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Two-loop renormalisation of the quark fields in the presence of four-fermion SMEFT operators

Claude Duhr, Giuseppe Ventura, Eleni Vryonidou

TL;DR

This work computes the two-loop renormalisation of quark fields and masses in the SMEFT when four-quark operators involving third-generation quarks are present. It performs the calculation in both NDR and BMHV gamma5 continuation schemes, providing renormalisation constants in the MSbar and on-shell schemes, and carefully accounting for evanescent operators and scheme-dependent finite counterterms. The authors deliver comprehensive results for the quark mass and field renormalisation, including the running of masses and the relations between MSbar and on-shell definitions, with cross-checks against existing LEFT results and explicit discussion of scheme choices. This advances the two-loop SMEFT program in QCD by supplying the necessary renormalisation inputs to enable precise phenomenological studies at this order.

Abstract

We compute the contributions of the dimension-6 SMEFT operators involving four third-generation quarks to the two-loop renormalisation of the quark fields and masses. We perform the computations in both the Naive Dimensional Regularisation (NDR) and the Breitenlohner-Maison-`t Hooft-Veltman (BMHV) schemes, and we present results for all relevant field and mass renormalisation constants in the on-shell and MS-bar schemes. We carefully discuss all scheme choices which affect the final results. This completes the computation of field and mass renormalisation constants relevant for two-loop computations in QCD involving dimension-six SMEFT operators.

Two-loop renormalisation of the quark fields in the presence of four-fermion SMEFT operators

TL;DR

This work computes the two-loop renormalisation of quark fields and masses in the SMEFT when four-quark operators involving third-generation quarks are present. It performs the calculation in both NDR and BMHV gamma5 continuation schemes, providing renormalisation constants in the MSbar and on-shell schemes, and carefully accounting for evanescent operators and scheme-dependent finite counterterms. The authors deliver comprehensive results for the quark mass and field renormalisation, including the running of masses and the relations between MSbar and on-shell definitions, with cross-checks against existing LEFT results and explicit discussion of scheme choices. This advances the two-loop SMEFT program in QCD by supplying the necessary renormalisation inputs to enable precise phenomenological studies at this order.

Abstract

We compute the contributions of the dimension-6 SMEFT operators involving four third-generation quarks to the two-loop renormalisation of the quark fields and masses. We perform the computations in both the Naive Dimensional Regularisation (NDR) and the Breitenlohner-Maison-`t Hooft-Veltman (BMHV) schemes, and we present results for all relevant field and mass renormalisation constants in the on-shell and MS-bar schemes. We carefully discuss all scheme choices which affect the final results. This completes the computation of field and mass renormalisation constants relevant for two-loop computations in QCD involving dimension-six SMEFT operators.
Paper Structure (24 sections, 77 equations, 5 tables)

This paper contains 24 sections, 77 equations, 5 tables.

Table of Contents

  1. Introduction
  2. Four-quark operators of the third generation in the SMEFT
  3. The QCD sector of the SMEFT
  4. Basis definition and Fierz-evanescent operators
  5. The choice of regularisation scheme
  6. Summary of our choices of regularisation schemes
  7. Two-loop self-energy amplitudes
  8. One-loop results
  9. Off-shell reduction and renormalisation
  10. On-shell reduction and renormalisation
  11. Results in the NDR-scheme
  12. Evanescent operators
  13. Running of the quark masses
  14. The on-shell scheme
  15. The relation between the $\overline{\textrm{MS}}$ and on-shell masses
  16. ...and 9 more sections