Leading logs in QCD axion effective field theory

• Published in: The journal of high energy physics Vol. 2021; no. 7; pp. 1 - 54
• Main Authors: Alonso-Álvarez, Gonzalo, Ertas, Fatih, Jaeckel, Joerg, Kahlhoefer, Felix, Thormaehlen, Lennert J.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-07-2021; Springer Nature B.V; SpringerOpen
• Subjects: Adequacy; Beyond Standard Model; Broken symmetry; Classical and Quantum Gravitation; Couplings; Degrees of freedom; Effective Field Theories; Elementary Particles; Energy; Experiments; Fermions; Field theory; High energy physics; Phenomenology; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Symmetry; Effective Field Theories; Beyond Standard Model
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2021)059

A
bstract
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.