Automatic Calculation of supersymmetric Renormalization Group Equations and Self Energies

Abstract: SARAH is a Mathematica package for studying supersymmetric models. It calculates for a given model the masses, tadpole equations and all vertices at tree-level. Those information can be used by \SARAH to write model files for CalcHep/CompHep or FeynArts/FormCalc. In addition, the second version of SARAH can derive the renormalization group equations for the gauge couplings, parameters of the superpotential and soft-breaking parameters at one and two-loop level. Furthermore, it calculates the one-loop self energies and the one-loop corrections to the tadpoles. SARAH can handle all N=1 SUSY models whose gauge sector is a direct product of SU(N) and U(1) gauge groups. The particle content of the model can be an arbitrary number of chiral superfields transforming as any irreducible representation with respect to the gauge groups. To implement a new model, the user has just to define the gauge sector, the particle, the superpotential and the field rotations to mass eigenstates.

• The paper introduces SARAH, a Mathematica package that automates the computation of mass spectra, vertices, and RGEs at one- and two-loop levels.
• It details the generation of model files for popular tools like CalcHep and FeynArts, streamlining SUSY phenomenological analyses.
• SARAH significantly reduces computational time, enabling efficient exploration of complex SUSY scenarios and parameter spaces.

Overview of SARAH: Computation of Supersymmetric RGEs and Loop Corrections

The paper presents SARAH, a sophisticated Mathematica package aimed at automating the calculation of several crucial aspects of supersymmetric models. This tool addresses the intricacies involved in deriving masses, vertices, renormalization group equations (RGEs), and loop corrections in supersymmetric (SUSY) theories, enhancing computational efficiency and accuracy. This essay provides an analytical overview of SARAH’s capabilities, its implications for theoretical and practical advancements in SUSY phenomenology, and potential future developments.

Functionality and Features

SARAH is engineered to handle the complexities of various $N=1$ SUSY models, underpinned by gauge sectors composed of direct products of $SU(N)$ and $U(1)$ groups. The key functionalities include:

• Mass Spectrum and Vertices Calculation: At tree-level, SARAH computes the complete mass spectrum, tadpole equations, and all vertices, providing essential data for simulations and theoretical validations.
• Generation of Model Files: SARAH seamlessly integrates with external software like CalcHep/CompHep and FeynArts/FormCalc, generating model files that aid in the exploration of particle interactions and decay processes.
• RGEs at One- and Two-loop Levels: A significant advancement in this version of SARAH is the ability to derive RGEs for gauge couplings, superpotential parameters, and soft-breaking terms at the one- and two-loop levels. This capability is critical for investigating the energy scale dependence of SUSY parameters.
• One-loop Corrections: SARAH provides one-loop corrections to tadpoles and particle self-energies, incorporating quantum corrections into the physical spectrum, vital for precision physics predictions.

Numerical Performance

SARAH exhibits impressive computational efficiency. For example, on an Intel Q8200 processor, the complete Lagrangian is computed in 12 seconds, while the RGEs take 50 seconds at two-loop precision. This performance is a testament to SARAH’s optimization, making it a desirable tool for researchers dealing with complex SUSY models.

Theoretical and Practical Implications

The ability to systematically test and simulate beyond the Standard Model scenarios fosters the understanding of potential SUSY signatures at colliders such as the Large Hadron Collider (LHC). SARAH’s capability to model a wide range of SUSY scenarios—including those beyond the Minimal Supersymmetric Standard Model (MSSM)—paves the way for exploring phenomenological implications of non-minimal SUSY frameworks.

One of the most profound theoretical implications is SARAH’s contribution to the study of radiative electroweak symmetry breaking. By providing intricate details of RGEs and loop corrections, researchers can gain insights into the viable parameter spaces of SUSY models that are consistent with observed electroweak parameters.

Future Prospects and Developments

The continual evolution of SARAH is likely to focus on extending its capabilities to more exotic SUSY models and integrating higher-order loop corrections. There is also potential for incorporating non-supersymmetric or partially supersymmetric cases, broadening its applicability to diverse theoretical frameworks.

Moreover, as experimental collaborations release more data, SARAH’s detailed outputs can aid in comparing theoretical predictions with experimental results, potentially paving the way for breakthroughs in identifying SUSY particles.

Conclusion

SARAH stands out as a robust tool, advancing the automation of complex calculations required for supersymmetric models. By significantly reducing the manual workload and potential for error in deriving RGEs and quantum corrections, SARAH fosters deeper investigations into the phenomenology of SUSY models. Its ongoing development promises further enhancements in precision theoretical physics, aligning closely with experimental data to explore and validate potential extensions to the Standard Model.