Recent progress on QCD inputs for axion phenomenology

Abstract

Abstract. The properties of the QCD axion are strictly related to the dependence of strong interactions on the topological parameter theta. We present a determination of the topological properties of QCD for temperatures up to around 600 MeV, obtained by lattice QCD simulations with 2+1 flavors and physical quark masses. Numerical results for the topological susceptibility, when compared to instanton gas computations, differ both in size and in the temperature dependence. We discuss the implications of such findings for axion phenomenology, also in comparison to similar studies in the literature, and the prospects for future investigations.

Axions, instantons, and the lattice

“…In some cases, discrepancies are found at high temperatures compared with the dilute instanton gas prediction. The free energies found in [12,13] differ by about an order of magnitude from the leadingorder semiclassical result above the GeV scale, while the computation and extrapolation obtained in [7,14] (see also [17]) differs by many orders of magnitude (although systematic effects are not under control in the extrapolation, and thus the level of compatibility with the controlled high-temperature computations in [12,13] is unclear.) These results suggest a level of uncertainty in the microscopic parameters (the zero temperature axion mass m a and possibly the misalignment angle θ 0 ) required to achieve a given relic density Ω.…”

“…Given T 0 = 1.5 GeV, values of T 2 of order 150 in fact correspond to n 8, equivalent to assuming instanton-like behavior persists significantly below T 0 . Larger values for T 2 above the critical temperature T c are not based on physical considerations, but instead are included to partially accommodate the lattice results of [7,14], which found very shallow falloff of χ(T ) above the chiral phase transition. This behavior is then approximated in the models of Eq.…”

“…Recently there have been a number of papers reporting lattice calculations of χ(T ) at temperatures above the critical temperature, both in pure gauge theory/quenched approximations [9,10,8] and in QCD [11,12,13,7,14,15,16]. In some cases, discrepancies are found at high temperatures compared with the dilute instanton gas prediction.…”

The dark-matter axion mass

“…sanyi et al at lower temperatures [36][37][38][39][40][41], although no group has reproduced these higher temperatures and even below 600 MeV there are some results which appear discrepant [42,43]. Therefore we will explore other n values but consider values near n = 7.5 to be likely correct.…”

Axion dark matter and the Lattice

“…It takes new techniques to reach higher temperatures, and only one recent paper [27] achieves this, reaching temperatures of 1500 MeV. Also, one group [28,29] finds results which are discrepant with the others, indicating that the matter is not yet settled. Here we will assume that the results of [27] are correct.…”