Abstract
We improve the precision of the topological susceptibility of QCD, and therefore of the QCD axion mass, by including O(αem) and NNLO corrections in the chiral expansion, which amount to 0.65(21)% and -0.71(29)% respectively. Both corrections are one order of magnitude smaller than the known NLO ones, confirming the very good convergence of the chiral expansion and its reliability. Using the latest estimates for the light quark masses the current uncertainty is dominated by the one of the low-energy constant ℓ7. When combined with possible improvements on the light quark mass ratio and ℓ7 from lattice QCD, our computation could allow to determine the QCD axion mass with per-mille accuracy.
Highlights
JHEP03(2019)033 physics at much higher scales, as well as physics of the early universe including inflation, reheating and pre-BBN evolution
We improve the precision of the topological susceptibility of QCD, and of the QCD axion mass, by including O(αem) and NNLO corrections in the chiral expansion, which amount to 0.65(21)% and -0.71(29)% respectively
We start by reporting the result for the computation of the leading EM corrections to the topological susceptibility, which begin at O(e2p2) in the chiral expansion once the leading order term is written in terms of the physical4 neutral pion mass mπ0 and the physical charged pion decay constant fπ+: χtop
Summary
While the QCD axion has a vanishing electric charge, its mass can receive O(αem) corrections from several sources. We start by reporting the result for the computation of the leading EM corrections to the topological susceptibility, which begin at O(e2p2) in the chiral expansion once the leading order term is written in terms of the physical neutral pion mass mπ0 (including EM corrections) and the physical charged pion decay constant fπ+ (defined in pure QCD, i.e. at αem = 0): χtop z (1 + z). The best determination comes from the charged pion leptonic decay, which according to the PDG [14] provides fπ+ = 92.28(9) This estimate involves EM corrections of the same order of δe, so that a consistent calculation of χtop within the chiral expansion should consider the two sources of EM corrections together. Given the compatibility of the chiral and the lattice results, and the fact that the latter has better precision and less model dependence, we will use eq (2.5) and this lattice estimation for fπ+, bearing in mind that numerically this choice is equivalent to using the PDG determination
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