Two Yang-Mills theories in the light-cone gauge:: Complete one-loop counterterms

Abstract

The Mandelstam-Leibbrandt prescription is used to study one-loop structures of the two-component (LCM2) and four-component (LCM4) formalisms of the same Yang-Mills theory in the light-cone gauge. The complete one-loop counter lagrangians are constructed by computing the one-loop two-, three- and four-point vertices. LCM2 is renormalizable order-by-order in g with δ L counter = (Z − 1) L, Z = 1 + 11g 2C 2/48π 2ϵ . For LCM4, both the two- and three-vertices generate anomalous counterterms which, however, cancel upon summation so that the total δ L counter is the same as LCM2. Slavnov-Taylor identities are satisfied in LCM4; they do not exist in LCM2. The method of analytic regularization is used in computation; all invariant and tensor integrals are evaluated using a single representation for light-cone invariant two-point integrals. The calculation is exceedingly simple in LCM2, far less so in LCM4.