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2\section{ISASUSY: Decay Modes in the Minimal Supersymmetric
3Model\label{SUSY}}
4
5 The code in patch ISASUSY of ISAJET calculates decay modes of
6supersymmetric particles based on the work of H. Baer, M. Bisset, M.
7Drees, D. Dzialo (Karatas), X. Tata, J. Woodside, and their
8collaborators. The calculations assume the minimal supersymmetric
9extension of the standard model. The user specifies the gluino mass,
10the pseudoscalar Higgs mass, the Higgsino mass parameter $\mu$,
11$\tan\beta$, the soft breaking masses for the first and third
12generation left-handed squark and slepton doublets and right-handed
13singlets, and the third generation mixing parameters $A_t$, $A_b$, and
14$A_\tau$. Supersymmetric grand unification is assumed by default in
15the chargino and neutralino mass matrices, although the user can
16optionally specify arbitrary $U(1)$ and $SU(2)$ gaugino masses at the
17weak scale. The first and second generations are assumed by default to
18be degenerate, but the user can optionally specify different values.
19These inputs are then used to calculate the mass eigenstates, mixings,
20and decay modes.
21
22 Most calculations are done at the tree level, but one-loop
23results for gluino loop decays, $H \to \gamma\gamma$ and $H \to gg$, loop
24corrections to the Higgs mass spectrum and couplings, and leading-log
25QCD corrections to $H \to q \bar q$ are included. The Higgs masses have
26been calculated using the effective potential approximation including
27both top and bottom Yukawa and mixing effects. Mike Bisset and Xerxes
28Tata have contributed the Higgs mass, couplings, and decay routines.
29Manuel Drees has calculated several of the three-body decays including
30the full Yukawa contribution, which is important for large tan(beta).
31Note that e+e- annihilation to SUSY particles and SUSY Higgs bosons
32have been included in ISAJET versions $>7.11$. ISAJET versions $>7.22$
33include the large $\tan\beta$ solution as well as non-degenerate
34sfermion masses.
35
36Other processes may be added in future versions as the physics
37interest warrants. Note that
38the details of the masses and the decay modes can be quite sensitive
39to choices of standard model parameters such as the QCD coupling ALFA3
40and the quark masses. To change these, you must modify subroutine
41SSMSSM. By default, ALFA3=.12.
42
43 All the mass spectrum and branching ratio calculations in ISASUSY
44are performed by a call to subroutine SSMSSM. Effective with version 7.23,
45the 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}
51where 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
104INTEGER, and all masses are in GeV. The notation is taken to
105correspond to that of Haber and Kane, although the Tata Lagrangian is
106used internally. All other standard model parameters are hard wired in
107this subroutine; they are not obtained from the rest of ISAJET. The
108theoretically 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*}
122It is assumed that the lightest supersymmetric particle is the lightest
123neutralino $\tilde Z_1$, the lighter stau $\tilde\tau_1$, or the
124gravitino $\tilde G$ in GMSB models. Some choices of the above
125parameters may violate this assumption, yielding a light chargino or
126light stop squark lighter than $\tilde Z_1$. In such cases SSMSSM does
127not compute any branching ratios and returns IALLOW = 1.
128
129 SSMSSM does not check the parameters or resulting masses against
130existing experimental data. SSTEST provides a minimal test. This routine
131is called after SSMSSM by ISAJET and ISASUSY and prints suitable warning
132messages.
133
134 SSMSSM first calculates the other SUSY masses and mixings and puts
135them in the common block /SSPAR/:
136\begin{verbatim}
137#include "sspar.inc"
138\end{verbatim}
139It then calculates the widths and branching ratios and puts them in the
140common block /SSMODE/:
141\begin{verbatim}
142#include "ssmode.inc"
143\end{verbatim}
144Decay modes for a given particle are not necessarily adjacent in this
145common block. Note that the branching ratio calculations use the full
146matrix elements, which in general will give nonuniform distributions in
147phase space, but this information is not saved in /SSMODE/. In
148particular, the decays $H \to Z + Z^* \to Z + f + \bar f$ give no
149indication that the $f \bar f$ mass is strongly peaked near the upper
150limit.
151
152 All IDENT codes are defined by parameter statements in the PATCHY
153keep sequence SSTYPE:
154\begin{verbatim}
155#include "sstype.inc"
156\end{verbatim}
157These are based on standard ISAJET but can be changed to interface with
158other generators. Since masses except the t mass are hard wired, one
159should check the kinematics for any decay before using it with possibly
160different masses.
161
162 Instead of specifying all the SUSY parameters at the electroweak
163scale using the MSSMi commands, one can instead use the SUGRA parameter
164to 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
166breaking parameter $A_0$ at the GUT scale, the ratio $\tan\beta$ of
167Higgs vacuum expectation values at the electroweak scale, and $\sgn\mu$,
168the sign of the Higgsino mass term. The \verb|NUSUGi| keywords allow one
169to break the assumption of universality in various ways. \verb|NUSUG1|
170sets the gaugino masses; \verb|NUSUG2| sets the $A$ terms; \verb|NUSUG3|
171sets the Higgs masses; \verb|NUSUG4| sets the first generation squark
172and slepton masses; and \verb|NUSUG5| sets the third generation masses.
173The keyword \verb|SSBCSC| can be used to specify an alternative scale
174(i.e., not the coupling constant unification scale) for the RGE boundary
175conditions.
