Three loop anomalous dimension of the non-singlet transversity operator in QCD

TL;DR

This paper computes the three-loop anomalous dimension of the non-singlet transversity operator in QCD, providing explicit formulas in Mellin-N and Bjorken-x space for a wide range of moments.

Contribution

It introduces a reconstructed general form of the three-loop anomalous dimension for arbitrary Mellin moments, extending previous calculations.

Findings

Derived explicit three-loop anomalous dimensions for N=1 to 15

Reconstructed a general formula for arbitrary N

Transformed results into Bjorken-x space for practical use

Abstract

We calculate the three-loop anomalous dimension of the non-singlet transverse operator from N=1 to N=15. Using some guess we have reconstructed a general form of three-loop anomalous dimension for arbitrary Mellin moment N. Obtained result is transformed into Bjorken-x space by an inverse Mellin transformation. The final expressions are presented in both Mellin-N and Bjorken-x space.