Abstract
We study axion effective field theories (EFTs), with a focus on axion couplings to massive chiral gauge fields. We investigate the EFT interactions that participate in processes with an axion and two gauge bosons, and we show that, when massive chiral gauge fields are present, such interactions do not entirely originate from the usual anomalous EFT terms. We illustrate this both at the EFT level and by matching to UV-complete theories. In order to assess the consistency of the Peccei-Quinn (PQ) anomaly matching, it is useful to introduce an auxiliary, non-dynamical gauge field associated to the PQ symmetry. When applied to the case of the Standard Model (SM) electroweak sector, our results imply that anomaly-based sum rules between EFT interactions are violated when chiral matter is integrated out, which constitutes a smoking gun of the latter. As an illustration, we study a UV-complete chiral extension of the SM, containing an axion arising from an extended Higgs sector and heavy fermionic matter that obtains most of its mass by coupling to the Higgs doublets. We assess the viability of such a SM extension through electroweak precision tests, bounds on Higgs rates and direct searches for heavy charged matter. At energies below the mass of the new chiral fermions, the model matches onto an EFT where the electroweak gauge symmetry is non-linearly realised.
Highlights
Axions are prime and ubiquitous candidates for physics beyond the Standard Model (BSM), and as such have motivated great theoretical and experimental efforts
We study axion effective field theories (EFTs), with a focus on axion couplings to massive chiral gauge fields
We show that the axion coupling to the gauge field must correspond to a UV PQ anomaly coefficient when the gauge field is massless, whereas there exist additional EFT coefficients when the gauge field is massive, that are not constrained by anomaly
Summary
Axions are prime and ubiquitous candidates for physics beyond the Standard Model (BSM), and as such have motivated great theoretical and experimental efforts. There exist more EFT operators involving massive gauge bosons than massless ones, due to the possibility that some symmetries are realized non-linearly in the EFT [7] This resonates with recent computations [32, 33] which showed that, in a given UV model, mixed anomalies between the PQ and the gauge symmetries do not control uniquely the couplings between the axion and massive chiral gauge fields, even at leading order when all the heavy degrees of freedom lie at arbitrarily high energy. We point out that non-anomalous operators exist there, and we discuss them in detail for the specific case of the SM electroweak sector We find that they allow to evade phenomenological correlations, which we express as sum-rules among Wilson coefficients of axion couplings to vector bosons, and which are linked to the structure of the mixed PQ anomalies with the SU(2)L × U(1)Y gauge symmetry. Appendix B further discusses the axion couplings, the UV PQ anomalies, as well as their relation, in the model of section 5
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