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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. |