The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements

Abstract

Future high luminosity polarized deep-inelastic scattering experiments will improve both the knowledge of the spin sub-structure of the nucleons and contribute further to the precision determination of the strong coupling constant, as well as, reveal currently yet unknown higher twist contributions in the polarized sector. For all these tasks to be performed, it is necessary to know the QCD leading twist scaling violations of the measured structure functions. Here an important ingredient consists in the polarized singlet anomalous dimensions and splitting functions in QCD. We recalculate these quantities to three-loop order in the M-scheme by using the traditional method of space-like off-shell massless operator matrix elements, being a gauge-dependent framework. Here one obtains the anomalous dimensions without referring to gravitational currents, needed when calculating them using the forward Compton amplitude. We also calculate the non-singlet splitting function ∆P(2),s,NS qq and compare the final results to the literature, also including predictions for the region of small values of Bjorken x.

The 3-loop anomalous dimensions from off-shell operator matrix elements

“…In these proceedings we report on recent results of the calculation of unpolarized and polarized three-loop anomalous dimensions based on massless off-shell operator matrix elements (OMEs) [1,2] and the unpolarized two-loop case [3] correcting previous results in Refs. [4,5].…”

“…Functions of the package HarmonicSums [17,18,[44][45][46][47] are used to compactify the final results. The automated calculation at Intel(R) Xeon(R) CPU E5-2643 v4 processors amounted to about 40 days of CPU time for the projects [1,2].…”

“…Here different techniques as off-shell massless OMEs, the forward Compton amplitude, in part also with scalar and gravitational currents, and massive on-shell OMEs have been used. In the latter case one obtains the contributions ∝ 𝑇 𝐹 , which are the complete anomalous dimensions in the cases (Δ)𝛾 (2),PS 𝑞𝑞 and (Δ)𝛾 (2) 𝑞𝑔 .…”

“…The unpolarized and polarized non-singlet and singlet anomalous dimensions have been calculated at one- [6], two- [3,7,8], and three-loop order [1,2,[9][10][11][12][13][14][15]. Here different techniques as off-shell massless OMEs, the forward Compton amplitude, in part also with scalar and gravitational currents, and massive on-shell OMEs have been used.…”

Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering

“…For completeness, we have included the most important structure function g 1 in spin-dependent DIS, for its coefficient functions and splitting functions at NNLO see refs. [70][71][72][73][74].…”