The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: zero temperature calibrations and numerical framework

This is the first in a series of papers which ultimately aims on improving on the present estimates on the axion mass by modeling the topological non-perturbative QCD dynamics. Axions couple to instantons and their mass is set by the topological susceptibility whose temperature dependence we estimate with the interacting instanton liquid model (IILM). Since accurate finite temperature instanton calculations have problems and do not consider fluctuations in the topological charge, we develop an improved grand canonical version of the IILM to study topological fluctuations in the quark gluon plasma. In this first paper we will calibrate the model against the topological susceptibility at zero temperature, in the chiral regime of physical quark masses.