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Register a new userNon-perturbative renormalization of left-left four-fermion operators in quenched lattice QCD
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We define a family of Schroedinger Functional renormalization schemes for the four-quark multiplicatively renormalizable operators of the $Delta F = 1$ and $Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization with quenched Wilson quarks, we compute non-perturbatively the renormalization group running of these operators in the continuum limit in a large range of renormalization scales. Continuum limit extrapolations are well controlled thanks to the implementation of two fermionic actions (Wilson and Clover). The ratio of the renormalization group invariant operator to its renormalized counterpart at a low energy scale, as well as the renormalization constant at this scale, is obtained for all schemes.
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We present non-perturbative renormalization factors for $Delta S=2$ four-quark operators in quenched domain-wall QCD using the Schroedinger functional method. Non-perturbative renormalization factor for $B_K$ is evaluated at hadronic scale. Combined with the non-perturbative RG running obtained by the Alpha collaboration, our result yields renormalization factor which converts lattice bare $B_K$ to the renormalization group invariant one. We apply the renormalization factor to bare $B_K$ previously obtained by the CP-PACS collaboration with the quenched domain-wall QCD(DWQCD). We compare our result with previous ones obtained by perturbative renormalization factors, different renormalization schemes or different quark actions. We also show that chiral symmetry breaking effects in the renormalization factor are numerically small.
Recent developments in non-perturbative renormalization for lattice QCD are reviewed with a particular emphasis on RI/MOM scheme and its variants, RI/SMOM schemes. Summary of recent developments in Schroedinger functional scheme, as well as the summary of related topics are presented. Comparison of strong coupling constant and the strange quark mass from various methods are made.
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.
We discuss a specific cut-off effect which appears in applying the non-perturbative RI/MOM scheme to compute the renormalization constants. To illustrate the problem a Dirac operator satisfying the Ginsparg-Wilson relation is used, but the arguments are more general. We propose a simple modification of the method which gets rid of the corresponding discretization error. Applying this to full-QCD simulations done at a=0.13 fm with the Fixed Point action we find that the renormalization constants are strongly distorted by the artefacts discussed. We consider also the role of global gauge transformations, a freedom which still remains after the conventional gauge fixing procedure is applied.
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.
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