The low-energy effective theory of axions and ALPs

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.

ALP — SMEFT interference

“…The renormalization-group (RG) evolution of the dimension-5 ALP couplings in the effective Lagrangian L SM+ALP has recently been studied in [43,44]. Here we point out the important fact that the existence of an ALP with couplings to the SM necessarily induces non-zero Wilson coefficients of the dimension-6 SMEFT operators contained in L SMEFT , which produce effects across a wide variety of observables.…”

“…In section 2 we briefly review the effective Lagrangian describing the interactions of ALPs with SM particles at dimension-5 order, following closely the presentation in [43]. In section 3 we explain our method for calculating the ALP contributions to the RG equations of the SMEFT operators.…”

“…The form of the effective Lagrangian (2.1) is the one in which the shift symmetry is most explicit. However, for our purposes it will be useful to consider an alternative but equivalent form, in which the ALP couplings to fermions are of a non-derivative type [43]. Integrating by parts in the last term in (2.1) and using the SM equations of motion (EOMs) along with the equation for the axial anomaly leads to (withH i = ij H * j )…”

“…In recent work, a detailed study of the RG evolution of the ALP couplings to SM particles in the effective ALP Lagrangians (2.1) and (2.2) from the new-physics scale Λ down to low energies has been performed [43,44]. We summarize the one-loop RG equations in JHEP06(2021)135 appendix B.…”

“…, where V denotes the CKM matrix. Following [21,43], we denote the ALP-fermion couplings in this basis by k U = c Q , k E = c L , and k f = c f for f = u, d, e. Moreover, we define k D = V † c Q V . With these definitions, the matrices k i specify the ALP-fermion couplings in the mass basis of the SM fermions.…”