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 Delta {P}_{mathrm{qq}}^{(2),mathrm{s},mathrm{NS}} and compare the final results to the literature, also including predictions for the region of small values of Bjorken x.
Highlights
The three-loop anomalous dimensions of transversity in ref. [20]
The singlet anomalous dimensions have been calculated by using the method of massless off-shell OMEs, which has been applied for this purpose for the first time
The calculation has been fully automated referring to the Larin scheme, performing a finite transformation to the M-scheme for the final results
Summary
The largest difference equation contributing has order o = 16 and degree d = 304 These numbers are of the order obtained in the non-singlet case in ref. In our previous paper [20] we had not yet calculated the non-singlet anomalous dimension ∆γq(2q),s,NS, which emerges from three-loop order onward. It is best calculated using the vector-axialvector interference term in the forward Compton amplitude, corresponding to the associated structure function g5−(x, Q2), ref. After insertion of the master integrals into the amplitude and subsequent expansion in the dimensional parameter ε, the anomalous dimension can be determined by using the command GetMoment[F[y],y,N] of the package HarmonicSums from the pole term O(1/ε) of the. One more logarithmic order allows a description below z ∼ 10−3
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