Three loop anomalous dimension of the second moment of the transversity operator in the \(\overline{MS}\) and \(RI^{\prime}\) schemes. (English) Zbl 1059.81577
Summary: We compute the anomalous dimension of the second moment of the transversity operator, \(\bar \psi\sigma^{\mu\nu}D^{\rho}\psi\), at three loops in both the \(\overline{MS}\) and \(RI^{\prime}\) 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 \(\overline{MS}\). In addition the \(RI^\prime\) anomalous dimension of the non-singlet twist-2 operator, \(\bar \psi\gamma^{\mu}D^{\nu}\psi\), is also determined.
MSC:
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
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