arXiv subjects
Publications and source records attributed to R. E. Browne.
We review the current status of the application of the local composite operator technique to the condensation of dimension two operators in quantum chromodynamics (QCD). We pay particular attention to the renormalization group aspects of the formalism and the renormalization of QCD in various gauges.
We compute the one loop corrections to the pole mass of the gluon in the MSbar scheme in the Landau gauge in both the Curci-Ferrari model and the local composite operator formalism with Nf flavours of massless quarks. For the latter we determine an estimate for the gluon mass using the effective potential of a local dimension two composite operator and find, for example, m_{gluon} = 2.10 Lambda_MSbar in Yang-Mills theory.
We discuss the 2PPI expansion, a summation of the bubble graphs up to all orders, by means of the 2D Gross-Neveu toy model, whose exact mass gap and vacuum energy are known. Then we use the expansion to give analytical evidence that a dimension two gluon condensate exists for pure Yang-Mills in the Landau gauge. This condensate consequently gives rise to a dynamical gluon mass.
We construct the effective potential for the dimension two composite operator 1/2 A^{a 2}_μin QCD with massless quarks in the Landau gauge for an arbitrary colour group at two loops. For SU(3) we show that an estimate for the effective gluon mass decreases as N_f increases.
We discuss the 2-point-particle-irreducible (2PPI) expansion, which sums bubble graphs to all orders, in the context of SU(N) Yang-Mills theory in the Landau gauge. Using the method we investigate the possible existence of a gluon condensate of mass dimension two, , and the corresponding non-zero vacuum energy. This condensate gives rise to a dynamically generated mass for the gluon.
Massive quarks are included in the Curci-Ferrari model and the theory is renormalized at two loops in the MSbar scheme in an arbitrary covariant gauge.