PyR@TE 2: A Python tool for computing RGEs at two-loop

Abstract

Renormalization group equations are an essential tool for the description of theories accross different energy scales. Even though their expressions at two-loop for an arbitrary gauge field theory have been known for more than thirty years, deriving the full set of equations for a given model by hand is very challenging and prone to errors. To tackle this issue, we have introduced in [1] a Python tool called PyR@TE; Python Renormalization group equations @ Two-loop for Everyone. With PyR@TE, it is easy to implement a given Lagrangian and derive the complete set of two-loop RGEs for all the parameters of the theory. In this paper, we present the new version of this code, PyR@TE 2, which brings many new features and in particular it incorporates kinetic mixing when several $\mathrm{U}(1)$ gauge groups are involved. In addition, the group theory part has been greatly improved as we introduced a new Python module dubbed PyLie that deals with all the group theoretical aspects required for the calculation of the RGEs as well as providing very useful model building capabilities. This allows the use of any irreducible representation of the $\mathrm{SU}(n)$, $\mathrm{SO}(2n)$ and $\mathrm{SO}(2n+1)$ groups. % Furthermore, it is now possible to implement terms in the Lagrangian involving fields which can be contracted into gauge singlets in more than one way. As a byproduct, results for a popular model (SM+complex triplet) for which, to our knowledge, the complete set of two-loop RGEs has not been calculated before are presented in this paper. Finally, the two-loop RGEs for the anomalous dimension of the scalar and fermion fields have been implemented as well. It is now possible to export the coupled system of beta functions into a numerical C++ function, leading to a consequent speed up in solving them.

26 pages

References in corpus (13)

• SARAH 4: A tool for (not only SUSY) model builders
• Two-loop Renormalization Group Equations in General Gauge Field Theories
• Gauge Kinetic Mixing and Leptophobic $Z^{\prime }$ in $E_6$ and SO(10)
• A Renormalisation Group Equation Study of the Scalar Sector of the Minimal B-L Extension of the Standard Model
• PyR@TE: Renormalization Group Equations for General Gauge Theories
• Calculating the renormalisation group equations of a SUSY model with Susyno
• Constraints on Abelian Extensions of the Standard Model from Two-Loop Vacuum Stability and $U(1{)}_{B-L}$
• Renormalization group equations and matching in a general quantum field theory with kinetic mixing
• Renormalization Group Equations in Gauge Theories with Multiple U(1) Groups
• Higgs Vacuum Stability in $B-L$ extended Standard Model
• Implications of the Stability and Triviality Bounds on the Standard Model with Three and Four Chiral Generations
• Automation of non-SUSY two-loop RGEs with PyR@TE: latest developments
• On the impact of kinetic mixing in beta functions at two-loop

Cited by in corpus (38)

• Running in the ALPs
• LieART 2.0 -- A Mathematica Application for Lie Algebras and Representation Theory
• Higgs-mass predictions in the MSSM and beyond
• Dark Matter meets Quantum Gravity
• PyR@TE 3
• Revisiting RGEs for general gauge theories
• Correlating the anomalous results in $b\to s$ decays with inert Higgs doublet dark matter and muon $(g-2)$
• Roadmap of left-right models based on GUTs
• On three-loop RGE for the Higgs sector of 2HDM
• A minimal model of inflation and dark radiation
• Gauge Coupling Unification without Supersymmetry
• Constraints on anomalous dimensions from the positivity of the S-matrix
• Flavoured gauge extension of singlet-doublet fermionic dark matter: neutrino mass, high scale validity and collider signatures
• Neutrino masses, vacuum stability and quantum gravity prediction for the mass of the top quark
• Asymptotic safety and gauged baryon number
• Computing Tools for Effective Field Theories
• Exploring triplet-quadruplet fermionic dark matter at the LHC and future colliders
• Matching renormalisable couplings: simple schemes and a plot
• Scalar dark matter explanation of the DAMPE data in the minimal Left-Right symmetric model
• Asymptotically safe dark matter with gauged baryon number
• General RGEs for dimensionful couplings in the $\overline{\mathrm{MS}}$ scheme
• Impact of Fermionic Electroweak Multiplet Dark Matter on Vacuum Stability with One-loop Matching
• Naturally small neutrino mass with asymptotic safety and gravitational-wave signatures
• Realizing unification in two different SO(10) models with one intermediate breaking scale
• How robust are particle physics predictions in asymptotic safety?
• Large loop-coupling enhancement of a heavy pseudoscalar from a light dark sector
• The Techni-Pati-Salam Composite Higgs
• Vacuum Stability and Perturbativity of SU(3) Scalars
• Two-loop matching of renormalizable operators: general considerations and applications
• Modifying dark matter indirect detection signals by thermal effects at freeze-out
• Leading Two-loop corrections to the mass of Higgs boson in the High scale Dirac gaugino supersymmetry
• Automation of non-SUSY two-loop RGEs with PyR@TE: latest developments
• Multiple point principle in the general Two-Higgs-Doublet model
• Low-scale seesaw from neutrino condensation
• Fate of false vacuum in singlet-doublet fermion extension model with RG improved effective action
• ARGES -- Advanced Renormalisation Group Equation Simplifier
• Gauge Coupling Unification with Hidden Photon, and Minicharged Dark Matter
• $\text{RGE++}:$ A $\text{C++}$ library to solve renormalisation group equations in quantum field theory