Numerical Stochastic Perturbation Theory was able to get three-(and even four-) loop results for finite Lattice QCD renormalization constants. More recently, a conceptual and technical framework has been devised to tame finite size effects, which had been reported to be significant for (logarithmically) divergent renormalization constants. In this work we present three-loop results for fermion bilinears in the Lattice QCD regularization defined by tree-level Symanzik improved gauge action and n f = 2 Wilson fermions. We discuss both finite and divergent renormalization constants in the RI'-MOM scheme. Since renormalization conditions are defined in the chiral limit, our results also apply to Twisted Mass QCD, for which non-perturbative computations of the same quantities are available. We emphasize the importance of carefully accounting for both finite lattice space and finite volume effects. In our opinion the latter have in general not attracted the attention they would deserve. arXiv:1310.4981v1 [hep-lat]

This is the third of a series of papers on threeloop computation of renormalization constants for Lattice QCD. Our main points of interest are results for the regularization defined by the Iwasaki gauge action and n f = 4 Wilson fermions. Our results for quark bilinears renormalized according to the RI'-MOM scheme can be compared to non-perturbative results. The latter are available for twisted mass QCD: being defined in the chiral limit, the renormalization constants must be the same. We also address more general problems. In particular, we discuss a few methodological issues connected to summing the perturbative series such as the effectiveness of boosted perturbation theory and the disentanglement of irrelevant and finite-volume contributions. Discussing these issues we consider not only the new results of this paper, but also those for the regularization defined by the tree-level Symanzik improved gauge action and n f = 2 Wilson fermions, which we presented in a recent paper of ours. We finally comment on the extent to which the techniques we put at work in the NSPT context can provide a fresher look into the lattice version of the RI'-MOM scheme.

We present three loops renormalization constants for Wilson fermion bilinears (vector, scalar, axial, pseudoscalar currents). Two gluonic regularizations are considered: tree level Symanzik improved action (with N f = 2) and Iwasaki action (with N f = 4). Both cases are amenable for comparisons with non-perturbative results. We discuss the issue of taming both finite lattice spacing and finite volume artifacts. As a byproduct, we comment on two loops matching of lattice and continuum couplings.

Clan concept has been introduced in multiparticle dynamics in order to interpret the wide occurrence of negative binomial (NB) regularity in n-charged particle multiplicity distributions (MDs) in various high energy collisions. The centrality of clan concept led to the attempt to justify its occurrence within a statistical model of clan formation and evolution. In this framework all thermodynamical potentials have been explicitely calculated in terms of NB parameters. Interestingly it was found that NB parameter k corresponds to the one particle canonical partition function. The goal of this paper is to explore a possible temperature T and volume V dependence of parameter k in various classes of events in high energy hadron-hadron collisions. It is shown that the existence of a phase transition at parton level from the ideal clan gas associated to the semihard component with k > 1 to the ideal clan gas of the hard component with k < 1 implies a discontinuity in the average number of particles at hadron level.

Theorems on zeroes of the truncated generating function in the complex plane are reviewed. When examined in the framework of a statistical model of high energy collisions based on the negative binomial (Pascal) multiplicity distribution, these results lead to maps of zeroes of the grand canonical partition function which allow to interpret in a novel way different classes of events in pp collisions at LHC c.m. energies.