One-loop calculations in Supersymmetric Lattice QCD

We study the self energies of all particles which appear in a lattice regularization of supersymmetric QCD (${\cal N}=1$). We compute, perturbatively to one-loop, the relevant two-point Green's functions using both the dimensional and the lattice regularizations. Our lattice formulation employs the Wilson fermion acrion for the gluino and quark fields. The gauge group that we consider is $SU(N_c)$ while the number of colors, $N_c$ and the number of flavors, $N_f$, are kept as generic parameters. We have also searched for relations among the propagators which are computed from our one-loop results. We have obtained analytic expressions for the renormalization functions of the quark field ($Z_\psi$), gluon field ($Z_u$), gluino field ($Z_\lambda$) and squark field ($Z_{A_\pm}$). We present here results from dimensional regularization, relegating to a forthcoming publication our results along with a more complete list of references. Part of the lattice study regards also the renormalization of quark bilinear operators which, unlike the non-supersymmetric case, exhibit a rich pattern of operator mixing at the quantum level.Comment: 6 pages, 5 figure, XII Quark Confinement proceeding

Perturbative Renormalization of Wilson line operators

We present results for the renormalization of gauge invariant nonlocal fermion operators which contain a Wilson line, to one loop level in lattice perturbation theory. Our calculations have been performed for Wilson/clover fermions and a wide class of Symanzik improved gluon actions. The extended nature of such `long-link' operators results in a nontrivial renormalization, including contributions which diverge linearly as well as logarithmically with the lattice spacing, along with additional finite factors. We present nonperturbative prescriptions to extract the linearly divergent contributions.Comment: 8 pages, 2 figures. Talk presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai

Gauge theories with overlap fermions in an arbitrary representation: Evaluation of the 3-loop beta-function

This work presents the calculation of the relation between the bare coupling constant g_0 and the MSbar-renormalized coupling g_MS, g_0 = Z_g(g_0,a\mu) g_MS, to 2 loops in perturbation theory, with fermions in an arbitrary representation of the gauge group SU(N). Our calculation is performed using overlap fermions and Wilson gluons, and the background field technique has been chosen for convenience. The corresponding results in the fundamental representation appear in our longer publication [arXiv:0709.4368]. The 3-loop coefficient of the bare beta-function, b_2^L, is extracted using the 2-loop expression for Z_g, and it is presented as a function of the overlap parameter rho, the number of fermion flavors (N_f) and the number of colors (N). We also provide the expression for the ratio Lambda_L/Lambda_MS, in an arbitrary representation. A plot of Lambda_L/Lambda_MS is given in the adjoint representation.Comment: 15 pages, 5 figure

The Critical Hopping Parameter in O(a) improved Lattice QCD

We calculate the critical value of the hopping parameter, $\kappa_c$, in O(a) improved Lattice QCD, to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for Wilson fermions. The quantity which we study is a typical case of a vacuum expectation value resulting in an additive renormalization; as such, it is characterized by a power (linear) divergence in the lattice spacing, and its calculation lies at the limits of applicability of perturbation theory. The dependence of our results on the number of colors $N$, the number of fermionic flavors $N_f$, and the clover parameter $c_{SW}$, is shown explicitly. We compare our results to non perturbative evaluations of $\kappa_c$ coming from Monte Carlo simulations.Comment: 11 pages, 2 EPS figures. The only change with respect to the original version is inclusion of the standard formulae for the gauge fixing and ghost parts of the action. Accepted for publication in Physical Review

Gauge invariant Field Strength Correlators in QCD

Gauge invariant correlators in QCD are studied on the lattice.A Systematic determination of the correlation lengths for gluon field strength correlators and quark correlators is made.The measurement of the gluon and quark condensates is discussed.Comment: 5 pages,4 figures.Presented by A.Di Giacomo to ICHEP98. To appear in the proceedings Misprints correcte

Improved Perturbation Theory for Improved Lattice Actions

We study a systematic improvement of perturbation theory for gauge fields on the lattice; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik coefficients, clover coefficient) by ``dressed'' values; the latter are solutions to certain coupled integral equations, which are easy to solve numerically. Some positive features of this method are: a) It is gauge invariant, b) it can be systematically applied to improve (to all orders) results obtained at any given order in perturbation theory, c) it does indeed absorb in the dressed parameters the bulk of tadpole contributions. Two different applications are presented: The additive renormalization of fermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector (axial) current. In many cases where non-perturbative estimates of renormalization functions are also available for comparison, the agreement with improved perturbative results is significantly better as compared to results from bare perturbation theory.Comment: 17 pages, 3 tables, 6 figure