SS is not LSP, 0 otherwise\\ | |

100 | \end{tabular} | |

101 | \smallskip | |

102 | ||

103 | \noindent All variables are of type REAL except IALLOW, which is | |

104 | INTEGER, and all masses are in GeV. The notation is taken to | |

105 | correspond to that of Haber and Kane, although the Tata Lagrangian is | |

106 | used internally. All other standard model parameters are hard wired in | |

107 | this subroutine; they are not obtained from the rest of ISAJET. The | |

108 | theoretically favored range of these parameters is | |

109 | \begin{eqnarray*} | |

110 | & 50 < M(\tilde g) < 2000\,\GeV &\\ | |

111 | & 50 < M(\tilde q) < 2000\,\GeV &\\ | |

112 | & 50 < M(\tilde\ell) < 2000\,\GeV &\\ | |

113 | & -1000 < \mu < 1000\,\GeV &\\ | |

114 | & 1 < \tan\beta < m_t/m_b &\\ | |

115 | & M(t) \approx 175\,\GeV &\\ | |

116 | & 50 < M(A) < 2000\,\GeV &\\ | |

117 | & M(\tilde t_l), M(t_r) < M(\tilde q) &\\ | |

118 | & M(\tilde b_r) \sim M(\tilde q) &\\ | |

119 | & -1000 < A_t < 1000\,\GeV &\\ | |

120 | & -1000 < A_b < 1000\,\GeV & | |

121 | \end{eqnarray*} | |

122 | It is assumed that the lightest supersymmetric particle is the lightest | |

123 | neutralino $\tilde Z_1$, the lighter stau $\tilde\tau_1$, or the | |

124 | gravitino $\tilde G$ in GMSB models. Some choices of the above | |

125 | parameters may violate this assumption, yielding a light chargino or | |

126 | light stop squark lighter than $\tilde Z_1$. In such cases SSMSSM does | |

127 | not compute any branching ratios and returns IALLOW = 1. | |

128 | ||

129 | SSMSSM does not check the parameters or resulting masses against | |

130 | existing experimental data. SSTEST provides a minimal test. This routine | |

131 | is called after SSMSSM by ISAJET and ISASUSY and prints suitable warning | |

132 | messages. | |

133 | ||

134 | SSMSSM first calculates the other SUSY masses and mixings and puts | |

135 | them in the common block /SSPAR/: | |

136 | \begin{verbatim} | |

137 | #include "sspar.inc" | |

138 | \end{verbatim} | |

139 | It then calculates the widths and branching ratios and puts them in the | |

140 | common block /SSMODE/: | |

141 | \begin{verbatim} | |

142 | #include "ssmode.inc" | |

143 | \end{verbatim} | |

144 | Decay modes for a given particle are not necessarily adjacent in this | |

145 | common block. Note that the branching ratio calculations use the full | |

146 | matrix elements, which in general will give nonuniform distributions in | |

147 | phase space, but this information is not saved in /SSMODE/. In | |

148 | particular, the decays $H \to Z + Z^* \to Z + f + \bar f$ give no | |

149 | indication that the $f \bar f$ mass is strongly peaked near the upper | |

150 | limit. | |

151 | ||

152 | All IDENT codes are defined by parameter statements in the PATCHY | |

153 | keep sequence SSTYPE: | |

154 | \begin{verbatim} | |

155 | #include "sstype.inc" | |

156 | \end{verbatim} | |

157 | These are based on standard ISAJET but can be changed to interface with | |

158 | other generators. Since masses except the t mass are hard wired, one | |

159 | should check the kinematics for any decay before using it with possibly | |

160 | different masses. | |

161 | ||

162 | Instead of specifying all the SUSY parameters at the electroweak | |

163 | scale using the MSSMi commands, one can instead use the SUGRA parameter | |

164 | to specify in the minimal supergravity framework the common scalar mass | |

165 | $m_0$, the common gaugino mass $m_{1/2}$, and the soft trilinear SUSY | |

166 | breaking parameter $A_0$ at the GUT scale, the ratio $\tan\beta$ of | |

167 | Higgs vacuum expectation values at the electroweak scale, and $\sgn\mu$, | |

168 | the sign of the Higgsino mass term. The \verb|NUSUGi| keywords allow one | |

169 | to break the assumption of universality in various ways. \verb|NUSUG1| | |

170 | sets the gaugino masses; \verb|NUSUG2| sets the $A$ terms; \verb|NUSUG3| | |

