Electromagnetic Simulation of Time-Reversal Violation in Mirror Spin-32Beta Decays

With time-reversal invariance, the $\beta$-decay correlation $\left(\frac{〈\mathrm{J}〉}{J}\right)·{\mathrm{p}}_l\times {\mathrm{p}}_{\nu }$, where $\frac{〈\mathrm{J}〉}{J}$ is the polarization of the decaying nucleus and ${\mathrm{p}}_l$ (${\mathrm{p}}_{\nu }$) is the momentum of the electron (neutrino), can arise only through a final-state electromagnetic interaction. For allowed transitions with vector and axial-vector couplings, this effect is recoil-dependent. It was shown by Callan and Treiman that this effect, for the special class of spin-½ mirror transitions, and the assumption of the conserved-vector-current (CVC) hypothesis, is dominated by weak magnetism. A corresponding calculation for the class of spin-$\frac{3}{2}$ mirror transitions, of which the decay ${\mathrm{Ar}}^{35}\to {\mathrm{Cl}}^{35}+e^{+}+{\nu }_e$ is an example, shows a similar domination by weak magnetism. The magnitude of this effect is estimated for several mirror $\beta$ transitions.