Lattice Monte Carlo study of pre-conformal dynamics in strongly flavoured QCD in the light of the chiral phase transition at finite temperature

We study the thermal phase transition in colour SU(Nc=3) Quantum Chromodynamics (QCD) with a variable number of fermions in the fundamental representation by using lattice Monte Carlo simulations. We collect the (pseudo) critical couplings βLc for Nf=(0,4,6, and 8), and we investigate the pre-conformal dynamics associated with the infra-red fixed point in terms of the Nf dependence of the transition temperature. We propose three independent estimates of the number of flavour Nf⁎ where the conformal phase would emerge, which give consistent results within the largish errors. We consider lines of fixed Nt in the space of (Nf, bare lattice coupling), and locate the vanishing of the step-scaling function for Nf⁎∼11.1±1.6. We define a typical interaction strength gTc at the scale of critical temperature Tc and we find that gTc meets the zero temperature critical couplings estimated by the two-loop Schwinger-Dyson equation or the IRFP coupling in the four-loop beta-function at Nf⁎∼12.5±1.6. Further, we study the Nf dependences of Tc/M where M is a UV Nf independent reference scale determined by utilising the coupling at the scale of the lattice spacing. Then, Tc/M turns out to be a decreasing function of Nf and the vanishing Tc/M indicates the emergence of the conformal window at Nf⁎∼10.4±1.2.