The massless three-loop Wilson coefficients for the deep-inelastic structure functions F2, FL, xF3 and g1

Abstract

We calculate the massless unpolarized Wilson coefficients for deeply inelastic scattering for the structure functions F2(x, Q2), FL(x, Q2), xF3(x, Q2) in the $$ \overline{\textrm{MS}} $$ MS ¯ scheme and the polarized Wilson coefficients of the structure function g1(x, Q2) in the Larin scheme up to three-loop order in QCD in a fully automated way based on the method of arbitrary high Mellin moments. We work in the Larin scheme in the case of contributing axial-vector couplings or polarized nucleons. For the unpolarized structure functions we compare to results given in the literature. The polarized three-loop Wilson coefficients are calculated for the first time. As a by-product we also obtain the quarkonic three-loop anomalous dimensions from the O(1/ε) terms of the unrenormalized forward Compton amplitude. Expansions for small and large values of the Bjorken variable x are provided.

Analytic solution for the revised helicity evolution at small x and large Nc : New resummed gluon-gluon polarized anomalous dimension and intercept

“…Reassuringly, this prediction for the anomalous dimension agrees with the fixed-order calculations out to the existing three-loop level (see [18][19][20][21][22][23][24][25][26][27][28][29][30]). These quantities -the intercept in Eq.…”

“…The intercept of 3.66 √ ᾱs appeared to agree with that derived earlier by Bartels, Ermolaev, and Ryskin (BER) using an infrared evolution equations (IREE) approach [4]. In addition, an iterative solution of the large-N c KPS-CTT equations in [1] indicated full agreement with the small-x, large-N c part of the glue-glue polarized anomalous dimension ∆γ GG (ω) out to the existing three-loop order of the fixed-order calculations [18][19][20][21] (see also [22][23][24][25][26][27][28][29][30]). Despite this good agreement, an analytic solution of these equations would nevertheless be valuable.…”

The inverse Mellin transform via analytic continuation

“…In previous calculations we have already made use of generating functions in t. However, in those cases we performed a formal Taylor expansion in which the N th Mellin moment arises as the coefficient of the expansion term t N . In many cases it is possible to obtain the Mellin space result analytically [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. One possibility is to calculate a large number of moments for the master integrals, assemble them into moments for the physical quantity that is being calculated, guess recurrences for them [28][29][30] and finally solve those recurrences using the algorithms of the package Sigma [31,32].…”

Orbital angular momentum small-x evolution: exact results in the large-Nc limit

“…The origin of the discrepancy is speculated on in the appendix of [3] (see also [50]). (Additionally, see [76][77][78] for a discrepancy due to scheme dependence between the IREE and the small-x limit of the exact 3-loop calculations of spin-dependent DGLAP anomalous dimensions. )…”