The Good Qualities of the Weak Axion

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, $\Lambda$. Existing Super-Kamiokande limits on these decay channels constrain the new physics scale to be $\Lambda \gtrsim 10^{12}$ 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.