Spin-dependent quark beam function at NNLO

Abstract

We calculate the beam function for longitudinally-polarized quarks through next-to-next-toleading order (NNLO) in QCD perturbation theory. This is the last missing ingredient needed to apply the factorization theorem for the N -jettiness event-shape variable in a variety of polarized collisions through the NNLO level. We present all technical details of our derivation. As a by-product of our calculation we provide the first independent check of the previously-obtained unpolarized quark beam function. We anticipate that our result will have phenomenological applications in describing data from polarized collisions.

Quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large-Ncapproximation

“…δ,h (z). (18) As we already mentioned, the NLO and NNLO contributions to the matching coefficient I (1),(2) qq are fully known [19,21]. Recently, in Ref.…”

NNLO zero-jettiness beam and soft functions to higher orders in the dimensional-regularization parameter $$\epsilon $$

“…An important part of these efforts is the development of methods that enable N 3 LO QCD calculations, at least for the simplest processes where color-singlet final states are produced. In the absence of fully-developed N 3 LO subtractions schemes, a promising approach is the slicing method [6][7][8][9] that has seen a recent resurgence in the context of LHC physics.…”

N -jettiness subtractions for gg→H at subleading power

“…They are expressed in terms of universal soft, jet, and beam functions. The required ingredients to compute the leadingpower subtraction terms at NNLO are the NNLO jet [28,29] and beam [30,31] functions (the spin-dependent quark beam functions were recently computed to NNLO [32]), which are process independent, as well as the soft function, which depends on the number of external colored partons, n, in the Born process. The soft function is known analytically at next-to-leading order (NLO) for arbitrary n [33], and at NNLO it is known analytically for n ¼ 2 [34][35][36][37], and numerically for n ¼ 3 [38], and with a third massive parton [39].…”