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Anomalous Dimension of a General Effective Gauge Theory II: Fermionic Sector

Jason Aebischer, Luigi C. Bresciani, Nudzeim Selimovic

TL;DR

The paper completes the one-loop RGE program for general EFTs by deriving the fermionic sector's anomalous dimensions and their mixing with bosonic operators up to mass dimension six, using an on-shell unitarity framework. It builds on prior bosonic results to provide a full template of RGEs valid for arbitrary gauge groups and field content, including 1/Λ^2 corrections. The work delivers explicit operator-class running across phi^6, D^2 phi^4, F^3, psi^4, with extensive cross-class mixing, and details the running of all renormalizable couplings (gauge, scalar quartic/trilinear, Yukawa, masses). This framework enables straightforward matching to specific EFTs and supports future automation with RGE solvers, offering a comprehensive tool for beyond-Standard-Model phenomenology in a model-independent setting.

Abstract

The complete set of one-loop anomalous dimensions for general Effective Field Theories (EFTs) is derived using on-shell methods. Combined with previous findings for the bosonic sector, the obtained results conclude the computation of the complete set of leading order Renormalization Group Equations (RGEs) in arbitrary gauge EFTs containing scalar and fermion fields. Renormalization effects are consistently taken into account at the order $1/Λ^2$ in the new physics scale $Λ$ for all renormalizable and non-renormalizable couplings. The obtained template RGEs include operator mixing across different dimensions and are valid for arbitrary gauge groups.

Anomalous Dimension of a General Effective Gauge Theory II: Fermionic Sector

TL;DR

The paper completes the one-loop RGE program for general EFTs by deriving the fermionic sector's anomalous dimensions and their mixing with bosonic operators up to mass dimension six, using an on-shell unitarity framework. It builds on prior bosonic results to provide a full template of RGEs valid for arbitrary gauge groups and field content, including 1/Λ^2 corrections. The work delivers explicit operator-class running across phi^6, D^2 phi^4, F^3, psi^4, with extensive cross-class mixing, and details the running of all renormalizable couplings (gauge, scalar quartic/trilinear, Yukawa, masses). This framework enables straightforward matching to specific EFTs and supports future automation with RGE solvers, offering a comprehensive tool for beyond-Standard-Model phenomenology in a model-independent setting.

Abstract

The complete set of one-loop anomalous dimensions for general Effective Field Theories (EFTs) is derived using on-shell methods. Combined with previous findings for the bosonic sector, the obtained results conclude the computation of the complete set of leading order Renormalization Group Equations (RGEs) in arbitrary gauge EFTs containing scalar and fermion fields. Renormalization effects are consistently taken into account at the order in the new physics scale for all renormalizable and non-renormalizable couplings. The obtained template RGEs include operator mixing across different dimensions and are valid for arbitrary gauge groups.

Paper Structure

This paper contains 147 sections, 156 equations, 3 tables.

Table of Contents

  1. Introduction
  2. General effective gauge theory
  3. Renormalizable interactions
  4. Dimension-5 operators
  5. Dimension-6 operators
  6. Review of the method
  7. Results
  8. Running of dimension-6 operators
  9. phi6 class
  10. $\phi^6 \leftarrow \phi^6$:
  11. phi6frompsi2phi3:
  12. phi6frompsi2phi2xpsi2phi2:
  13. phi6frompsi2phi2xphi5:
  14. D2phi4 class
  15. $D^2\phi^4 \leftarrow D^2\phi^4$:
  16. ...and 132 more sections