Three loop anomalous dimension of the second moment of the transversity operator in the (MS)over-bar and RI′ schemes

We compute the anomalous dimension of the second moment of the transversity operator, (ψ) over bar sigma(munu)D(rho)psi, at three loops in both the (MS) over bar and RI' schemes. As a check on the result we also determine the O(1/N-f) critical exponent of the nth 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 (MS) over bar. In addition the RI' anomalous dimension of the non-singlet twist-2 operator, (ψ) over bar gamma(mu)D(nu)psi, is also determined. (C) 2003 Elsevier B.V. All rights reserved.