Axion Quality Problem: Keep Calm and Baryon

TL;DR

This work tackles the axion quality problem by proposing a simple composite axion where the Peccei–Quinn symmetry is the baryon number $U(1)_B$ of a confining SQCD sector with $N_f=N_c$. The SM color is embedded within a flavor subgroup to generate the QCD anomaly, and confinement spontaneously breaks $U(1)_B$, producing a pNGB axion that couples to gluons. Gravity-induced PQ-violating operators arise at high dimension, with leading breaking occurring at dimension $N_c+2$ after SUSY breaking, yielding a highly suppressed axion potential. For the minimal realization $N_c=N_f=10$ (with SM embedded in an $SO(10)$ subgroup of $SU(10)_L$), and a decay constant in the range $10^8\,\text{GeV} \lesssim f_a \lesssim 5\times 10^{11}\,\text{GeV}$, the induced effective theta angle satisfies $\theta_{\rm eff} \lesssim 10^{-11}$, providing a high-quality axion without extra model-building complexity and suggesting rich avenues for SUSY-breaking and holographic extensions.

Abstract

Axion models generically suffer from a severe quality problem when coupled to gravity. In this article we provide a very simple model with a high quality axion. The axion is a pseudo-Nambu-Goldstone boson of the baryon number symmetry, $U(1)_B$, of a new composite sector that breaks $U(1)_B$ spontaneously when it confines. A controlled example is a supersymmetric QCD (SQCD) with $N_c = N_f$. The axion shift symmetry is automatically protected due to the high dimension of the gauge-invariant baryon operator, with the Peccei-Quinn breaking operators arising at dimension $N_c+2$. The standard model gauge group is embedded as a subgroup of the flavor symmetry group of SQCD that has an anomaly with $U(1)_B$, generating the standard coupling with gluons.

Figures (2)

• Figure 1: A cartoon of the relevant energy scales and the different phases of the $SU(N_c)$ theory. Below the scale $F_X/M_{\rm pl}$ only the axion survives as a massless degree of freedom up to effects from QCD and higher-dimensional operators breaking its shift-symmetry.
• Figure 2: Effective theta angle $\theta_{\rm eff}$ as a function of the decay constant for theories with different number of colors, $N_c$, in blue, orange red and teal. Dotted, dashed and solid lines correspond to different SUSY breaking scales, $\sqrt{F_X}=10^{11}, 10^9,10^7$ GeV, respectively, for each $N_c$. More choices for $\sqrt{F_X}$ and $N_c$ are in principle allowed, with the predicted $\theta_{\rm eff}$ changing accordingly. For reference, the lower bound to $f_a$ from astrophysics Carenza:2019pxuBuschmann:2021juvSpringmann:2024ret (see Caputo:2024oqc for a recent review), as well as upper bound to $\theta_{\rm eff}$Abel:2020pzs are shown in shaded red and blue, respectively.