Source-linked AI summary
SuperIso: A program for calculating the isospin asymmetry of B -> K* gamma in the MSSM
F. Mahmoudi
TL;DR
The paper addresses the need for restrictive and complementary observables of supersymmetric parameter space in rare b →sγ decays. It introduces SuperIso, which calculates B →K∗γ isospin asymmetry in the MSSM using the stated calculation framework and also computes the inclusive branching ratio. The package is tested against literature and other calculations, while the results show that isospin breaking can strongly constrain supersymmetric parameters, especially at high tan β.
Problem
Rare b →sγ decays are used to constrain supersymmetric parameter space, but the paper focuses on adding isospin asymmetry as a complementary observable to the inclusive branching ratio.
Method
SuperIso calculates B →K∗γ isospin symmetry breaking in the MSSM with minimal flavor violation for mSUGRA, AMSB, GMSB, or SLHA inputs, and computes the inclusive branching ratio for comparison.
Results
Isospin symmetry breaking can strongly constrain supersymmetric parameter space, especially for high tan β, while the code shows globally good agreement with literature and micrOMEGAS calculations.
Takeaways & Limitations
The package enables comparison between constraints from B →K∗γ isospin asymmetry and the inclusive B →Xsγ branching ratio across supported supersymmetric parameter spaces.
Takeaways & Limitations
The calculation includes a logarithmically divergent integral parameterized by X, with its phase arbitrary and Λh ≈0.5 GeV treated as a typical hadronic scale.
Abstract
from arXiv · showhide
We present a program for calculating the isospin symmetry breaking of the B -> K* gamma decay in the MSSM with minimal flavor violation. This program calculates the NLO supersymmetric contributions to the isospin asymmetry, using the effective Hamiltonian approach and within the QCD factorization method. We show that isospin symmetry breaking proves to be a very restrictive observable, in particular in the mSUGRA parameter space. The program also calculates the inclusive branching ratio associated to b -> s gamma transition, as a comparison reference.
1 Introduction
The paper motivates studying supersymmetry and rare b →sγ decays, then introduces SuperIso to calculate B →K∗γ isospin breaking and compare it with the inclusive branching ratio.
- Supersymmetry is presented as a motivated framework for addressing theoretical problems beyond the Standard Model, including the hierarchy and dark matter/energy problems.
- The MSSM with minimal flavor violation is considered, with supersymmetry breaking scenarios reducing the model’s free parameters for phenomenological studies.
- Rare B decays, especially b →sγ transitions, constrain supersymmetric parameter space through the inclusive branching ratio and the complementary isospin asymmetry.
- SuperIso calculates isospin symmetry breaking for mSUGRA, AMSB, and GMSB, supports user-provided models, and also computes the inclusive branching ratio for comparison.
- The paper summarizes the calculation, describes the package and its use, and presents results in a later section.
2 Calculation of the isospin symmetry breaking
The calculation uses the leading-order isospin-asymmetry expression and related spectator-dependent quantities, Wilson coefficients, hard-scattering functions, and meson distribution amplitudes. SuperIso implements these equations to calculate the asymmetry and the inclusive branching ratio.
- The isospin asymmetry Δ0− is calculated from the leading-order expression and spectator-dependent coefficients bq.
- The functions K1 and K2q are expressed through Wilson coefficients Ci evaluated at the scale μb, with N = 3 and CF = 4/3 as color factors.
- The needed numerical parameters are summarized in Table 1, while convolution integrals and the logarithmically divergent integral are parameterized using X and Λh ≈0.5 GeV.
- The Wilson-coefficient convention adopted follows references, in which C1 and C2 are inverted relative to reference.
- The calculation uses hard-scattering functions, light-cone and B-meson distribution amplitudes, and the parameter λB associated with the first negative moment of ΦB1.
- SuperIso applies these equations to calculate the B →K∗γ isospin asymmetry and uses relations from earlier work for the inclusive branching ratio.
3 Content of the SuperIso package
SuperIso is a modular C99 package that computes B → K*γ isospin asymmetry and inclusive b → sγ branching ratios across major SUSY-breaking scenarios.
