SuSpect: A Fortran code for the Supersymmetric and Higgs particle spectrum in the MSSM☆
Introduction
Supersymmetric theories (SUSY) [1], which provide an elegant way to stabilize the large hierarchy between the Grand Unification (GUT) and the electroweak scales and to cancel the quadratic divergences of the radiative corrections to the Higgs boson masses, are by far the most studied extensions of the Standard Model (SM). The most economical low-energy SUSY extension of the SM, the Minimal Supersymmetric Standard Model (MSSM), which allows for a consistent unification of the SM gauge couplings and provides a natural solution of the Dark Matter problem, has been widely investigated; for reviews, see Refs. [2], [3], [4], [5]. As a corollary, the search for Supersymmetric particles and for the extended Higgs spectrum has become one of the main goal of present and future high-energy colliders [6].
It is well known that in the unconstrained MSSM, it is a rather tedious task to deal with the basic parameters of the Lagrangian and to derive in an exhaustive manner their relationship with the physical parameters, i.e. the particle masses and couplings. This is mainly due to the fact that in the MSSM, despite of the minimal gauge group, minimal particle content, minimal couplings imposed by R-parity conservation and the minimal set of soft SUSY-breaking parameters, there are more than a hundred new parameters [7]. Even if one constrains the model to have a viable phenomenology (we will call later such a model the phenomenological MSSM), assuming, for instance, no intergenerational mixing to avoid flavor changing neutral currents, no new source of CP violation, universality of first and second generation sfermions to cope with constraints from kaon physics, etc., there are still more than 20 free parameters left. This large number of input enters in the evaluation of the masses of SUSY particles and Higgs bosons as well as their complicated couplings, which involve several non-trivial aspects, such as the mixing between different states, the Majorana nature of some particles, etc. The situation becomes particularly difficult if one aims at rather precise calculations and hence, attempts to include some refinements such as higher order corrections, which for the calculation of a single parameter need the knowledge of a large part of, if not the whole, spectrum.
Thus, the large number of free parameters in the unconstrained or even phenomenological MSSM, makes a detailed phenomenological analysis of the spectra and the comparison with the outcome or expectation from experiment, a daunting task, if possible at all. Fortunately, there are well motivated theoretical models where the soft SUSY-breaking parameters obey a number of universal boundary conditions at the high (GUT) scale, leading to only a handful of basic parameters. This is the case for instance of the minimal Supergravity model (mSUGRA) [8], where it is assumed that SUSY-breaking occurs in a hidden sector which communicates with the visible sector only through “flavor-blind” gravitational interactions. This leads to the simpler situation where the entire spectrum of superparticles and Higgs bosons is determined by the values of only five free parameters and makes comprehensive scans of the parameter space and detailed studies of the spectrum feasible.
However, there are also similarly constrained and highly predictive alternative SUSY-breaking models in the literature, such as anomaly mediated [9], [10], [11] or gauge mediated [12], [13] SUSY-breaking models, for instance, which should be investigated as well. We then have to trade a complicated situation where we have one model with many input parameters, with a not less complicated situation where we have many models with a small number of basic parameters. In addition, in these unified models, the low-energy parameters are derived from the high-energy (GUT and/or possibly some intermediate scales) input parameters through Renormalization Group Equations (RGE) and they should also necessarily involve radiative electroweak symmetry breaking (EWSB), which sets additional constraints on the model. The implementation of the RG evolution and the EWSB mechanism poses numerous non-trivial technical problems if they have to be done in an accurate way, i.e. including higher order effects. This complication has to be added to the one from the calculation of the particle masses and couplings with radiative corrections (RC) which is still present.
Therefore, to deal with the supersymmetric spectrum in all possible cases, one needs very sophisticated programs to encode all the information and, eventually, to pass it to other programs or Monte Carlo generators to simulate the physical properties of the new particles, decay branching ratios, production cross sections at various colliders, etc. These programs should have a high degree of flexibility in the choice of the model and/or the input parameters and an adequate level of approximation at different stages, for instance, in the incorporation of the RGEs, the handling of the EWSB and the inclusion of radiative corrections to (super)particle masses, which in many cases can be very important. They should also be reliable, quite fast to allow for rapid comprehensive scans of the parameter space and simple enough to be linked with other programs. There are several public codes, in particular ISASUGRA [14], SOFTSUSY [15] and SPHENO [16], as well as a number of private codes, which deal with this problem. In this paper we present our program SuSpect.
SuSpect, in its latest version 2.3 that we present here, is a Fortran code which calculates the supersymmetric and Higgs particle spectrum in the constrained and unconstrained MSSMs. The acronym is an abbreviation of SusySpectrum and successive previous public versions of the code were available starting from 1997 and have been described in Ref. [17]. At the present stage, it deals with the “phenomenological MSSM” with 22 free parameters defined either at a low or high energy scale, with the possibility of RG evolution to arbitrary scales, and the most studied constrained models, namely mSUGRA, AMSB and GMSB. Many “intermediate” models (e.g., constrained models but without unification of gaugino or scalar masses, etc.) are easily handled. The program includes the three major ingredients which should be incorporated in any algorithm for the constrained MSSMs: (i) renormalization group evolution of parameters between a low energy scale (e.g., and/or the EWSB scale) and a high-energy scale (e.g., ) [18], [19], [20], [21]; (ii) consistent implementation of radiative electroweak symmetry breaking (loop corrections to the effective potential are included using the tadpole method) [22], [23], [24], [25]; (iii) calculation of the physical (pole) masses of the superparticles and Higgs bosons, including all relevant features such as the mixing between various states and the radiative corrections when important [26], [27], [28], [29], [30], [31], [32], [33], [34], [35].
