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 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.
The momemtum dependence of the off-shell $rho$-$omega$ mixing amplitude is calculated through a two-quark loop diagram, using non-perturbative meson-quark vertex functions for the $rho$ and $omega$ mesons, as well as non-perturbative quark propagators. Both these quantities are generated self-consistently through an interlinked BSE-cum-SDE approach with a 3D support for the BSE kernel with two basic constants which are pre- checked against a wide cross section of both meson and baryon spectra within a common structural framework for their respective 3D BSEs. With this pre-calibration, the on-shell strength works out at -2.434$delta(m_q^2)$ in units of the change in constituent mass squared, which is consistent with the $e^+e^-$ to $pi^+pi^-$ data for a u-d mass difference of ~4 MeV ,while the relative off-shell strength (0.99 $pm$ 0.01) lies midway between quark-loop and QCD-SR results. We also calculate the photon-mediated $rho$-$omega$ propagator whose off-shell structure has an additional pole at $q^2$=0. The implications of these results vis-a-vis related investigations are discussed.
We calculate the unpolarized and polarized three--loop anomalous dimensions and splitting functions $P_{rm NS}^+, P_{rm NS}^-$ and $P_{rm NS}^{rm s}$ in QCD in the $overline{sf MS}$ scheme by using the traditional method of space--like off shell massless operator matrix elements. This is a gauge--dependent framework. For the first time we also calculate the three--loop anomalous dimensions $P_{rm NS}^{rm pm tr}$ for transversity directly. We compare our results to the literature.
We evaluate the one-loop $beta$ functions of all dimension 6 parity-preserving operators in the Abelian Higgs-Kibble model. No on-shell restrictions are imposed; and the (generalized) non-polynomial field redefinitions arising at one-loop order are fully taken into account. The operator mixing matrix is also computed, and its cancellation patterns explained as a consequence of the functional identities of the theory and power-counting conditions.
We calculate the two loop correction to the quark 2-point function with the non-zero momentum insertion of the flavour singlet axial vector current at the fully symmetric subtraction point for massless quarks in the modified minimal subtraction (MSbar) scheme. The Larin method is used to handle $gamma^5$ within dimensional regularization at this loop order ensuring that the effect of the chiral anomaly is properly included within the construction.