171 | sets the Higgs masses; \verb|NUSUG4| sets the first generation squark | |

172 | and slepton masses; and \verb|NUSUG5| sets the third generation masses. | |

173 | The keyword \verb|SSBCSC| can be used to specify an alternative scale | |

174 | (i.e., not the coupling constant unification scale) for the RGE boundary | |

175 | conditions. | |

176 | ||

177 | The renormalization group equations now include all the two-loop | |

178 | terms for both gauge and Yukawa couplings and the possible contributions | |

179 | from right-handed neutrinos. These equations are solved iteratively using | |

180 | Runge-Kutta numerical integration to determine the weak scale parameters | |

181 | from the GUT scale ones: | |

182 | \begin{enumerate} | |

183 | % | |

184 | \item The RGE's are run from the weak scale $M_Z$ up to the GUT scale, | |

185 | where $\alpha_1 = \alpha_2$, taking all thresholds into account. We use | |

186 | two loop RGE equations for the gauge couplings only. | |

187 | % | |

188 | \item The GUT scale boundary conditions are imposed, and the RGE's are | |

189 | run back to $M_Z$, again taking thresholds into account. | |

190 | % | |

191 | \item The masses of the SUSY particles and the values of the soft | |

192 | breaking parameters B and mu needed for radiative symmetry are | |

193 | computed, e.g. | |

194 | $$ | |

195 | \mu^2(M_Z) = {M_{H_1}^2 - M_{H_2}^2 \tan^2\beta \over | |

196 | \tan^2\beta-1} - M_Z^2/2 | |

197 | $$ | |

198 | These couplings are frozen out at the scale $\sqrt{M(t_L)M(t_R)}$. | |

199 | % | |

200 | \item The 1-loop radiative corrections are computed. | |

201 | % | |

202 | \item The process is then iterated until stable results are obtained. | |

203 | \end{enumerate} | |

204 | This is essentially identical to the procedure used by several other | |

205 | groups. Other possible constraints such as $b$-$\tau$ unification and | |

206 | limits on proton decay have not been included. | |

207 | ||

208 | An alternative to the SUGRA model is the Gauge Mediated SUSY | |

209 | Breaking (GMSB) model of Dine and Nelson, Phys.\ Rev.\ {\bf D48}, 1277 | |

210 | (1973); Dine, Nelson, Nir, and Shirman, Phys.\ Rev.\ {\bf D53}, 2658 | |

211 | (1996). In this model SUSY is broken dynamically and communicated to the | |

212 | MSSM through messenger fields at a messenger mass scale $M_m$ much less | |

213 | than the Planck scale. If the messenger fields are in complete | |

214 | representations of $SU(5$), then the unification of couplings suggested | |

215 | by the LEP data is preserved. The simplest model has a single $5+\bar5$ | |

216 | messenger sector with a mass $M_m$ and and a SUSY-breaking VEV $F_m$ of | |

217 | its auxiliary field $F$. Gauginos get masses from one-loop graphs | |

218 | proportional to $\Lambda_m = F_m / M_m$ times the appropriate gauge | |

219 | coupling $\alpha_i$; sfermions get squared-masses from two-loop graphs | |

220 | proportional to $\Lambda_m$ times the square of the appropriate | |

221 | $\alpha_i$. If there are $N_5$ messenger fields, the gaugino masses and | |

222 | sfermion masses-squared each contain a factor of $N_5$. | |

223 | ||

224 | The parameters of the GMSB model implemented in ISAJET are | |

225 | \begin{itemize} | |

226 | \item $\Lambda_m = F_m/M_m$: the scale of SUSY breaking, typically | |

227 | 10--$100\,{\rm TeV}$; | |

228 | \item $M_m > \Lambda_m$: the messenger mass scale, at which the boundary | |

229 | conditions for the renormalization group equations are imposed; | |

230 | \item $N_5$: the equivalent number of $5+\bar5$ messenger fields. | |

231 | \item $\tan\beta$: the ratio of Higgs vacuum expectation values at the | |

232 | electroweak scale; | |

233 | \item $\sgn\mu=\pm1$: the sign of the Higgsino mass term; | |

234 | \item $C_{\rm grav}\ge1$: the ratio of the gravitino mass to the value it | |

235 | would have had if the only SUSY breaking scale were $F_m$. | |

236 | \end{itemize} | |

237 | The solution of the renormalization group equations is essentially the | |

238 | same as for SUGRA; only the boundary conditions are changed. In | |

239 | particular it is assumed that electroweak symmetry is broken radiatively | |

