Leading logs in QCD axion effective field theory

Abstract

The axion is much lighter than all other degrees of freedom introduced by the Peccei-Quinn mechanism to solve the strong CP problem. It is therefore natural to use an effective field theory (EFT) to describe its interactions. Loop processes calculated in the EFT may however explicitly depend on the ultraviolet cutoff. In general, the UV cutoff is not uniquely defined, but the dimensionful couplings suggest to identify it with the Peccei-Quinn symmetry-breaking scale. An example are K+ → π+ + a decays that will soon be tested to improved precision in NA62 and KOTO and whose amplitude is dominated by the term logarithmically dependent on the cutoff. In this paper, we critically examine the adequacy of using such a naive EFT approach to study loop processes by comparing EFT calculations with ones performed in complete QCD axion models. In DFSZ models, for example, the cutoff is found to be set by additional Higgs degrees of freedom and to therefore be much closer to the electroweak scale than to the Peccei-Quinn scale. In fact, there are non-trivial requirements on axion models where the cutoff scale of loop processes is close to the Peccei-Quinn scale, such that the naive EFT result is reproduced. This suggests that the existence of a suitable UV embedding may impose restrictions on axion EFTs. We provide an explicit construction of a model with suitable fermion couplings and find promising prospects for NA62 and IAXO.

Precision axion physics with running axion couplings

“…(2.13) and eq. (2.15), while it can be non-vanishing for more generic DFSZ-like axions [34]. In fact, for the standard DFSZ axions, n t (f a ) =c A (f a ) = 0 (A = G, W, B), and the RG running is present only below the BSM scale after the BSM Higgs doublet or Higgsinos are integrated out giving rise to a non-zero C t (m BSM ) orc W,B (m BSM ), while the running byc G is present only after the top quark is integrated out.…”

“…One can consider more generic models of field-theoretic axions other than those presented above, e.g. models with different Higgs sector for the Yukawa couplings of the SM fermions, or additional U(1) PQ -charged fields, or even flavor-dependent U(1) PQ -charges [30][31][32][33][34][35][36][37]. In the following, we use the term "DFSZ-like axions" for generic field-theoretic axions with C 0 Ψ = O(1) (Ψ = u, d, e) and the term "KSVZ-like axions" for those with C 0 Ψ = 0 (or more generically C 0…”

ALPINIST: Axion-Like Particles In Numerous Interactions Simulated and Tabulated

“…where Λ denotes the unknown scale of new physics (which may or may not be connected to the symmetry breaking scale [60]) and the parameters C denote the Wilson coefficients of the various effective operators. For the remainder of this discussion we will set C qq = 0 at tree level.…”

ALPINIST: Axion-Like Particles In Numerous Interactions Simulated and Tabulated

“…where Λ denotes the unknown scale of new physics (which may or may not be connected to the symmetry breaking scale [58]) and the parameters C denote the Wilson coefficients of the various effective operators. For the remainder of this discussion we will set C qq = 0 at tree level.…”