Finite-width effects in unstable-particle production at hadron colliders

TL;DR

This paper introduces a systematic, gauge-invariant formalism for calculating finite-width effects in unstable-particle production at hadron colliders, demonstrated through top-antitop production at NLO, revealing small effects on total cross sections but significant impacts on certain distributions.

Contribution

The paper develops a gauge-invariant effective-theory framework for including finite-width effects in unstable-particle production, reducing computational complexity compared to full complex-mass calculations.

Findings

Finite-width effects are small (~1%) for total cross sections.

Finite-width effects can exceed 10% near kinematic edges.

Results depend on the mass renormalization scheme, affecting top-quark mass extraction.

Abstract

We present a general formalism for the calculation of finite-width contributions to the differential production cross sections of unstable particles at hadron colliders. In this formalism, which employs an effective-theory description of unstable-particle production and decay, the matrix element computation is organized as a gauge-invariant expansion in powers of $\Gamma_X/m_X$, with $\Gamma_X$ and $m_X$ the width and mass of the unstable particle. This framework allows for a systematic inclusion of off-shell and non-factorizable effects whilst at the same time keeping the computational effort minimal compared to a full calculation in the complex-mass scheme. As a proof-of-concept example, we give results for an NLO calculation of top-antitop production in the $q \bar{q}$ partonic channel. As already found in a similar calculation of single-top production, the finite-width effects are small for the total cross section, as expected from the na\" ive counting $\sim \Gamma_t/m_t \sim 1%$. However, they can be sizeable, in excess of 10%, close to edges of certain kinematical distributions. The dependence of the results on the mass renormalization scheme, and its implication for a precise extraction of the top-quark mass, is also discussed.