Abstract
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\overline{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 naïve counting ~ Γ t /m t ~ 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.
Highlights
Most of the phenomenologically interesting processes at the LHC, such as W and Z boson production, top-quark production and Higgs production, not to mention beyondthe-Standard-Model (BSM) processes, like supersymmetric (SUSY) particle production, involve massive unstable particles
We present a general formalism for the calculation of finite-width contributions to the differential production cross sections of unstable particles at hadron colliders
Non-negligible off-shell effects (∼ 10%) were observed even in light Higgs production and decay to massive vector bosons [5, 6], and shown to arise from Higgs-continuum interference at large values of the boson-pair invariant mass. While these off-shell effects can be suppressed by means of suitable experimental cuts, and are not relevant to present Higgs measurements at the LHC, they show that the error associated with the narrow-width approximation (NWA) can be significantly larger than its naıve estimate
Summary
The effective-theory framework for the description of unstable-particle production used in this work was first formulated for the total cross section in ref. [15] and applied to the case of inclusive W +W − production at an e+e− collider in refs. [16, 17]. In the effective theory only low-virtuality modes with p2 m2X δ are kept as dynamical degrees of freedom, and are described by effective fields in the Lagrangian These include, 1Note that in (2.1) we assume that the unstable-particle decay proceeds via electroweak decay channels, √. Φc,s generically represent collinear and soft fields and Ci,P and Cj,D are the hard matching coefficients of the production and decay effective vertices, which are computed from on-shell SM amplitudes. In this context “on-shell” has to be understood as p2X = m 2X + mX ΩX = μ2X , meaning that the effective couplings in the Lagrangian are in general complex. The kinetic terms will contain two velocities v and vwhich are generally different
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