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

TL;DR

The paper develops an effective-field-theory framework to compute finite-width contributions in unstable-particle production at hadron colliders, organizing amplitudes in a gauge-invariant expansion in $\delta = \Gamma_X/m_X$ and resumming the width in the EFT propagator. It applies the formalism to top-quark pair production in the $q\bar q$ channel, showing that inclusive cross sections are only mildly affected by finite-width effects, while differential distributions near kinematic edges can receive sizable corrections. The work details the separation of hard matching coefficients from soft, non-factorizable dynamics and discusses real-correction handling via a strict $\delta$-expansion, with explicit comparisons to the narrow-width and complex-mass approaches. It also analyzes mass-scheme choices (pole vs PS) and their impact on top-mass extraction, highlighting scheme-dependent ambiguities and practical prescriptions for robust determinations.

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 $Γ_X/m_X$, with $Γ_X$ 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 $\sim Γ_t/m_t \sim 1%$. 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.

Figures (18)

• Figure 1: Feynman-diagram topologies contributing to the process $i_1 i_2 \rightarrow f_1 f_2$. (a) resonant production through an intermediate unstable $X$; (b) non-resonant production.
• Figure 2: Correspondence between the expansion by regions and the EFT calculation: the hard-region contribution (top left) corresponds to a ${\cal O}(\alpha_s)$ correction to the production matching coefficient $C_{i,P}$ (top right), while the soft-region contribution (bottom left) reproduces one-loop soft-gluon corrections in the EFT (bottom right).
• Figure 3: Examples of triangle and box diagrams contributing to the production and decay of the scalar $X$ at one loop.
• Figure 4: Real gluonic corrections to the process $i_1 i_2 \rightarrow f_1 f_2$.
• Figure 5: Leading tree-level doubly-resonant contribution to $q \bar{q} \rightarrow b \bar{b} W^+ W^-$ in the SM and its EFT counterpart. The grey square and circles represent EFT production and decay matching coefficients.