0(αs2) corrections to polarized heavy flavour production at Q2 ⪢ m2

Abstract

In this paper we present the analytic form of the heavy flavour coefficient functions for polarized deep inelastic lepton-hadron scattering. The expressions are valid in the kinematical regime Q 2 ≫ m 2 where Q 2 and m 2 stand for the masses squared of the virtual photon and heavy quark respectively. Using these coefficient functions we have computed the next-to-leading order α s corrections to polarized charm production at HERA collider energies, where both the electron and proton beams are polarized. We also give an estimate of these corrections at fixed target experiments where the typical Q 2 values are much smaller than at HERA.

Extraction ofαsfrom the Gross–Llewellyn Smith sum rule using Borel resummation

“…The calculation of the heavy flavor contribution to the GLS sum rule up to the second order (∼ a 2 ) was performed in Ref. [40] and discussed in [41]. According to this approach: (a) the quarks u, d, s are massless and result in the dominant n f = 3 massless QCD contribution to the GLS sum rule ∆(Q 2 ); (b) for Q 2 ≈ 2-4 GeV 2 , the massive flavor is the c-quark and it contributes a relatively small correction to the aforementioned n f = 3 massless contribution.…”

The contributions to the gluonic massive operator matrix elements

“…The massless Wilson coefficients are known to 3-loop order [6]. At NLO the massive OMEs were calculated in [4,[7][8][9][10][11][12] in the unpolarized and polarized case, including the O(α 2 s ε) contributions, and in [13] for transversity. The heavy flavor corrections for charged current reactions are available at one loop and in the asymptotic case at two-loops [14,15].…”

The use of Mellin-Barnes Integrals for the Calculation of Two-loop massive Operator Matrix Elements

“…For the general kinematic range, the next-to-leading order corrections were given semi-analytically in [3], with a fast implementation of these corrections in Mellin-space given in [4]. In the region Q 2 m 2 , Q 2 denoting the virtuality of the gauge boson exchanged in deep-inelastic scattering, and m the mass of the heavy quark under consideration, the heavy flavor Wilson coefficients were derived analytically to O¡ α 2 s ¢ in [1,5]. These calculations were done in x-space using the integration-by-parts method, making the integrals obtained more easy to solve, however, leading to a proliferation of a huge set of terms.…”

“…The unpolarized and polarized massive operator matrix elements can be used to calculate the asymptotic heavy-flavor Wilson coefficients for [8]. In contrast to the work in [1,5], our calculation is performed in Mellin space using harmonic sums [9,10], without applying the integration-by-parts technique. In this way, we can significantly compactify both, the intermediary and final results, which are found to be in agreement with the results obtained in [1,5].…”

“…In contrast to the work in [1,5], our calculation is performed in Mellin space using harmonic sums [9,10], without applying the integration-by-parts technique. In this way, we can significantly compactify both, the intermediary and final results, which are found to be in agreement with the results obtained in [1,5]. The calculation was done using two methods: On the one hand we used generalized hypergeometric functions to express and expand the integrals in ε…”