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A minimal set of top anomalous couplings

J. A. Aguilar-Saavedra

TL;DR

The paper shows that, when encoded in a gauge-invariant dimension-six effective-operator framework, all top-quark trilinear couplings to W, Z, photon, and gluon (including off-shell fermions) can be described by a minimal set of $\gamma^\mu$ and $\sigma^{\mu\nu} q_\nu$ interactions. By systematically applying equations of motion and identifying redundant operators, the author reduces the operator basis and associated quartic terms, yielding simplified, independent couplings for $Wtb$, $Ztt$, $\gamma tt$, $gtt$ and the flavor-changing counterparts $Ztc$, $\gamma tc$, $gtc$. The work provides explicit expressions linking the couplings to dimension-six operator coefficients and discusses how measurements of anomalous couplings could, in principle, determine these coefficients, enabling a more economical interpretation of future collider data. This framework enhances both theoretical clarity and practical feasibility for top-quark EFT analyses and Monte Carlo implementations. Overall, the paper delivers a streamlined, gauge-consistent parameterization with reduced complexity and clear pathways to extract new-physics information from experimental results.

Abstract

We simplify the general form of the fermion-fermion-gauge boson interactions generated by dimension-six gauge-invariant effective operators by using the equations of motion to remove redundant operators. It is found that the most general vertex for off-shell fermions fi, fj and an off-shell boson V=W,Z,gamma,g only involves gamma^mu and sigma^{mu nu} q_nu terms, with q=p_i-p_j. Examples are given for the Wtb, Ztt, gamma tt and gtt interactions, whose general expression is greatly simplified with respect to previous results in the literature. The same arguments apply to top flavour-changing neutral interactions with the Z boson, the photon or the gluon, which can also be parameterised in full generality with only gamma^mu and sigma^{mu nu} q_nu couplings. Explicit expressions are given for these vertices in terms of dimension-six gauge-invariant operators. We also discuss how effective operator coefficients might be determined from eventual measurements of anomalous couplings.

A minimal set of top anomalous couplings

TL;DR

The paper shows that, when encoded in a gauge-invariant dimension-six effective-operator framework, all top-quark trilinear couplings to W, Z, photon, and gluon (including off-shell fermions) can be described by a minimal set of and interactions. By systematically applying equations of motion and identifying redundant operators, the author reduces the operator basis and associated quartic terms, yielding simplified, independent couplings for , , , and the flavor-changing counterparts , , . The work provides explicit expressions linking the couplings to dimension-six operator coefficients and discusses how measurements of anomalous couplings could, in principle, determine these coefficients, enabling a more economical interpretation of future collider data. This framework enhances both theoretical clarity and practical feasibility for top-quark EFT analyses and Monte Carlo implementations. Overall, the paper delivers a streamlined, gauge-consistent parameterization with reduced complexity and clear pathways to extract new-physics information from experimental results.

Abstract

We simplify the general form of the fermion-fermion-gauge boson interactions generated by dimension-six gauge-invariant effective operators by using the equations of motion to remove redundant operators. It is found that the most general vertex for off-shell fermions fi, fj and an off-shell boson V=W,Z,gamma,g only involves gamma^mu and sigma^{mu nu} q_nu terms, with q=p_i-p_j. Examples are given for the Wtb, Ztt, gamma tt and gtt interactions, whose general expression is greatly simplified with respect to previous results in the literature. The same arguments apply to top flavour-changing neutral interactions with the Z boson, the photon or the gluon, which can also be parameterised in full generality with only gamma^mu and sigma^{mu nu} q_nu couplings. Explicit expressions are given for these vertices in terms of dimension-six gauge-invariant operators. We also discuss how effective operator coefficients might be determined from eventual measurements of anomalous couplings.

Paper Structure

This paper contains 21 sections, 82 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Effective operator equalities
  3. Equalities for $O_{qW}^{ij}$, $O_{qB}^{ij}$, $O_{uB}^{ij}$, $O_{qG}^{ij}$ and $O_{uG}^{ij}$
  4. Equalities for $O_{Du}^{ij}$, $O_{\bar{D}u}^{ij}$, $O_{Dd}^{ij}$ and $O_{\bar{D}d}^{ij}$
  5. General $Wtb$, $Ztt$, $\gamma tt$ and $gtt$ interactions
  6. $Wtb$ vertex
  7. $Ztt$ vertex
  8. $\gamma tt$ vertex
  9. $gtt$ vertex
  10. Determination of effective operator coefficients
  11. General top flavour-changing interactions
  12. $Ztc$ vertex
  13. $\gamma tc$ vertex
  14. $gtc$ vertex
  15. Determination of effective operator coefficients
  16. ...and 6 more sections

Figures (1)

  • Figure 1: Left: Feynman diagram for single top production in the $u \bar{d} \to t \bar{b}$ process. Center, right: diagrams contributing to $gb \to tW^-$.