The Planar Gauge in a New Formalism

Abstract

The main feature of the planar gauge, apart from the decoupling of ghosts, is the nontransversality of the Yang-Mills self-energy with the resulting appearance of a pincer diagram in the Ward identity. We employ the general prescription for axial-type gauges, recently developed by one of the authors, to check this Ward identity and derive BRS-invariant counterterms in the planar gauge.

Light-cone gauge and the calculation of the two-loop splitting functions

“…For the renormalization of the loop diagrams, one needs to subtract their UV poles, which is achieved in the easiest way by inserting the UV-divergent one-loop structures as calculated for the light-cone gauge in the ML prescription in [6,18,20,21]. All structures have also been compiled in [2].…”

“…They can be straightforwardly obtained 1 using the UV-singular structure of the one-loop quark self-energy, determined for the ML prescription in [18]. One finds [7]:…”

Next-to-leading order calculation of a fragmentation function in a light-cone gauge

“…The result using the ML prescription is known only for the UV poles. We have full agreement in the UV poles if we use the ML prescription : the gluon propagator correction term is proportional to the QCD beta function as Π = (33 − 2n f )α s /(12πǫ UV ) [21,40] and δZ LC Q = α s /(3πǫ UV ) [41]. All of them are listed, for example, in Ref.…”

“…( 19) agrees with the result using the ML prescription in Refs. [41,42] where only the UV contribution is given :…”