Eur. Phys. J. C (2006) 46: 433-438
https://doi.org/10.1140/epjc/s2006-02475-0

Theoretical Physics

Chiral phase structure of QCD with many flavors

¹ Institut für theoretische Physik, Philosophenweg 16, 69120, Heidelberg, Germany
² Deutsches Elektronen Synchrotron, Notkestraße 85, 22607, Hamburg, Germany

^* e-mail: jjaeckel@mail.desy.de

Received: 12 August 2005
Revised: 12 December 2005
Published online: 17 March 2006

Abstract

We investigate QCD with a large number of massless flavors with the aid of renormalization group flow equations. We determine the critical number of flavors separating the phases with and without chiral symmetry breaking in SU(N_c) gauge theory with many fermion flavors. Our analysis includes all possible fermionic interaction channels in the pointlike four-fermion limit. Constraints from gauge invariance are resolved explicitly and regulator-scheme dependencies are studied. Our findings confirm the existence of an N_f window where the system is asymptotically free in the ultraviolet, but remains massless and chirally invariant on all scales, approaching a conformal fixed point in the infrared. Our prediction for the critical number of flavors of the zero-temperature chiral phase transition in SU(3) is N_f ^cr=10.0±0.29 (fermion)^+1.55 _-0.63 (gluon), with the errors arising from approximations in the fermionic and gluonic sectors, respectively.