Abstract
Axions and axion-like particles (ALPs) are well-motivated low-energy relics of high-energy extensions of the Standard Model, which interact with the known particles through higher-dimensional operators suppressed by the mass scale Λ of the new-physics sector. Starting from the most general dimension-5 interactions, we discuss in detail the evolution of the ALP couplings from the new-physics scale to energies at and below the scale of electroweak symmetry breaking. We derive the relevant anomalous dimensions at two-loop order in gauge couplings and one-loop order in Yukawa interactions, carefully considering the treatment of a redundant operator involving an ALP coupling to the Higgs current. We account for one-loop (and partially two-loop) matching contributions at the weak scale, including in particular flavor-changing effects. The relations between different equivalent forms of the effective Lagrangian are discussed in detail. We also construct the effective chiral Lagrangian for an ALP interacting with photons and light pseudoscalar mesons, pointing out important differences with the corresponding Lagrangian for the QCD axion.
Highlights
The results of this work apply to the cases of the QCD axion and of a more general axion-like particles (ALPs), and on we use the term ALP to represent both options
Starting from the most general effective Lagrangian at dimension-5 order, we calculate the effects of renormalization-group (RG) evolution from the new-physics scale down to the scale of electroweak symmetry breaking and below, systematically including all contributions to the anomalous dimensions arising at two-loop order in gauge couplings and one-loop order in Yukawa interactions
Once the effective Lagrangian has been evolved to the weak scale μw, it is appropriate to express it in terms of fields defined in the broken phase of the electroweak symmetry, which correspond to the mass eigenstates of physical particles
Summary
We consider a gauge-singlet, pseudoscalar resonance a, whose couplings to SM fields are, at the classical level, protected by an approximate shift symmetry a → a + c, broken softly. Such a coupling structure arises, for example, if the particle a can be identified with the phase of a complex scalar field
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