Spectrum of SU(2) gauge theory at large number of flavors

Abstract

We present a numerical study of the spectrum of an asymptotically non-free $SU(2)$ gauge theory with $N_f=24$ massive fermion flavors. For such 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 behaviour.