Chiral observables and topology in hot QCD with two families of quarks

Abstract

We present results on QCD with four dynamical flavors in the temperature range 150 MeV T 500 MeV. We have performed lattice simulations with Wilson fermions at maximal twist and measured Polyakov loop, chiral condensate and disconnected susceptibility, on lattices with spacings as fine as 0.065 fm. For most observables spacing effects are below statistical errors, which enables us to identify lattice results with continuum estimates. Our estimate of the pseudocritical temperature compares favorably with continuum results from staggered and domain wall fermions, confirming that a dynamical charm does not contribute in the transition region. From the high temperature behaviour of the disconnected chiral susceptibility we infer the topological susceptibility, which encodes relevant properties of the QCD axion, a plausible Dark Matter candidate. The topological susceptibility thus measured exhibits a power-law decay for T /Tc 2, with an exponent close to the one predicted by the Dilute Instanton Gas Approximation (DIGA). Close to Tc the temperature dependent effective exponent seems to approach the DIGA result from above, a behaviour which would support recent analytic calculations based on an Instantons-dyons model. These results constrain the mass of a hypothetic QCD post-inflationary axion, once an assumption concerning the relative contribution of axions to Dark Matter is made.

Axion misalignment driven to the bottom

“…where n = 4 for the SM is obtained by the dilute instanton gas approximation (see the lattice simulations in Refs. [54][55][56][57][58], whose results indicate that n ranges from 3.0 to 3.7 depending on the temperature). The equation of motion and the energy density read where n = 0 is understood for f a 10 17 GeV as the axion mass reaches the zero-temperature value before the oscillation starts.…”

Axion misalignment driven to the hilltop

“…(2.4) and (2.5) assume the topological susceptibility of QCD given by the dilute instanton gas approximation (see the lattice results in Refs. [58][59][60][61][62]) but our results are insensitive to this uncertainty.…”

The holographic QCD axion

“…The derivative axion-nucleon couplings defined by the effective interaction term 21) where N = (p, n) is the nucleon field, are given by 22) where m N is the (large) nucleon mass and g η N N , g πN N are the CP-even couplings of the η and the pions with the nucleons. To leading order in the chiral limit 4c 2χ WYM Tr[M −1 ], which sets the pion mass to be much smaller than that of the η , the above expressions reduce to…”

“…For recent computations of the topological susceptibility at finite temperature on the lattice see also[16][17][18][19][20][21][22][23][24].…”