Effective four-fermion operators in top physics: a roadmap

TL;DR

This paper establishes a comprehensive basis for dimension-six four-fermion operators involving top quarks, classifies their contributions, and calculates various top decay and production processes, providing a detailed framework for new physics searches.

Contribution

It introduces a minimal, simplified basis for four-fermion operators and systematically computes their effects on top quark decays and production processes, including interference with the Standard Model.

Findings

Calculated all relevant top decay widths mediated by four-fermion operators.

Derived cross sections for single and pair top production in various collider settings.

Provided a general framework without specific assumptions on operator coefficients.

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.