A New Method of Calculating the Running Coupling Constant
Abstract
We propose a new method to compute the running coupling constant of gauge theories on the lattice. We first give the definition of the running coupling in the new scheme using the Wilson loops in a finite volume, and explain how the running of the coupling constant is extracted from the measurement of the volume dependence. The perturbative calculation of the renormalization constant to define the scheme is also given at the leading order. As a benchmark test of the new scheme we apply the method the case of the quenched QCD. We show the preliminary result from our numerical simulations which are carried out with plaquette gauge action for various lattice sizes and bare lattice couplings. With techniques to improve the statistical accuracy, we show that we can determine the non-perturbative running of the coupling constant in a wide range of the energy scale with relatively small number of gauge configurations in our scheme. We compare our lattice data of the running coupling constant with perturbative renormalization group evolution at one- and two-loop order, and confirm the consistency between them at high energy.
Cite
@article{arxiv.0808.2875,
title = {A New Method of Calculating the Running Coupling Constant},
author = {Erek Bilgici and Antonino Flachi and Etsuko Itou and Masafumi Kurachi and C. -J David Lin and Hideo Matsufuru and Hiroshi Ohki and Tetsuya Onogi and Takeshi Yamazaki},
journal= {arXiv preprint arXiv:0808.2875},
year = {2010}
}
Comments
13 pages, 6 figures, based on talks given by E. Itou and M. Kurachi at The XXVI International Symposium on Lattice Field Theory, July 14 - 19, 2008, Williamsburg, Virginia, USA; barely visible changes in Figs. 5 and 6