Three loop anomalous dimension of the second moment of the transversity operator in the MSbar and RI' schemes

TL;DR

The paper determines the three‑loop anomalous dimension of the second moment of the transversity operator, renormalized in both the MSbar and RI' schemes, and provides scheme‑conversions to facilitate lattice matching. It also performs an independent cross‑check via a large‑Nf critical‑exponent analysis for arbitrary moment n, confirming the n=2 three‑loop coefficient and delivering a four‑loop leading term. In addition to the transversity results, the authors compute the RI' anomalous dimension for the non‑singlet twist‑2 operator as a cross‑check against known MSbar results. These results advance precise evolution and lattice extraction of transversity matrix elements and set the stage for higher‑moment analyses.

Abstract

We compute the anomalous dimension of the second moment of the transversity operator, \barψ σ^{μν} D^ρψ, at three loops in both the MSbar and RI' schemes. As a check on the result we also determine the O(1/N_f) critical exponent of the n-th moment of the transversity operator in d-dimensions in the large N_f expansion and determine leading order information on the n dependence of the anomalous dimension at three and four loops in MSbar. In addition the RI' anomalous dimension of the non-singlet twist-2 operator, \barψ γ^μD^νψ, is also determined.