On three-loop RGE for the Higgs sector of 2HDM

Abstract

We discuss renormalization group equations (RGE) for the parameters of the Higgs sector in general Two-Higgs-Doublet Model (2HDM). We present the three-loop results but consider only contributions due to self-couplings of the Higgs doublets. We study the structure of RGE and express beta-functions in terms of reparametrization invariants with respect to higgs-basis rotations. The Cayley-Hamilton theorem is utilized to reduce both the number of independent tensor structures in matrix RGE and the number of invariants to a minimal set. As a by-product of our calculation we discovered that two-loop RGE of the scalar sector in general QFT with multiple higgses were not properly implemented in a number of public packages. The latter give rise to a wrong result when mixing in the scalar sector is allowed.

21 pages, results can be found in ancillary files, matches published version

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• MSSM Higgs Benchmark Scenarios for Run 2 and Beyond: the low $\tan \beta$ region
• Four-Loop Gauge and Three-Loop Yukawa Beta-Functions in a General Renormalizable Theory
• Systematic construction of basis invariants in the 2HDM
• Flavor Invariants and Renormalization-group Equations in the Leptonic Sector with Massive Majorana Neutrinos
• Quartic Coupling Unification in the Maximally Symmetric 2HDM
• General scalar renormalisation group equations at three-loop order
• $Z_2$ breaking effects in 2-loop RG evolution of 2HDM
• Matching renormalisable couplings: simple schemes and a plot
• Towards general scalar-Yukawa renormalisation group equations at three-loop order
• 2 Higgs Doublet Model Evolver -- Manual
• Two-loop matching of renormalizable operators: general considerations and applications
• The invariant space of multi-Higgs doublet models
• Minima of Classically Scale-Invariant Potentials
• Scalar Kinetic Mixing and the Renormalization Group
• Muon Electric Dipole Moment as a Probe of Flavor-Diagonal CP Violation
• A fully basis invariant Symmetry Map of the 2HDM
• The general Two-Higgs Doublet Model in a gauge-invariant form
• GOOFy -- a systematic approach
• The Hilbert Series and the Flavor Invariants of the 3HDM
• Flavour Invariants of the N Higgs Doublet Model