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Register a new userBilinear quark operators in the RI/SMOM scheme at three loops
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We consider the renormalization of the matrix elements of the bilinear quark operators $bar{psi}psi$, $bar{psi}gamma_mupsi$, and $bar{psi}sigma_{mu u}psi$ at next-to-next-to-next-to-leading order in QCD perturbation theory at the symmetric subtraction point. This allows us to obtain conversion factors between the $overline{rm MS}$ scheme and the regularization invariant symmetric momentum subtraction (RI/SMOM) scheme. The obtained results can be used to reduce the errors in determinations of quark masses from lattice QCD simulations. The results are given in Landau gauge.
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We study the renormalization of the matrix elements of the twist-two non-singlet bilinear quark operators, contributing to the $n=2$ and $n=3$ moments of the structure functions, at next-to-next-to-next-to-leading order in QCD perturbation theory at the symmetric subtraction point. This allows us to obtain conversion factors between the $overline{rm MS}$ scheme and the regularization-invariant symmetric momentum subtraction (RI/SMOM, RI${}$/SMOM) schemes. The obtained results can be used to reduce errors in determinations of moments of structure functions from lattice QCD simulations. The results are given in Landau gauge.
Light quark masses can be determined through lattice simulations in regularization invariant momentum-subtraction(RI/MOM) schemes. Subsequently, matching factors, computed in continuum perturbation theory, are used in order to convert these quark masses from a RI/MOM scheme to the MS-bar scheme. We calculate the two-loop corrections in quantum chromodynamics(QCD) to these matching factors as well as the three-loop mass anomalous dimensions for the RI/SMOM and RI/SMOM_gamma_mu schemes. These two schemes are characterized by a symmetric subtraction point. Providing the conversion factors in the two different schemes allows for a better understanding of the systematic uncertainties. The two-loop expansion coefficients of the matching factors for both schemes turn out to be small compared to the traditional RI/MOM schemes. For nf=3 quark flavors they are about 0.6-0.7% and 2%, respectively, of the leading order result at scales of about 2 GeV. Therefore, they will allow for a significant reduction of the systematic uncertainty of light quark mass determinations obtained through this approach. The determination of these matching factors requires the computation of amputated Greens functions with the insertions of quark bilinear operators. As a by-product of our calculation we also provide the corresponding results for the tensor operator.
We construct the two loop Greens functions for a quark bilinear operator inserted at non-zero momentum in a quark 2-point function for the most general off-shell configuration. In particular we consider the quark mass operator, vector and tensor currents as well as the second moment of the flavour non-singlet Wilson operator.
We extend the Rome-Southampton regularization independent momentum-subtraction renormalization scheme(RI/MOM) for bilinear operators to one with a nonexceptional, symmetric subtraction point. Two-point Greens functions with the insertion of quark bilinear operators are computed with scalar, pseudoscalar, vector, axial-vector and tensor operators at one-loop order in perturbative QCD. We call this new scheme RI/SMOM, where the S stands for symmetric. Conversion factors are derived, which connect the RI/SMOM scheme and the MSbar scheme and can be used to convert results obtained in lattice calculations into the MSbar scheme. Such a symmetric subtraction point involves nonexceptional momenta implying a lattice calculation with substantially suppressed contamination from infrared effects. Further, we find that the size of the one-loop corrections for these infrared improved kinematics is substantially decreased in the case of the pseudoscalar and scalar operator, suggesting a much better behaved perturbative series. Therefore it should allow us to reduce the error in the determination of the quark mass appreciably.
Renormalization constants (RCs) of overlap quark bilinear operators on 2+1-flavor domain wall fermion configurations are calculated by using the RI/MOM and RI/SMOM schemes. The scale independent RC for the axial vector current is computed by using a Ward identity. Then the RCs for the quark field and the vector, tensor, scalar and pseudoscalar operators are calculated in both the RI/MOM and RI/SMOM schemes. The RCs are converted to the $overline{rm MS}$ scheme and we compare the numerical results from using the two intermediate schemes. The lattice size is $48^3times96$ and the inverse spacing $1/a = 1.730(4) {rm~GeV}$.
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