Gauge theories with overlap fermions in an arbitrary representation: Evaluation of the 3loop βfunction
Abstract
This work presents the calculation of the relation between the bare coupling constant g_{0} and the M Smacr renormalized coupling g_{M Smacr }, g_{0}=Z_{g}(g_{0},aμ)g_{M Smacr }, to 2 loops in perturbation theory, with fermions in an arbitrary representation of the gauge group SU(N). Our calculation is performed using overlap fermions and Wilson gluons, and the background field technique has been chosen for convenience. The corresponding results in the fundamental representation appear in our longer publication [M. Constantinou and H. Panagopoulos, Phys. Rev. D 76, 114504 (2007)PRVDAQ0556282110.1103/PhysRevD.76.114504]. The 3loop coefficient of the bare βfunction, b_{2}^{L}, is extracted using the 2loop expression for Z_{g}, and it is presented as a function of the overlap parameter ρ, the number of fermion flavors (N_{f}) and the number of colors (N). We also provide the expression for the ratio of energy scales Λ_{L}/Λ_{M Smacr }, in an arbitrary representation. A plot of Λ_{L}/Λ_{M Smacr } is given in the adjoint representation.
 Publication:

Physical Review D
 Pub Date:
 March 2008
 DOI:
 10.1103/PhysRevD.77.057503
 arXiv:
 arXiv:0711.4665
 Bibcode:
 2008PhRvD..77e7503C
 Keywords:

 11.15.Ha;
 11.10.Gh;
 12.38.Bx;
 12.38.Gc;
 Lattice gauge theory;
 Renormalization;
 Perturbative calculations;
 Lattice QCD calculations;
 High Energy Physics  Lattice
 EPrint:
 15 pages, 5 figures