We study the θ dependence of the spectrum of four-dimensional SU(N) gauge theories, where θ is the coefficient of the topological term in the Lagrangian, for N ≥ 3 and in the large-N limit. We compute the O(θ 2 ) terms of the expansions around θ = 0 of the string tension and the lowest glueball mass, respectively σ(θ) = σ (1 + s 2 θ 2 + ...) and M(θ) = M (1 + g 2 θ 2 + ...), where σ and M are the values at θ = 0. For this purpose we use numerical simulations of the Wilson lattice formulation of SU(N) gauge theories for N = 3, 4, 6. The O(θ 2 ) coefficients turn out to be very small for all N ≥ 3. For example, s 2 = −0.08(1) and g 2 = −0.06(2) for N = 3. Their absolute values decrease with increasing N. Our results are suggestive of a scenario in which the θ dependence in the string and glueball spectrum vanishes in the large-N limit, at least for sufficiently small values of |θ|. They support the general large-N scaling arguments that indicateθ ≡ θ/N as the relevant Lagrangian parameter in the large-N expansion.-1 -

We compute the two-loop renormalization functions, in the RI 0 scheme, of local bilinear quark operators "c Àc , where À corresponds to the vector, axial-vector, and tensor Dirac operators, in the lattice formulation of QCD. We consider both the flavor nonsinglet and singlet operators. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in c SW , in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. Finally, we present our results in the MS scheme, for easier comparison with calculations in the continuum. The corresponding results, for fermions in an arbitrary representation, together with some special features of superficially divergent integrals, are included in the appendices.

We present an unquenched N f = 2 lattice computation of the B K parameter which controls K 0 −K 0 oscillations. A partially quenched setup is employed with two maximally twisted dynamical (

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 [1], 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.

We compute the two-loop renormalization functions, in the RI ′ scheme, of local bilinear quark operatorsψΓψ, where Γ denotes the Scalar and Pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor non-singlet and singlet operators; the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, Z m .As a prerequisite for the above, we also compute the quark field renormalization, Z ψ , up to two loops.We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in c SW , in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. We also confirm the 1-loop renormalization functions, for generic gauge.Finally, we present our results in the M S scheme, for easier comparison with calculations in the continuum.The corresponding results, for fermions in an arbitrary representation, are included in an Appendix.