- Package overview: SuperIso calculates B → K*γ isospin symmetry breaking in the MSSM with minimal flavor violation.The package is implemented as a C program respecting the C99 standard.
- Supported scenarios: The package supports mSUGRA, AMSB, and GMSB calculations through ISAJET and/or SOFTSUSY mass-spectrum and coupling generation.These routines return SLHA files containing the generated model information.
- Calculation pipeline: Its calculation pipeline scans an SLHA file, computes the required Wilson coefficients, and evaluates the isospin asymmetry.The delta0_calculator routine combines initialization, SLHA reading, Wilson-coefficient calculation, and the final asymmetry computation.
- Extensibility: Users can extend the modular package with their own models or observables, provided model inputs follow SUSY Les Houches Accord conventions.The shared routines include SLHA scanning and Wilson-coefficient calculations.
- Additional routines: The package also computes the inclusive b → sγ branching ratio and checks whether the LSP is charged or a parameter point violates collider mass constraints.For a gravitino LSP, the charged-particle check is applied to the NLSP.
4 Compilation and installation instructions
The package provides source code, build files, sample programs, and an example SLHA input for installation and testing.
- Installation files: The distribution contains the src/ directory, Makefile, README, five sample main programs, and an example SLHA input file.The package is downloaded and unpacked into a main directory named superiso_vX.X.
- Example program: main_example.x runs hardcoded test points and can serve as a basis for writing a user-defined main program.It demonstrates calculations using generated spectra, an SLHA file, or directly supplied Standard Model inputs.
- SLHA workflow: slha.x calculates the isospin asymmetry and inclusive branching ratio from a supplied SLHA file.The SLHA filename is passed as an input parameter.
- Scenario programs: amsb.x, gmsb.x, and msugra.x first generate mass spectra and couplings with SOFTSUSY and/or ISAJET before calculating both observables.The programs accept the usual scenario-specific input parameters.
5 Sample input and output
The sample programs accept SUSY-breaking parameters or SLHA files, calculate the observables, and report input-reading or parameter-space checks.
- Output interpretation: A zero isospin-asymmetry or branching-ratio output indicates an SLHA-reading problem or an improperly generated or formatted SLHA file.The file must be generated by ISAJET or SOFTSUSY or conform to the SLHA format.
- mSUGRA: msugra.x generates observables from mSUGRA inputs and checks collider mass exclusions and whether the LSP is charged.Its required inputs include m0, m1/2, A0, and tan β.
- Command examples: The sample commands illustrate direct execution of the mSUGRA, AMSB, and GMSB programs with numerical parameters.Examples include ./msugra.x 500 500 0 50, ./amsb.x 400 10000 30 -1, and ./gmsb.x 60000 80000 5 50.
- AMSB: amsb.x generates observables from AMSB inputs and checks experimental mass exclusions.Its required inputs include m0 and m3/2, with tan β also specified among the parameters.
- GMSB: gmsb.x generates observables from GMSB inputs supplied to SOFTSUSY.The listed inputs include Λ, N5, tan β, and the optional cGrav parameter.
6 Results
SuperIso agrees well with existing Standard Model and micrOMEGAS calculations, while its isospin-asymmetry results strongly constrain SUSY parameter space at high tan β.
- Validation: The code shows globally good agreement with literature calculations of the Standard Model isospin asymmetry and with micrOMEGAS Wilson coefficients and inclusive branching ratios.These comparisons cover both the isospin-asymmetry calculation and b → sγ observables.
- Parameter-space constraints: Isospin symmetry breaking can strongly constrain supersymmetric parameter space, especially for high tan β.Figure 1 presents this dependence in the mSUGRA and AMSB parameter spaces.
7 Conclusion
SuperIso calculates B → K*γ isospin asymmetry in the MSSM with minimal flavor violation and compares its constraints with those from B → X_sγ branching ratios.
- SuperIso calculates the B → K*γ isospin asymmetry for any SLHA-format parameter file.
- The package can generate SLHA parameter files in the mSUGRA, AMSB, and GMSB scenarios using ISAJET or SOFTSUSY.
- It also computes the inclusive B → X_sγ branching ratio to compare constraints on supersymmetric parameters from the two observables.