Abstract
We calculate the unpolarized and polarized three–loop anomalous dimensions and splitting functions PNS+,PNS− and PNSs in QCD in the MS‾ scheme by using the traditional method of space–like off shell massless operator matrix elements. This is a gauge–dependent framework. For the first time we also calculate the three–loop anomalous dimensions PNS±,tr for transversity directly. We compare our results to the literature.
Highlights
The anomalous dimensions of local quark and gluon operators determine the scaling violations of the deep–inelastic scattering structure functions [1, 2] by the scale evolution of the parton densities and are instrumental in the measurement of the strong coupling constant a(MZ2 ) = αs(MZ2 )/(4π) [3] for this inclusive precision data
At four–loop order a series of low moments for the non–singlet anomalous dimensions has been calculated in Refs. [8] and at five–loop order in [9]
In this paper we are calculating the unpolarized and polarized three–loop anomalous dimensions for the first time using the method of massless off shell operator matrix elements (OMEs) in the flavor non–singlet case, which is the first complete independent recalculation of the results obtained in Ref. [4]
Summary
The anomalous dimensions of local quark and gluon operators determine the scaling violations of the deep–inelastic scattering structure functions [1, 2] by the scale evolution of the parton densities and are instrumental in the measurement of the strong coupling constant a(MZ2 ) = αs(MZ2 )/(4π) [3] for this inclusive precision data They have been calculated to 3–loop order both in the unpolarized and polarized case [4,5,6,7] using the method of on–shell forward. In this paper we are calculating the unpolarized and polarized three–loop anomalous dimensions for the first time using the method of massless off shell OMEs in the flavor non–singlet case, which is the first complete independent recalculation of the results obtained in Ref. In an appendix we briefly summarize the transition from the Larin to the MS scheme for the polarized anomalous dimension in the vector case
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