Abstract
We present a numerical study of the spectrum of an asymptotically nonfree SU(2) gauge theory with ${N}_{f}=24$ massive fermion flavors. For such a large number of flavors, asymptotic freedom is lost and the massless theory is governed by a Gaussian fixed point at long distances. If fermions are massive they decouple at low energy scales and the theory is confining. We present a scaling law for the masses of the hadrons, glueballs and string tension as functions of fermion mass. The hadrons become effectively heavy quark systems, with masses approximately twice the fermion mass, whereas the energy scale of the confinement, probed by e.g., the string tension, is much smaller and vanishes asymptotically as ${m}_{\text{fermion}}^{2.18}$. Our results from lattice simulations are compatible with this behavior.
Highlights
Free non-Abelian gauge-fermion theories are a cornerstone of our theoretical understanding of the elementary particle interactions of ordinary matter
Let us turn to the details of the simulations and the results we have obtained on the spectrum of physical states
We have presented scaling relations for the hadron masses and for the confinement scale as functions of the quark mass
Summary
Free non-Abelian gauge-fermion theories are a cornerstone of our theoretical understanding of the elementary particle interactions of ordinary matter. On the lattice the properties of these types of theory have been studied for SU(2) gauge theory with matter fields in the fundamental [5,6,7,8,9] or adjoint [10,11,12,13,14,15,16,17,18] representation. Analyses have been extended to the SU(4) gauge group with fermions in fundamental and higher representations [34,35]
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