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Register a new userA complete non-perturbative renormalization prescription for quasi-PDFs
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In this work we present, for the first time, the non-perturbative renormalization for the unpolarized, helicity and transversity quasi-PDFs, in an RI scheme. The proposed prescription addresses simultaneously all aspects of renormalization: logarithmic divergences, finite renormalization as well as the linear divergence which is present in the matrix elements of fermion operators with Wilson lines. Furthermore, for the case of the unpolarized quasi-PDFs, we describe how to eliminate the unwanted mixing with the twist-3 scalar operator. We utilize perturbation theory for the one-loop conversion factor that brings the renormalization functions to the MS-scheme at a scale of 2 GeV. We also explain how to improve the estimates on the renormalization functions by eliminating lattice artifacts. The latter can be computed in one-loop perturbation theory and to all orders in the lattice spacing. We apply the methodology for the renormalization to an ensemble of twisted mass fermions with Nf=2+1+1 dynamical light quarks, and a pion mass of around 375 MeV.
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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.
Renormalization constants of vector ($Z_V$) and axial-vector ($Z_A$) 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 $Z_V$ and $Z_A$ turn out to be smaller than the one-loop perturbative values by $O(10%)$ at $a^{-1}approx 1$ GeV. A sizable scaling violation of meson decay constants $f_pi$ and $f_rho$ observed with the one-loop renormalization factors remains even with non-perturbative renormalization.
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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