Effective Theory Approach to Unstable Particle Production

Abstract

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Electroweak non-resonant NLO corrections to in the resonance region

“…The solid (black) line is the total contribution σ (1) non-res in (13), and the contributions from the diagram h 1 , from the sum of diagrams h 2 -h 4 and from the truly single-resonant diagrams h 5 -h 10 are shown by the dashed (purple), dash-dotted (red) and dotted (blue) lines, respectively. with X = V, A, V A, are obtained from diagrams i = 1, ...10, and depend only on the ratios 2 (M W /m t ) 2 and (∆/m t ) 2 but not on the centre-of-mass energy √ s. To define the function h V 1 we subtracted from the integrand of diagram h 1 its leading singular behaviour as p 2 t → m 2 t (see (33) in Appendix A). Adding back the subtracted expression yields the terms in the first line of (13) upon p 2 t integration.…”

“…In the energy region √ s ≈ 2m t close to the top anti-top production threshold, the amplitude is dominated by the production of resonant top quarks with small virtuality. This allows us to integrate out hard modes with scale m t and represent the forward-scattering amplitude as the sum of two terms [32,33],…”

“…The calculation is performed with unstable-particle effective field theory [32,33], which provides the framework for consistently including resonant and non-resonant effects while maintaining an expansion in the small parameters of the problem. There are many similarities with W -pair production considered in [34,35], though the top-quark case is technically more complicated due to the presence of a massive particle (the W boson) in top decay.…”

Four-fermion production near the W pair-production threshold

“…In Section 2 we explain our method of calculation. We focus on aspects of unstable-particle effective theory that are specific to pair production near threshold and refer to [13] for those, which are in complete analogy with the line-shape calculation of a single resonance. The section ends with a list of all terms that contribute to the NLO result.…”

“…This approximation was supposed to break down for kinematic reasons in the threshold region. Thus, when this project was begun [9], there existed only LO calculations in the threshold region as well as studies of the effect of Coulomb photon exchanges [10,11], rendering the effective field theory approach [12][13][14] the method of choice for the NLO calculation. Meanwhile a full NLO calculation of four-fermion production has been performed in the complex mass scheme [15,16] without any kinematic approximations, and for the fully differential cross sections in the continuum or near threshold.…”