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.
Highlights
In this Letter we focus on the jet function JqðsÞ for the case that the corresponding hard parton initiating the jet is a masslessquark (i 1⁄4 q)
Four extra IBP relations among the master integrals (MIs) are revealed by the following tricks: The first is to search for identities between integrals based on their Feynman parameter representation using the algorithm of Ref. [36], which is implemented in the FindRules command of FIRE
Summary.—In this Letter we have presented our calculation of the quark jet function JqðsÞ at three loops
Summary
; ð3Þ where T is the time-ordering operator, nμ is the lightlike jet direction (n · n 1⁄4 2, n2 1⁄4 n 2 1⁄4 0), pμ is the jet momentum. Four extra (one-to-one) IBP relations among the MIs are revealed by the following tricks: The first is to search for identities between integrals based on their Feynman parameter representation using the algorithm of Ref. Expressing the full three-loop amplitude of the quark jet function in terms of these MIs the dependence on the gauge parameter ξ manifestly vanishes as expected This provides a first cross check of our setup. [49] Once a quasifinite integral is found in this way it can be related to the original MI plus integrals with less propagators in d 1⁄4 4 − 2ε dimensions by dimensional recurrence and another IBP reduction. To perform the remaining convergent Feynman parameter integrals of the quasifinite MIs we first expand the integrands to sufficiently high order in ε. The coefficients of the (lightlike) cusp anomalous dimension (Γqn) [61,62,63] and the collinear jet anomalous dimension (γqn) [21] for n 1⁄4 0, 1, 2 are, e.g., listed in Ref. [60]
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