The present version includes new options to read input files and write output files in the recently adopted format of the SUSY Les Houches Accord (SLHA) for interfacing the spectrum generators with other computer codes [36]. The code contains three types of source files: (i) the main subroutine suspect2.f together with a separate routine twoloophiggs.f for the two-loop radiative corrections in the Higgs sector, (ii) a separate calling routine file suspect2_call.f, and (iii) two possible input files suspect2.in (in the original SuSpect format) or suspect2_lha.in (in the SLHA format). Any choice and option is driven either from one of the two input files (which is sufficient and convenient when dealing with a few model points) or alternatively directly from the suspect2_call.f file, which also provides examples of calls for different model choices with all the necessary features (this option being useful when interfacing with other routines or when performing scans over the parameter space). The program has several flags which allow to select the model to be studied and its input parameters, the level of accuracy of the algorithm (e.g., the iterations for the RGEs and the convergence of the EWSB), the level of approximation in the calculation of the various (s)particle masses (e.g., inclusion or not of RC). Besides the fact that it is flexible, the code is self-contained (the default version includes all routines needed for the calculation), rather fast (thus allowing large scans of the parameter space) and can be easily linked to other routines or Monte-Carlo generators (e.g., to calculate branching ratios, cross sections, relic densities). All results, including comments when useful and some theoretical and experimental constraints, are found in the output file suspect2.out (in the original SuSpect format by default) or alternatively in the output file suspect2_lha.out, which are created at any run of the program. It is hoped that the code may be readily usable even without much prior knowledge of the MSSM.
This “users' manual” for the program, is organized as follows. In Section 2, we briefly discuss the main ingredients of the unconstrained and phenomenological MSSMs as well as the constrained models mSUGRA, AMSB and GMSB, to set the notations and conventions used in the program. In Section 3, we summarize the procedure for the calculation of the (s)particle spectrum: the soft SUSY-breaking terms (including the treatment of the input, the RG evolution and the implementation of EWSB), the physical particle masses (summarizing our conventions for the sfermion, gaugino and Higgs sectors). We also discuss the theoretical (CCB, UFB, fine-tuning) and experimental (electroweak precision observables, muon , branching fraction) constraints which can be imposed on the spectra, and how these are implemented in the code. In Section 4, we summarize the basic practical facts about the program and discuss the content of the input and output files with the possible choices; we then make a brief comparison with other existing codes, discuss the interface with other programs and how the program is maintained on the web. A conclusion will be given in Section 5. In Appendix A, the control parameters of the main routine and the important input and output commons in the program are explicited.
Section snippets
The constrained and unconstrained MSSMs
In this section, we summarize the basic assumptions which define the MSSM and the various constraints which can be imposed on it. This will also set the notations and conventions used in the program. We mainly focus on the unconstrained MSSM, the phenomenological MSSM with 22 free parameters, as well as on constrained models such as the minimal Supergravity (mSUGRA), anomaly mediated (AMSB) and gauge mediated (GMSB) supersymmetry breaking models.
The particle spectrum calculation with Suspect
In this section, we discuss our procedure for calculating the SUSY and Higgs particle spectrum. We will take as example the sophisticated cases of the constrained MSSMs with universal boundary conditions at the high scale, mSUGRA AMSB and GMSB, where all ingredients included in the SuSpect algorithm are present: RGEs, radiative EWSB and calculation of the physical particle masses. We first describe the general algorithm, then discuss the calculation of the soft SUSY-breaking terms, the
Basic facts about SuSpect
The program Suspect is composed of several files and routines:
- (i)
The input files suspect2.in (standard format) or alternatively suspect2_lha.in (the SLHA format): here one can select the model to be investigated, the accuracy of the algorithm, the input data (SM fermion masses and gauge couplings). Some reasonable default values are set in the example which is provided. One would then simply select the SUSY model (pMSSM, mSUGRA, GMSB and AMSB), choose the corresponding input parameters and
Conclusion
We have presented the version 2.3 of the Fortran code SuSpect which calculates the Supersymmetric and Higgs particle spectrum in the MSSM. The calculation can be performed in constrained models with universal boundary conditions at high scales such as the gravity (mSUGRA), anomaly (AMSB) or gauge (GMSB) mediated breaking models, but also in the non-universal or unconstrained MSSM case, with up to 22 free input parameters which can be set either at the electroweak symmetry breaking scale or
Acknowledgements
In its latest present version, the code SuSpect benefited largely from the invaluable help and many cross-checks of Pietro Slavich, in particular, in implementing a consistent interface with his routine for the calculation of the Higgs masses including the leading two-loop contributions. In former stages the code has been developed in the framework of the French working group (GDR-SUSY), organized by the Centre National de la Recherche Scientifique (CNRS), and has been checked and
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