Abstract
We recently obtained an estimate of the axion mass based on the hypothesis that axions make up most of the dark matter in the universe. A key ingredient for this calculation was the temperature-dependence of the topological susceptibility of full QCD. Here we summarize the calculation of the susceptibility in a range of temperatures from well below the finite temperature cross-over to around 2 GeV. The two main difficulties of the calculation are the unexpectedly slow convergence of the susceptibility to its continuum limit and the poor sampling of nonzero topological sectors at high temperature. We discuss how these problems can be solved by two new techniques, the first one with reweighting using the quark zero modes and the second one with the integration method.
Highlights
One of the most viable candidates for dark matter is the axion [1]
A crucial ingredient for estimating the axion mass is the temperaturedependence of the QCD topological susceptibility, a quantity that proved to be notoriously hard to compute
Small instantons are badly resolved by a non-chiral Dirac operator and the would-be topological zero modes are far away from zero
Summary
One of the most viable candidates for dark matter is the axion [1]. experimental search for this so far hypothetical particle is seriously hampered by the lack of information regarding its mass. The second problem, that of insufficient statistics for higher topological sectors, can be solved by noting that derivatives of the susceptibility (with respect to temperature and quark mass) are much easier to calculate than the susceptibility itself. These derivatives can be written in terms of the average action and the quark condensates measured in different topological sectors. Using these derivatives, the susceptibility can be integrated up to any point in parameter space, starting from a point (low temperature, heavy quarks) where a direct calculation is feasible. Our final results pertain to the real physical situation including the continuum limit and the effects of dynamical u, d, s and c quarks with their physical masses along with a correction for the u − d isospin splitting
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