Eur. Phys. J. C (2011) 71: 1567
https://doi.org/10.1140/epjc/s10052-011-1567-8

Regular Article - Theoretical Physics

RI′/SMOM scheme amplitudes for quark currents at two loops

Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, P.O. Box 147, Liverpool, L69 3BX, UK

^* e-mail: gracey@liv.ac.uk

Received: 15 December 2010
Revised: 14 January 2011
Published online: 4 March 2011

Abstract

We determine the two loop corrections to the Green’s function of a quark current inserted in a quark 2-point function at the symmetric subtraction point. The amplitudes for the scalar, vector and tensor currents are presented in both the and RI′/SMOM renormalization schemes. The RI′/SMOM scheme two loop renormalization for the scalar and tensor cases agree with previous work. The vector current renormalization requires special treatment as it must be consistent with the Slavnov–Taylor identity which we demonstrate. We also discuss the possibility of an alternative definition of the RI′/SMOM scheme in the case of the tensor current.