Finite-size scaling tests for spectra in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions

Abstract

I carry out a finite-size scaling study of the correlation length in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions, using recent data published by Fodor, Holland, Kuti, N\'ogradi and Schroeder [Z. Fodor, K. Holland, J. Kuti, D. Nogradi, and C. Schroeder, Phys. Lett. B 703, 348 (2011).]. I make the assumption that the system is conformal in the zero-mass, infinite volume limit, that scaling is violated by both nonzero fermion mass and by finite volume, and that the scaling function in each channel is determined self-consistently by the data. From several different observables I extract a common exponent for the scaling of the correlation length $\ensuremath{\xi}$ with the fermion mass ${m}_{q}$, $\ensuremath{\xi}\ensuremath{\sim}{m}_{q}^{\ensuremath{-}1/{y}_{m}}$ with ${y}_{m}\ensuremath{\sim}1.35$. Shortcomings of the analysis are discussed.