The Gluon Beam Function at Two Loops

Abstract

The virtuality-dependent beam function is a universal ingredient in the resummation for observables probing the virtuality of incoming partons, including N-jettiness and beam thrust. We compute the gluon beam function at two-loop order. Together with our previous results for the two-loop quark beam function, this completes the full set of virtuality-dependent beam functions at next-to-next-to-leading order (NNLO). Our results are required to account for all collinear ISR effects to the N-jettiness event shape through N^3LL order. We present numerical results for both the quark and gluon beam functions up to NNLO and N^3LL order. Numerically, the NNLO matching corrections are important. They reduce the residual matching scale dependence in the resummed beam function by about a factor of two.

21 pages, 6 figures; v2: journal version

References in corpus (4)

• Parton distributions for the LHC
• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• The Quark Beam Function at NNLL
• The Beam Thrust Cross Section for Drell-Yan at NNLL Order

Cited by in corpus (5)

• The N-jettiness soft function at next-to-next-to-leading order
• Fragmentation in Jets at NNLO
• Rapidity-Dependent Jet Vetoes
• The Fully-Differential Quark Beam Function at NNLO
• The Evolution of Soft Collinear Effective Theory