Perturbative and Nonperturbative Renormalization in Lattice QCD

We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations.Comment: 54 pages, 15 figures; v2: several clarifications and additions, two more figures, results unchanged; v3: typos in eqs.(C33) and (E2) corrected, results unchange

Lattice QCD evaluation of the Compton amplitude employing the Feynman-Hellmann theorem

Published 8 December 2020The forward Compton amplitude describes the process of virtual photon scattering from a hadron and provides an essential ingredient for the understanding of hadron structure. As a physical amplitude, the Compton tensor naturally includes all target mass corrections and higher twist effects at a fixed virtuality, Q². By making use of the second-order Feynman-Hellmann theorem, the nucleon Compton tensor is calculated in lattice QCD at an unphysical quark mass across a range of photon momenta 3 ≲ Q² ≲ 7 GeV². This allows for the Q² dependence of the low moments of the nucleon structure functions to be studied in a lattice calculation for the first time. The results demonstrate that a systematic investigation of power corrections and the approach to parton asymptotics is now within reach.K. U. Can, A. Hannaford-Gunn, R. Horsley, Y. Nakamura, H. Perlt, P. E. L. Rakow, G. Schierholz, K. Y. Somfleth, H. Stüben, R. D. Young, and J. M. Zanotti (QCDSF/UKQCD/CSSM Collaborations

Flavour breaking effects in the pseudoscalar meson decay constants

The SU(3) flavour symmetry breaking expansion in up, down and strange quark masses is extended from hadron masses to meson decay constants. This allows a determination of the ratio of kaon to pion decay constants in QCD. Furthermore when using partially quenched valence quarks the expansion is such that SU(2) isospin breaking effects can also be determined. It is found that the lowest order SU( 3) flavour symmetry breaking expansion (or Gell-Mann-Okubo expansion) works very well. Simulations are performed for 2 + 1 flavours of clover fermions at four lattice spacings. (C) 2017 The Author(s). Published by Elsevier B.V

Electric form factors of the octet baryons from lattice QCD and chiral extrapolation

We apply a formalism inspired by heavy-baryon chiral perturbation theory with finite-range regularization to dynamical 2+1-flavor CSSM/QCDSF/UKQCD Collaboration lattice QCD simulation results for the electric form factors of the octet baryons. The electric form factor of each octet baryon is extrapolated to the physical pseudoscalar masses, after finite-volume corrections have been applied, at six fixed values of Q2 in the range 0.2–1.3  GeV2. The extrapolated lattice results accurately reproduce the experimental form factors of the nucleon at the physical point, indicating that omitted disconnected quark loop contributions are small relative to the uncertainties of the calculation. Furthermore, using the results of a recent lattice study of the magnetic form factors, we determine the ratio μpGpE/GpM. This quantity decreases with Q2 in a way qualitatively consistent with recent experimental results

Electric form factors of the octet baryons from lattice QCD and chiral extrapolation

We apply a formalism inspired by heavy-baryon chiral perturbation theory with finite-range regularization to dynamical $2+1$-flavor CSSM/QCDSF/UKQCD Collaboration lattice QCD simulation results for the electric form factors of the octet baryons. The electric form factor of each octet baryon is extrapolated to the physical pseudoscalar masses, after finite-volume corrections have been applied, at six fixed values of ${Q}^{2}$ in the range $0.2–1.3\text{}\text{}{\mathrm{GeV}}^{2}$. The extrapolated lattice results accurately reproduce the experimental form factors of the nucleon at the physical point, indicating that omitted disconnected quark loop contributions are small relative to the uncertainties of the calculation. Furthermore, using the results of a recent lattice study of the magnetic form factors, we determine the ratio ${\mu }_{p}{G}_{E}^{p}/{G}_{M}^{p}$. This quantity decreases with ${Q}^{2}$ in a way qualitatively consistent with recent experimental results

Perturbative and nonperturbative renormalization in lattice QCD

We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations.Comment: 54 pages, 15 figures; v2: several clarifications and additions, two more figures, results unchanged; v3: typos in eqs.(C33) and (E2) corrected, results unchange