Three-Loop Quark Jet Function

Abstract

We calculate the massless quark jet function to three-loop order. The quark jet function is a universal ingredient in SCET factorization for many collider and decay processes with quark initiated final state jets. Our three-loop result contributes to the resummation for observables probing the invariant mass of final state quark jets at primed next-to-next-to-next-to-leading-logarithmic accuracy. It represents the first complete three-loop result for a factorization ingredient describing collinear radiation. Furthermore it constitutes a major component of the N-jettiness subtraction method at next-to-next-to-next-to-leading order accuracy, which eventually may enable the calculation of fully differential cross sections with a colorful final state at this order.

Three-loop soft function for heavy-to-light quark decays

“…(2.16) and performed very much along the lines of our jet function calculation in ref. [10], to which we refer for more details. We work in general covariant gauge with gauge parameter ξ, where ξ = 0 corresponds to Feynman gauge.…”

“…Demanding this yields another eight independent relations between MIs belonging to the same family, see also ref. [10]. 6 The total number of linearly independent MIs across all families is 64, but only 45 contribute to S hl .…”

“…To solve the remaining 33 MIs we proceed in the same way as for our jet function calculation in ref. [10]. The method was inspired by refs.…”

“…In ref. [10] we directly computed the massless quark jet function anomalous dimension γ Jq 2 . It was initially derived indirectly from the RG invariance of the factorized DIS cross section in the threshold region [52] using the three-loop results of refs.…”

“…Our three-loop calculation of the jet function in ref. [10] represents a first step toward this goal. In the present paper we calculate the soft function S hl at three loops, while the three-loop hard function is left for future work.…”