The Good Qualities of the Weak Axion

TL;DR

The paper investigates a good-quality weak axion, $a_W$, arising as the pseudo-Nambu–Goldstone boson of a spontaneously broken $U(1)_{B+L}$ in the Standard Model’s electroweak sector. It shows that $a_W$ is photophobic because tree-level $a_W\gamma\gamma$ couplings vanish, and its mass is nonperturbatively suppressed by electroweak instantons, while anomaly-induced couplings to EW gauge bosons and fermions are controlled by the decay constant $f_W$. A distinctive portal, $(\langle \Phi_W\rangle/\Lambda^3)\,qqql$, induces baryon-violating interactions that generate proton-decay channels such as $p\to e^+\pi^0$ and $p\to e^+a_W$, allowing current bounds to constrain $\Lambda$ (and $f_W$) to high scales: $\Lambda \gtrsim 8.3\times 10^{12}$ GeV for $f_W=10^6$ GeV from Super-Kamiokande, with Hyper-Kamiokande improving to $\sim 9.7\times 10^{12}$ GeV; the $p\to e^+a_W$ channel yields a weaker bound. The loop-induced electron coupling yields a strong stellar cooling bound, $f_W \gtrsim 10^3$ TeV. Overall, the proton-decay portal provides the most stringent experimental handle on the weak-axion scenario, and future proton-decay experiments offer the most promising path to test this paradigm.

Abstract

The presence of a topological susceptibility in the electroweak sector of the Standard Model motivates the existence of a good quality weak axion $a_W$, associated with the spontaneous breaking of $B\!+\!L$. Its anomalous couplings and tiny mass, generated from electroweak instantons, render $a_W$ photophobic. We find that the strongest bound on the associated decay constant, $f_W$, stems from a loop-induced coupling to electrons, leading to $f_W \gtrsim 1000$ TeV from stellar cooling. Spontaneous breaking of the abelian ${B\!+\!L}$ symmetry induces proton decay via higher dimensional operators controlled by a new physics scale, $Λ$. Existing Super-Kamiokande limits on these decay channels constrain the new physics scale to be $Λ\gtrsim 10^{12}$ GeV. The characteristic channel $p\to e^+ a_W$ and other possible operators mediating interactions with the Standard Model fields yield signals which are not detectable within the allowed parameter space. Future proton decay searches at the next-generation of neutrino experiments offer the most promising avenues to test the good qualities of the weak axion paradigm.

Figures (1)

• Figure 1: Exclusion limits on the $f_W$--$\Lambda$ plane from red giant cooling (red) and proton decay (blue) from Super-Kamiokande. The solid lines correspond to the elementary case ($\langle\Phi_W\rangle=f_W$) and the dashed one to the composite one ($\langle\Phi_W\rangle=4\pi f_W$).