176
177 The renormalization group equations now include all the two-loop
178terms for both gauge and Yukawa couplings and the possible contributions
179from right-handed neutrinos. These equations are solved iteratively using
180Runge-Kutta numerical integration to determine the weak scale parameters
181from 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,
185where $\alpha_1 = \alpha_2$, taking all thresholds into account. We use
186two loop RGE equations for the gauge couplings only.
187%
188\item The GUT scale boundary conditions are imposed, and the RGE's are
189run back to $M_Z$, again taking thresholds into account.
190%
191\item The masses of the SUSY particles and the values of the soft
192breaking parameters B and mu needed for radiative symmetry are
193computed, e.g.
194$$195\mu^2(M_Z) = {M_{H_1}^2 - M_{H_2}^2 \tan^2\beta \over 196\tan^2\beta-1} - M_Z^2/2 197$$
198These 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}
204This is essentially identical to the procedure used by several other
205groups. Other possible constraints such as $b$-$\tau$ unification and
206limits on proton decay have not been included.
207
208 An alternative to the SUGRA model is the Gauge Mediated SUSY
209Breaking (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
212MSSM through messenger fields at a messenger mass scale $M_m$ much less
213than the Planck scale. If the messenger fields are in complete
214representations of $SU(5$), then the unification of couplings suggested
215by the LEP data is preserved. The simplest model has a single $5+\bar5$
216messenger sector with a mass $M_m$ and and a SUSY-breaking VEV $F_m$ of
217its auxiliary field $F$. Gauginos get masses from one-loop graphs
218proportional to $\Lambda_m = F_m / M_m$ times the appropriate gauge
219coupling $\alpha_i$; sfermions get squared-masses from two-loop graphs
220proportional to $\Lambda_m$ times the square of the appropriate
221$\alpha_i$. If there are $N_5$ messenger fields, the gaugino masses and
222sfermion 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
22710--$100\,{\rm TeV}$;
228\item $M_m > \Lambda_m$: the messenger mass scale, at which the boundary
229conditions 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
232electroweak 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
235would have had if the only SUSY breaking scale were $F_m$.
236\end{itemize}
237The solution of the renormalization group equations is essentially the
238same as for SUGRA; only the boundary conditions are changed. In
239particular it is assumed that electroweak symmetry is broken radiatively
240by the top Yukawa coupling.
241
242 In GMSB models the lightest SUSY particle is always the nearly
243massless gravitino $\tilde G$. The phenomenology depends on the nature
244of the next lightest SUSY particle (NLSP) and on its lifetime to decay
245to a gravitino. The NLSP can be either a neutralino $\tilde\chi_1^0$ or
246a slepton $\tilde\tau_1$. Its lifetime depends on the gravitino mass,
247which is determined by the scale of SUSY breaking not just in the
248messenger sector but also in any other hidden sector. If this is set by
249the messenger scale $F_m$, i.e., if $C_{\rm grav}\approx1$, then this
250lifetime is generally short. However, if the messenger SUSY breaking
251scale $F_m$ is related by a small coupling constant to a much larger
252SUSY breaking scale $F_b$, then $C_{\rm grav}\gg1$ and the NLSP can be
253long-lived. The correct scale is not known, so $C_{\rm grav}$ should be
254treated as an arbitrary parameter. More complicated GMSB models may be
255run by using the GMSB2 keyword.
256
257 Patch ISASSRUN of ISAJET provides a main program SSRUN and some
258utility programs to produce human readable output. These utilities must
259be rewritten if the IDENT codes in /SSTYPE/ are modified. To create the
260stand-alone version of ISASUSY with SSRUN, run YPATCHY on isajet.car
261with 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
268&QUIT. Quit
269\end{verbatim}
270Compile, link, and run the resulting program, and follow the prompts for
271input. Patch ISASSRUN also contains a main program SUGRUN that reads
272the minimal SUGRA, non-universal SUGRA, or GMSB parameters, solves the
273renormalization group equations, and calculates the masses and branching
274ratios. To create the stand-alone version of ISASUGRA, run YPATCHY with
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
282&QUIT. Quit
283\end{verbatim}
284The documentation for ISASUSY and ISASUGRA is included with that for
285ISAJET.
286
287 ISASUSY is written in ANSI standard Fortran 77 except that
288IMPLICIT NONE is used if +USE,IMPNONE is selected in the Patchy cradle.
289All variables are explicitly typed, and variables starting with
290I,J,K,L,M,N are not necessarily integers. All external names such as
291the names of subroutines and common blocks start with the letters SS.
292Most calculations are done in double precision. If +USE,NOCERN is
293selected in the Patchy cradle, then the Cernlib routines EISRS1 and its
294auxiliaries to calculate the eigenvalues of a real symmetric matrix and
295DDILOG to calculate the dilogarithm function are included. Hence it is
296not necessary to link with Cernlib.
297
298 The physics assumptions and details of incorporating the Minimal
299Supersymmetric Model into ISAJET have appeared in a conference
300proceedings entitled Simulating Supersymmetry with ISAJET 7.0/ISASUSY
3011.0'' by H. Baer, F. Paige, S. Protopopescu and X. Tata; this has
302appeared in the proceedings of the workshop on {\sl Physics at Current
303Accelerators and Supercolliders}, ed.\ J. Hewett, A. White and D.
304Zeppenfeld, (Argonne National Laboratory, 1993). Detailed references
305may be found therein. Users wishing to cite an appropriate source may
306cite the above report.