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Register a new userNon-perturbative renormalization in lattice QCD
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Authors
Yasumichi Aoki
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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.
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We present lattice results for the isovector unpolarized parton distribution with nonperturbative RI/MOM-scheme renormalization on the lattice. In the framework of large-momentum effective field theory (LaMET), the full Bjorken-$x$ dependence of a momentum-dependent quasi-distribution is calculated on the lattice and matched to the ordinary lightcone parton distribution at one-loop order, with power corrections included. The important step of RI/MOM renormalization that connects the lattice and continuum matrix elements is detailed in this paper. A few consequences of the results are also addressed here.
We propose a new strategy for the determination of the QCD coupling. It relies on a coupling computed in QCD with $N_{rm f} geq 3$ degenerate heavy quarks at a low energy scale $mu_{rm dec}$, together with a non-perturbative determination of the ratio $Lambda/mu_{rm dec}$ in the pure gauge theory. We explore this idea using a finite volume renormalization scheme for the case of $N_{rm f} = 3$ QCD, demonstrating that a precise value of the strong coupling $alpha_s$ can be obtained. The idea is quite general and can be applied to solve other renormalization problems, using finite or infinite volume intermediate renormalization schemes.
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.
We report on a non-perturbative computation of the renormalization factor Z_A of the axial vector current in three-flavour O(a) improved lattice QCD with Wilson quarks and tree-level Symanzik improved gauge action and also recall our recent determination of the improvement coefficient c_A. Our normalization and improvement conditions are formulated at constant physics in a Schrodinger functional setup. The normalization condition exploits the full, massive axial Ward identity to reduce finite quark mass effects in the evaluation of Z_A and correlators with boundary wave functions to suppress excited state contributions in the pseudoscalar channel.
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.
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