Abstract
We investigate the topological properties of $N_f = 2+1$ QCD with physical quark masses, both at zero and finite temperature. We adopt stout improved staggered fermions and explore a range of lattice spacings $a \sim 0.05 - 0.12$ fm. At zero temperature we estimate both finite size and finite cut-off effects, comparing our continuum extrapolated results for the topological susceptibility $\chi$ with predictions from chiral perturbation theory. At finite temperature, we explore a region going from $T_c$ up to around $4\, T_c$, where we provide continuum extrapolated results for the topological susceptibility and for the fourth moment of the topological charge distribution. While the latter converges to the dilute instanton gas prediction the former differs strongly both in the size and in the temperature dependence. This results in a shift of the axion dark matter window of almost one order of magnitude with respect to the instanton computation.
Highlights
Given the strong bounds on its couplings, the axion field can be safely treated as a nondynamical external field
We explore a region going from Tc up to around 4 Tc, where we provide continuum extrapolated results for the topological susceptibility and for the fourth moment of the topological charge distribution
In order to further inquire about the reliability of our continuum extrapolation and the importance of the partial breaking of chiral symmetry in the staggered discretization, we studied the combination χ1tc/4(a) aχ1/4(a) mpπhys amngb(a)
Summary
Given the strong bounds on its couplings, the axion field can be safely treated as a nondynamical external field. Because of the strict connection, in the presence of light fermions, between the topological content of gauge configurations and the spectrum of the fermion matrix (in particular regarding the presence of zero modes), a reliable study of topological quantities requires a discretization of the theory in which the chiral properties of fermions fields are correctly implemented For standard discretizations, such properties are recovered only for small enough lattice spacings, so that a careful investigation of the continuum limit becomes essential. We consider simulations at zero temperature and various different values of the lattice spacing, in a range ∼ 0.05 − 0.12 fm and staying on a line of constant physics, in order to identify a proper scaling window where the continuum limit can be taken without incurring in severe problems with the freezing of topological modes. These results are taken as an input to fix the parameters of the axion potential in the same range of temperatures and perform a phenomenological analysis
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