Freezing-in the Axiverse

TL;DR

This work develops a comprehensive effective field theory framework for an axiverse with ${ m N}$ axions coupled to the SM at dimension $d=5$ and $d=6$, including a previously unidentified charge-radius operator. It demonstrates that dim-5 interactions couple only ${ m N}_{ m ind}$ axions to the SM, while dim-6 operators generically couple the full axion spectrum, making $ rm eff$ highly sensitive to the flavor structure of the couplings. By analyzing benchmark EFTs—Hadronic, Anarchy, Froggatt–Nielsen textures, and Minimal Flavor Violation—the authors compute freeze-in production rates and forecast the discovery space for Planck-era and future CMB experiments (Simons Observatory, CMB-S4, CMB-HD), highlighting rich interplay with terrestrial probes. The results indicate that current data already constrain high reheating temperatures or large ${ m N}$ and that upcoming surveys can substantially tighten these bounds, providing a powerful probe of UV completions with many axions and guiding top-down model building for axion couplings.

Abstract

The presence of multiple light axions in the infrared is a generic feature of many ultraviolet (UV) scenarios. In many cases the number of axions ${\cal N}$ is ${\cal O}(10-100)$ or more. Even in the scenario where these axions interact very weakly with the Standard Model (SM), the presence of ${\cal N}$ light axions poses a challenge to the stringent constraint on the number of relativistic degrees of freedom $N_{\rm eff}$. In order to remain agnostic about the UV, we adopt an effective field theory (EFT) approach, and parametrize the interactions of ${\cal N}$ axions with the SM to quantify the contribution to $N_{\rm eff}$. We consider operators up to dimension six, uncovering one previously-unconsidered charge radius operator, and pay particular attention to the flavor structure of the axion-SM fermion couplings and consider EFTs based on anarchy, textures, and minimal flavor violation. For various choices of such EFTs, we identify the discovery space for current and future cosmic microwave background surveys, including the Simons Observatory and CMB-HD. We show this discovery space depends sensitively on the flavor structure and exhibits a rich interplay with terrestrial and astrophysical probes.

Figures (13)

• Figure 1: The decoupling temperatures $T_d$ for the independent axion degrees of freedom, assuming that the axion couplings to the SM are hadronic (Eq. \ref{['eq:had_ax']}). There are three independent axions, the QCD axion $a_{\rm QCD}$ (blue), the electroweak axion $a_2$ (orange), and the hypercharge axion $a_1$ (green). We also show the $T_d$ for a scenario where the three axion states arise from a GUT (Eq. \ref{['eq:gut_ax']}), so that there is one independent axion (red). These lines are cut off at $T_d=f_a$ above which our EFT treatment requires inclusion of additional states.
• Figure 2: Representative diagrams relevant for freeze-in involving axion-fermion coupling. Since these diagrams are computed at temperatures greater than the weak scale, the full Higgs doublet $H$ participates in the processes. The leading contribution comes from diagrams where the vertex involving $H$ contains the top quark.
• Figure 3: As in Fig. \ref{['fig:Hadronic_Tdec']}, but assuming that the axion couplings to fermions are anarchic (Sec. \ref{['sec:anarchy']}) with unit magnitudes \ref{['eq:c_Anarchy']}. The legend labels $F_{nm}$ indicate that the associated axion is $a_F^{nm}$ and is listed in ascending order of $T_d$. The subscript $n \in \{1,2\}$ is such that those axions are flavor-violating. The $T_d$ for axions coupled to $F_{ij}$ and $F_{ji}$ is equal, so we only show curves for those with $i>j$. Axion states with no corresponding label have $T_d>f_a$ for all $f_a$ considered (this applies for any state coupled to only first-generation fermions).
• Figure 4: As in Fig. \ref{['fig:Hadronic_Tdec']}, but assuming that the axion couplings to fermions are set by a texture (Sec. \ref{['sec:FN']}, Eq. \ref{['eq:texture']}). The convention for legend labels is as in Fig. \ref{['fig:Anarchy_Tdec']}. Axions are not shown when $T_d>f_a$, including those coupled only to first-generation fermions and to $Q_{21}$, $d_{21}$, and $e_{21}$.
• Figure 5: As in Fig. \ref{['fig:Hadronic_Tdec']}, but assuming that the axion couplings to fermions satisfy MFV (Sec. \ref{['sec:MFV']}). The axion states $a_F^{(i)}$ are defined as those which couple to fermions $F$ with strength $c_F^{(i)}$; see discussion after Eq. \ref{['eq:MFV']}.