The three-loop beta function in SU(N) lattice gauge theories

Abstract

We calculate the third coefficient of the lattice $\beta$ function in pure Yang-Mills theory. We make use of a computer code for solving perturbation theory analytically on the lattice. We compute the divergent integrals by using a method based on a Taylor expansion of the integrand in powers of the external momenta in $4-\epsilon$ dimensions. Our results are in agreement with a previous calculation by M. Lüscher and P. Weisz where the authors used a different technique. We also show how this new coefficient modifies the scaling function on the lattice in both the standard and energy schemes. In particular we show that asymptotic scaling is extremely well achieved in the energy scheme.

17 pages, 2 postcript files corresponding to a figure

References in corpus (5)

• Computation of the relation between the bare lattice coupling and the MSbar coupling in SU(N) gauge theories to two loops
• The Three-Loop Lattice Free Energy
• Background field technique and renormalization in lattice gauge theory
• Coordinate space methods for the evaluation of Feynman diagrams in lattice field theory
• Lattice Perturbation Theory by Computer Algebra: A Three-Loop Result for the Topological Susceptibility

Cited by in corpus (27)

• QCD forces and heavy quark bound states
• Thermodynamics of the QCD plasma and the large-N limit
• SU(N) gauge theories at large N
• Precision computation of a low-energy reference scale in quenched lattice QCD
• Accurate Scale Determinations for the Wilson Gauge Action
• Computation of the strong coupling in QCD with two dynamical flavours
• Non-perturbative improvement of the axial current for dynamical Wilson fermions
• Thermodynamics of SU(N) Yang-Mills theories in 2+1 dimensions II - The deconfined phase
• The three-loop beta function of SU(N) lattice gauge theories with Wilson fermions
• The three-loop beta-fuction of QCD with the clover action
• Scaling and the continuum limit of gluoN_c plasmas
• The Asymptotic Expansion of Lattice Loop Integrals Around the Continuum Limit
• Deconfinement, gradient and cooling scales for pure SU(2) lattice gauge theory
• Resummation of Cactus Diagrams in Lattice QCD
• Gauge Theories on a 2+2 Anisotropic Lattice
• Perturbative Wilson loops from unquenched Monte Carlo simulations at weak couplings
• QCD with overlap fermions: Running coupling and the 3-loop beta-function
• Scaling and confinement aspects of tadpole improved SU(2) lattice gauge theory and its abelian projection
• Asymptotic scaling and continuum limit of pure SU(3) lattice gauge theory
• Gauge theories with overlap fermions in an arbitrary representation: Evaluation of the 3-loop beta-function
• Large $N$ scaling and factorization in SU($N$) Yang-Mills gauge theory
• Relation between bare lattice coupling and MSbar coupling at one loop with general lattice fermions
• Perturbative determination of $\mathcal{O}(am)$ improvement on the QCD running coupling
• Scale Setting and Topological Observables in Pure SU(2) LGT
• Estimates of Scaling Violations for Pure SU(2) LGT
• Resummation of Cactus Diagrams in Lattice QCD, to all Orders
• Three-Loop Results in QCD with Wilson Fermions