Low-energy effective field theory below the electroweak scale: one-loop renormalization in the 't Hooft-Veltman scheme

Abstract

The low-energy effective field theory below the electroweak scale (LEFT) describes the effects at low energies of both the weak interaction and physics beyond the Standard Model. We study the one-loop renormalization of the LEFT in the 't Hooft-Veltman scheme, which offers an algebraically consistent definition of the Levi-Civita symbol and ${\gamma }_5$ in dimensional regularization. However, in connection with minimal subtraction this scheme leads to a spurious breaking of chiral symmetry in intermediate steps of the calculation. Based on the 't Hooft-Veltman prescription, we define a renormalization scheme that restores chiral symmetry by including appropriate finite counterterms. To this end, we extend the physical LEFT operator basis by a complete set of off-shell and one-loop-evanescent operators and we perform the renormalization at one loop. We determine the finite counterterms to the physical parameters that compensate both the insertions of evanescent operators, as well as the chiral-symmetry-breaking terms from the renormalizable part of the Lagrangian in $D$ dimensions. Our results can be applied in next-to-leading-log calculations in the 't Hooft-Veltman scheme: using our renormalization scheme instead of pure minimal subtraction separates the physical sector from the unphysical evanescent sector and leads to results that are manifestly free of spurious chiral-symmetry-breaking terms.

38 pages, 11 tables

References in corpus (8)

• Measurement of the permanent electric dipole moment of the neutron
• Renormalization-group evolution of new physics contributions to (semi)leptonic meson decays
• Compilation of low-energy constraints on 4-fermion operators in the SMEFT
• DsixTools 2.0: The Effective Field Theory Toolkit
• The $\mu \to e\gamma$ decay in a systematic effective field theory approach with dimension 6 operators
• General neutrino interactions with sterile neutrinos in light of coherent neutrino-nucleus scattering and meson invisible decays
• Dimensional Regularization and Breitenlohner-Maison / 't Hooft-Veltman Scheme for ${\gamma }_5$ applied to Chiral YM Theories: Full One-Loop Counterterm and RGE Structure
• One-loop matching of the $CP$-odd three-gluon operator to the gradient flow

Cited by in corpus (8)

• On sum rules for semi-leptonic $b\to c$ and $b\to u$ decays
• Renormalization-group equations of the LEFT at two loops: dimension-six baryon-number-violating operators
• Renormalization-group equations of the LEFT at two loops: dimension-five effects
• Renormalization-group equations of the LEFT at two loops: dimension-six operators
• Baryon Number Violation: From Nuclear Matrix Elements to BSM Physics
• Symmetry Restoration in the SMEFT: Finite Counterterms for a Non-Anticommuting ${\gamma }_5$
• Two loops, four tops and two ${\gamma }_5$ schemes: a renormalization story
• One-loop matching of the LEFT to the QCD gradient flow