Soft anomalous dimensions for single-top production at three loops

Abstract

I present results for soft anomalous dimensions in single top-quark production processes through three loops. I first discuss the cusp anomalous dimension with one massive and one massless line at three loops. I then calculate the three-loop soft anomalous dimension for tW production and for related processes with new physics such as tZ, tγ, and tH − production. This is followed by results at two and three loops for the soft anomalous dimension matrix in s-channel single-top production and, finally, in t-channel single-top production. These new results are needed for soft-gluon resummation at N 3 LL accuracy and for calculations of soft-gluon corrections at N 3 LO.

Soft Anomalous Dimensions and Resummation in QCD

“…Soft anomalous dimensions for t-channel single-top production were calculated at one loop in references [12,48,51], at two loops in [50,51], and at three loops in [50].…”

“…We next present the soft anomalous dimension for the associated production of a top quark with a W-boson via bg → tW − which is known at one-loop [35,48], two loops [52], and three loops [50]. The soft anomalous dimension for tW production is identical to that for other related processes in models of new physics, such as the associated production of a top quark with a charged Higgs boson via bg → tH − in two-Higgs-doublet models, and flavor-changing-neutral-current (FCNC) processes that proceed via anomalous top-quark couplings, such qg → tZ (or tZ ) and qg → tγ (see [12] for a review).…”

Three-loop soft anomalous dimensions for top-quark production

“…A basic ingredient of soft anomalous dimensions for partonic processes is the cusp anomalous dimension [3][4][5][6][7] (see Fig. 1 for representative eikonal diagrams at one, two, and three loops).…”

“…We begin with single-top-quark production [1,7,[12][13][14]. Before presenting the analytical form of the soft anomalous dimensions, we show in Fig.…”

Momentum-space threshold resummation in tW production at the LHC

“…The three-loop soft anomalous dimension for tW production was calculated by ref. [27] which can be used to study the full NNNLO threshold effects.…”