Abstract
At low energies, the strong interaction is governed by the Goldstone bosons associated with the spontaneous chiral symmetry breaking, which can be systematically described by chiral perturbation theory. In this paper, we apply this theory to study the θ-vacuum energy density and hence the QCD axion potential up to next-to-leading order with N non-degenerate quark masses. By setting N = 3, we then derive the axion mass, self-coupling, topological susceptibility and the normalized fourth cumulant both analytically and numerically, taking the strong isospin breaking effects into account. In addition, the model-independent part of the axion-photon coupling, which is important for axion search experiments, is also extracted from the chiral Lagrangian supplemented with the anomalous terms up to mathcal{O}left({p}^6right) .
Highlights
Some important quantities in axion physics, such as the axion mass and self-coupling, are dictated by the axion potential
We would like to stress that a similar study was performed in ref. [53], where the QCD axion potential derived in two-flavor Chiral perturbation theory (CHPT) up to next-to-leading order (NLO) is used, and a matching between two-flavor and three-flavor CHPT is performed to determine the axion-photon coupling
From the above θ-vacuum energy density, the lowest two cumulants of the topological charge distribution up to NLO can be extracted. It can be checked from eq (2.29) that we can reproduce the expression of topological susceptibility at NLO keeping all orders in strong isospin breaking exactly given in ref
Summary
The discovery of instantons solved the U(1)A problem, and implied that there is a θ-term in the QCD Lagrangian. Which arises from a U(1)A chiral rotation on the quark fields eliminating the θ-term in the QCD Lagrangian. In this case, the θ-dependence is completely captured by the quark mass term. By expanding the LO Lagrangian in terms of the meson fields to quadratic order, the LO θ-dependent meson masses including isospin breaking effects are obtained as. To simultaneously shift the θ angle to the quark mass matrix phase and align the vacuum properly This is a convenient choice for the aγγ coupling (with θ changed to the dynamical axion field a/fa) to be discussed in section 4 since this removes the leading order a-π0 and a-η mixing. We will compute the one-loop contribution of the Goldstone bosons to the energy density
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