Soft Anomalous Dimensions and Resummation in QCD

Abstract

I discuss and review soft anomalous dimensions in QCD that describe soft-gluon threshold resummation for a wide range of hard-scattering processes. The factorization properties of the cross section in moment space and renormalization-group evolution are implemented to derive a general form for differential resummed cross sections. Detailed expressions are given for the soft anomalous dimensions at one, two, and three loops, including some new results, for a large number of partonic processes involving top quarks, electroweak bosons, Higgs bosons, and other particles in the standard model and beyond.

Higher-order corrections for tW production at high-energy hadron colliders

“…The formalism for soft-gluon resummation will be briefly described in this section (see refs. [11,13,15,16,[24][25][26][27][28][29][30][31][32][33][34]). We study the process b(p 1 ) + g (p 2 ) → t(p 3 ) + W − (p 4 ) and define the usual kinematical variables s = (p 1 + p 2 ) 2 , t = (p 1 − p 3 ) 2 , u = (p 2 − p 3 ) 2 .…”

“…We then find the transform-space expression dσ bg→tW (N ) =φ(N 1 )φ(N 2 ) dσ bg→tW (N ) , (2.2) where N 1 = N (m 2 W − u)/s and N 2 = N (m 2 W − t)/s. The cross section for tW production can be rewritten under Laplace transforms in refactorized form as a product of separate functions: a short-distance, infrared safe, hard function, H bg→tW ; a soft function, S bg→tW , which describes the emission of noncollinear soft gluons in the process; and functions ψ that describe collinear emission from the incoming partons [15,16,25,[28][29][30][31][32][33][34]. We have…”

“…ref. [25] for explicit expressions). The soft anomalous dimension has a perturbative expansion…”

“…More recently, three-loop calculations for the soft anomalous dimensions in single-top production, including tW production, were presented in ref. [24] (see also a recent review paper on soft anomalous dimensions for QCD processes [25]).…”

“….14) with α = e 2 /(4π), θ W the weak mixing angle, and V tb a CKM matrix element. For explicit analytical expressions at higher orders see refs [15,16,25]…”