Precise MS-bar light-quark masses from lattice QCD in the RI/SMOM scheme

We compute the conversion factors needed to obtain the MS-bar and RGI up, down, and strange-quark masses at next-to-next-to-leading order from the corresponding parameters renormalized in the recently proposed RI/SMOM and RI/SMOM_gamma_mu renormalization schemes. This is important for obtaining the MS-bar masses with the best possible precision from numerical lattice-QCD simulations, because the customary RI(')/MOM scheme is afflicted with large irreducible uncertainties both on the lattice and in perturbation theory. We find that the smallness of the known one-loop matching coefficients is accompanied by even smaller two-loop contributions. From a study of residual scale dependences, we estimate the resulting perturbative uncertainty on the light-quark masses to be about 2% in the RI/SMOM scheme and about 3% in the RI/SMOM_gamma_mu scheme. Our conversion factors are given in fully analytic form, for general covariant gauge and renormalization point. We provide expressions for the associated anomalous dimensions.Comment: Added results for the RI/SMOM_gamma_mu scheme and anomalous dimensions; typos fixed (results unchanged); added reference

Long-Range Coulomb Forces in DIS: Missed Radiative Corrections?

The Born approximation, one photon exchange, used for DIS is subject to virtual radiative corrections which are related to the long-range Coulomb forces. They may be sizeable for heavy nuclei since Z\alpha is not a small parameter. So far these corrections are known only for two processes, elastic scattering and bremsstrahlung on the Coulomb field of a point-like target. While the former amplitude acquires only a phase, in the latter case the cross section is modified also. Although the problem of Coulomb corrections for DIS on nuclei is extremely difficult, it should be challenged rather than 'swept under the carpet'. The importance of these radiative corrections is questioned in present paper. We show that in the simplest case of a constant hadronic current the Coulomb corrections provide a phase to the Born amplitude, therefore the cross section remains the same. Inclusion of more realistic hadronic dynamics changes this conclusion. The example of coherent production of vector mesons off nuclei reveals large effects. So far a little progress has been made deriving exact lepton wave functions in the Coulomb field of an extended target. Employing available results based on the first-order approximation in Z\alpha, we conclude that the Coulomb corrections are still important for heavy nuclei. We also consider an alternative approach for extended nuclear targets, the eikonal approximation, which we demonstrate to reproduce the known exact results for Coulomb corrections. Calculating electroproduction of vector mesons we again arrive at a large deviation from the Born approximation. We conclude that one should accept with caution the experimental results for nuclear effects in DIS based on analyses done in the Born approximation.Comment: 24 pages including 4 figures. Fig.4 is modified and stylistic corrections are made. The final version to appear in Eur.Phys.J.