240 | by the top Yukawa coupling. | |

241 | ||

242 | In GMSB models the lightest SUSY particle is always the nearly | |

243 | massless gravitino $\tilde G$. The phenomenology depends on the nature | |

244 | of the next lightest SUSY particle (NLSP) and on its lifetime to decay | |

245 | to a gravitino. The NLSP can be either a neutralino $\tilde\chi_1^0$ or | |

246 | a slepton $\tilde\tau_1$. Its lifetime depends on the gravitino mass, | |

247 | which is determined by the scale of SUSY breaking not just in the | |

248 | messenger sector but also in any other hidden sector. If this is set by | |

249 | the messenger scale $F_m$, i.e., if $C_{\rm grav}\approx1$, then this | |

250 | lifetime is generally short. However, if the messenger SUSY breaking | |

251 | scale $F_m$ is related by a small coupling constant to a much larger | |

252 | SUSY breaking scale $F_b$, then $C_{\rm grav}\gg1$ and the NLSP can be | |

253 | long-lived. The correct scale is not known, so $C_{\rm grav}$ should be | |

254 | treated as an arbitrary parameter. More complicated GMSB models may be | |

255 | run by using the GMSB2 keyword. | |

256 | ||

257 | Patch ISASSRUN of ISAJET provides a main program SSRUN and some | |

258 | utility programs to produce human readable output. These utilities must | |

259 | be rewritten if the IDENT codes in /SSTYPE/ are modified. To create the | |

260 | stand-alone version of ISASUSY with SSRUN, run YPATCHY on isajet.car | |

261 | with the following cradle (with \verb|&| replaced by \verb|+|): | |

262 | \begin{verbatim} | |

263 | &USE,*ISASUSY. Select all code | |

264 | &USE,NOCERN. No CERN Library | |

265 | &USE,IMPNONE. Use IMPLICIT NONE | |

266 | &EXE. Write everything to ASM | |

267 | &PAM,T=C. Read PAM file | |

268 | &QUIT. Quit | |

269 | \end{verbatim} | |

270 | Compile, link, and run the resulting program, and follow the prompts for | |

271 | input. Patch ISASSRUN also contains a main program SUGRUN that reads | |

272 | the minimal SUGRA, non-universal SUGRA, or GMSB parameters, solves the | |

273 | renormalization group equations, and calculates the masses and branching | |

274 | ratios. To create the stand-alone version of ISASUGRA, run YPATCHY with | |

275 | the following cradle: | |

276 | \begin{verbatim} | |

277 | &USE,*ISASUGRA. Select all code | |

278 | &USE,NOCERN. No CERN Library | |

279 | &USE,IMPNONE. Use IMPLICIT NONE | |

280 | &EXE. Write everything to ASM | |

281 | &PAM. Read PAM file | |

282 | &QUIT. Quit | |

283 | \end{verbatim} | |

284 | The documentation for ISASUSY and ISASUGRA is included with that for | |

285 | ISAJET. | |

286 | ||

287 | ISASUSY is written in ANSI standard Fortran 77 except that | |

288 | IMPLICIT NONE is used if +USE,IMPNONE is selected in the Patchy cradle. | |

289 | All variables are explicitly typed, and variables starting with | |

290 | I,J,K,L,M,N are not necessarily integers. All external names such as | |

291 | the names of subroutines and common blocks start with the letters SS. | |

292 | Most calculations are done in double precision. If +USE,NOCERN is | |

293 | selected in the Patchy cradle, then the Cernlib routines EISRS1 and its | |

294 | auxiliaries to calculate the eigenvalues of a real symmetric matrix and | |

295 | DDILOG to calculate the dilogarithm function are included. Hence it is | |

296 | not necessary to link with Cernlib. | |

297 | ||

298 | The physics assumptions and details of incorporating the Minimal | |

299 | Supersymmetric Model into ISAJET have appeared in a conference | |

300 | proceedings entitled ``Simulating Supersymmetry with ISAJET 7.0/ISASUSY | |

301 | 1.0'' by H. Baer, F. Paige, S. Protopopescu and X. Tata; this has | |

302 | appeared in the proceedings of the workshop on {\sl Physics at Current | |

303 | Accelerators and Supercolliders}, ed.\ J. Hewett, A. White and D. | |

304 | Zeppenfeld, (Argonne National Laboratory, 1993). Detailed references | |

305 | may be found therein. Users wishing to cite an appropriate source may | |

306 | cite the above report. |