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Effective four-fermion operators in top physics: a roadmap

J. A. Aguilar-Saavedra

TL;DR

The paper builds a minimal, gauge-invariant basis for dimension-6 four-fermion operators and classifies all contributions involving one or two top quarks. It then computes top three-body decays, single-top, and top-pair production observables in pp, p p̄, and e^+e^− collisions, including SM, interference, and quadratic EFT terms, with results expressed through compact, process-mapped coefficient tables. The work provides a practical, symmetry-aware framework and ready-to-use formulas to probe heavy new physics in the top sector at current and future colliders, highlighting when quadratic EFT effects dominate and how to relate observables across channels. This offers a valuable reference for model-independent EFT analyses and guides experimental sensitivity studies at the LHC and future linear colliders.

Abstract

We write down a minimal basis for dimension-six gauge-invariant four-fermion operators, with some operator replacements with respect to previous ones which make it simpler for calculations. Using this basis we classify all four-fermion operator contributions involving one or two top quarks. Taking into account the different fermion chiralities, possible colour contractions and independent flavour combinations, a total number of 572 gauge-invariant operators are involved. We apply this to calculate all three-body top decay widths t -> d_k u_i dbar_j, t -> d_k e_i+ nu_j, t -> u_k u_i ubar_j, t -> u_k e_j+ e_i-, t -> u_k nu_j nu_i (with i,j,k generation indices) mediated by dimension-six four-fermion operators, including the interference with the Standard Model amplitudes when present. All single top production cross sections in pp, p pbar and e+ e- collisions are calculated as well, namely u_i d_k -> d_j t, dbar_j d_k -> ubar_i t, u_i dbar_j -> dbar_k t, u_i u_k -> u_j t, u_i ubar_j -> ubar_k t, e+ e- -> ubar_k t and the charge conjugate processes. We also compute all top pair production cross sections, ubar_i u_j -> t tbar, dbar_i d_j -> t tbar, u_i u_j -> t t and e+ e- -> t tbar. Our results are completely general, without assuming any particular relation among effective operator coefficients.

Effective four-fermion operators in top physics: a roadmap

TL;DR

The paper builds a minimal, gauge-invariant basis for dimension-6 four-fermion operators and classifies all contributions involving one or two top quarks. It then computes top three-body decays, single-top, and top-pair production observables in pp, p p̄, and e^+e^− collisions, including SM, interference, and quadratic EFT terms, with results expressed through compact, process-mapped coefficient tables. The work provides a practical, symmetry-aware framework and ready-to-use formulas to probe heavy new physics in the top sector at current and future colliders, highlighting when quadratic EFT effects dominate and how to relate observables across channels. This offers a valuable reference for model-independent EFT analyses and guides experimental sensitivity studies at the LHC and future linear colliders.

Abstract

We write down a minimal basis for dimension-six gauge-invariant four-fermion operators, with some operator replacements with respect to previous ones which make it simpler for calculations. Using this basis we classify all four-fermion operator contributions involving one or two top quarks. Taking into account the different fermion chiralities, possible colour contractions and independent flavour combinations, a total number of 572 gauge-invariant operators are involved. We apply this to calculate all three-body top decay widths t -> d_k u_i dbar_j, t -> d_k e_i+ nu_j, t -> u_k u_i ubar_j, t -> u_k e_j+ e_i-, t -> u_k nu_j nu_i (with i,j,k generation indices) mediated by dimension-six four-fermion operators, including the interference with the Standard Model amplitudes when present. All single top production cross sections in pp, p pbar and e+ e- collisions are calculated as well, namely u_i d_k -> d_j t, dbar_j d_k -> ubar_i t, u_i dbar_j -> dbar_k t, u_i u_k -> u_j t, u_i ubar_j -> ubar_k t, e+ e- -> ubar_k t and the charge conjugate processes. We also compute all top pair production cross sections, ubar_i u_j -> t tbar, dbar_i d_j -> t tbar, u_i u_j -> t t and e+ e- -> t tbar. Our results are completely general, without assuming any particular relation among effective operator coefficients.

Paper Structure

This paper contains 21 sections, 60 equations, 1 figure, 28 tables.

Table of Contents

  1. Introduction
  2. Four-fermion operator basis
  3. Four-fermion contributions
  4. Four-fermion terms $t \bar{b} \bar{u}_i d_j$, $t \bar{t} \bar{u}_i u_j$, $t \bar{t} \bar{d}_i d_j$
  5. Four-fermion terms $t \bar{b} e_i \bar{\nu}_j$, $t \bar{t} e_i \bar{e}_j$, $t \bar{t} \nu_i \bar{\nu}_j$
  6. Four-fermion terms $t \bar{d}_k \bar{u}_i d_j$, $t \bar{u}_k \bar{u}_i u_j$, $t t \bar{u}_k \bar{u}_i$
  7. Four-fermion terms $t \bar{d}_k e_i \bar{\nu}_j$, $t \bar{u}_k e_i \bar{e}_j$, $t \bar{u}_k \nu_i \bar{\nu}_j$
  8. Top decay widths
  9. $t \to d_k u_i \bar{d}_j$
  10. $t \to d_k e_i^+ \nu_j$
  11. $t \to u_k u_i \bar{u}_j$
  12. $t \to u_k e_i^+ e_j^-$ and $t \to u_k \bar{\nu}_i \nu_j$
  13. Single top production
  14. Charged current processes in $pp$, $p \bar{p}$ collisions
  15. Flavour-changing neutral processes in $pp$, $p \bar{p}$ collisions
  16. ...and 6 more sections

Figures (1)

  • Figure 1: Normalised $u \bar{d}$ invariant mass distribution for the decay $t \to b u \bar{d}$ within the SM and with $C_{qq'}^{3113} = 10$, $\Lambda = 1$ TeV.