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Register a new userNon-perturbative running of renormalization constants from correlators in coordinate space using step scaling
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Working in a quenched setup with Wilson twisted mass valence fermions, we explore the possibility to compute non-perturbatively the step scaling function using the coordinate (X-space) renormalization scheme. This scheme has the advantage of being on-shell and gauge invariant. The step scaling method allows us to calculate the running of the renormalization constants of quark bilinear operators. We describe here the details of this calculation. The aim of this exploratory study is to identify the feasibility of the X-space scheme when used in small volume simulations required by the step scaling technique. Eventually, we translate our final results to the continuum MSbar scheme and compare against four-loop analytic formulae finding satisfactory agreement.
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We perform a benchmark study of the step scaling procedure for the ratios of renormalization constants extracted from position space correlation functions. We work in the quenched approximation and consider the pseudoscalar, scalar, vector and axial vector bilinears. The pseudoscalar/scalar cases allow us to obtain the non-perturbative running of the quark mass over a wide range of energy scales - from around 17 GeV to below 1.5 GeV - which agrees well with the 4-loop prediction of continuum perturbation theory. We find that step scaling is feasible in X-space and we discuss its advantages and potential problems.
Renormalization constants ($Z$-factors) of vector and axial-vector currents are determined non-perturbatively in quenched QCD for a renormalization group improved gauge action and a tadpole improved clover quark action using the Schrodinger functional method. Non-perturbative values of $Z$-factors turn out to be smaller than one-loop perturbative values by $O(15%)$ at lattice spacing of $a^{-1}approx$ 1 GeV. The pseudoscalar and vector meson decay constants calculated with the non-perturbative $Z$-factors show a much better scaling behavior compared to previous results obtained with tadpole improved one-loop $Z$-factors. In particular, the non-perturbative $Z$-factors normalized at infinite physical volume show that scaling violation of the decay constants are within about 10% up to the lattice spacing $a^{-1}sim 1$ GeV. The continuum estimates obtained from data in the range $a^{-1}=$ 1 -- 2 GeV agree with those determined from finer lattices ($a^{-1}sim 2-4$ GeV) with the standard action.
This PhD dissertation is devoted to a non-perturbative study of QCD correlators. The main tool that we use is lattice QCD. We concentrated our efforts on the study of the main correlators of the pure Yang - Mills theory in the Landau gauge, namely the ghost and the gluon propagators. We are particularly interested in determining the $Lqcd$ parameter. It is extracted by means of perturbative predictions available up to NNNLO. The related topic is the influence of non-perturbative effects that show up as appearance of power-corrections to the low-momentum behaviour of the Green functions. A new method of removing these power corrections allows a better estimate of $Lqcd$. Our result is $Lambda^{n_f=0}_{ms} = 269(5)^{+12}_{-9}$ MeV. Another question that we address is the infrared behaviour of Green functions, at momenta of order and below $Lqcd$. At low energy the momentum dependence of the propagators changes considerably, and this is probably related to confinement. The lattice approach allows to check the predictions of analytical methods because it gives access to non-perturbative correlators. According to our analysis the gluon propagator is finite and non-zero at vanishing momentum, and the power-law behaviour of the ghost propagator is the same as in the free case.
A method for computing renormalization constants in the Rome Southampton scheme with volume sources and arbitrary momenta is described. This new method is found to enable controlled and precise continuum extrapolations and opens the way to compute the running of operators nonperturbatively in the Rome Southampton scheme. We describe this in detail and exhibit several examples of lattice step scaling functions.
We present preliminary results of a non-perturbative study of the scale-dependent renormalization constants of a complete basis of Delta F=2 parity-odd four-fermion operators that enter the computation of hadronic B-parameters within the Standard Model (SM) and beyond. We consider non-perturbatively O(a) improved Wilson fermions and our gauge configurations contain two flavors of massless sea quarks. The mixing pattern of these operators is the same as for a regularization that preserves chiral symmetry, in particular there is a physical mixing between some of the operators. The renormalization group running matrix is computed in the continuum limit for a family of Schrodinger Functional (SF) schemes through finite volume recursive techniques. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale, together with the non-perturbative matching matrix between the lattice regularized theory and the various SF schemes.
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