Algebraic algorithm for the computation of one-loop Feynman diagrams in lattice QCD with Wilson fermions

Abstract

We describe an algebraic algorithm which allows to express every one-loop lattice integral with gluon or Wilson-fermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although the presentation is restricted to four dimensions the technique can be generalized to every space dimension. Various examples are given, including the one-loop self-energies of the quarks and gluons and the renormalization constants for some dimension-three and dimension-four lattice operators. We also give a method to express the lattice free propagator for Wilson fermions in coordinate space as a linear function of its values in eight points near the origin. This is an essential step in order to apply the recent methods of Lüscher and Weisz to higher-loop integrals with fermions.

Postscript file avalaible at http://www1.le.infn.it:8080/~caraccio/TCMS.html

References in corpus (4)

• Coordinate space methods for the evaluation of Feynman diagrams in lattice field theory
• Deep Inelastic Scattering in Improved Lattice QCD. I. The first moment of structure functions
• Perturbative Renormalization of Lattice Bilinear Quark Operators
• Four-Loop Perturbative Expansion for the Lattice $N$-Vector Model

Cited by in corpus (15)

• Study of QCD Phase Diagram with Non-Zero Chiral Chemical Potential
• Two-loop critical mass for Wilson fermions
• A calculation of the $B_B$ parameter in the static limit
• The Asymptotic Expansion of Lattice Loop Integrals Around the Continuum Limit
• Gauge Theories on a 2+2 Anisotropic Lattice
• Exact integration of height probabilities in the Abelian Sandpile Model
• Asymptotic expansion of the lattice scalar propagator in coordinate space
• Renormalization of the energy-momentum tensor in three-dimensional scalar $SU(N)$ theories using the Wilson flow
• High-precision computation of two-loop Feynman diagrams with Wilson fermions
• Spectral Functions, Maximum Entropy Method and Unconventional Methods in Lattice Field Theory
• Continuum methods in lattice perturbation theory
• Relation between bare lattice coupling and MSbar coupling at one loop with general lattice fermions
• Calculation of $c_{\mathrm{SW}}$ at one-loop order for Brillouin fermions
• Functional Forms for Lattice Correlators at Small Times
• Lattice Coulomb propagators, effective energy and confinement