$\Delta B=1$ Nucleon Radiative Decays

SuperKamiokande experiment tightly bounds the decay widths of the baryon number violating proton decays. The proton decay can be induced by the tree-level amplitudes in which either scalar or vector leptoquarks are mediators of a new interaction. Such leptoquarks probe the physics beyond the Standard Model at a scale $10^{16}$ GeV. However, such decays can occur at a much lower scale if they proceed at the loop level. The decay widths for the nucleon to antilepton and photon are not so well bounded. We investigate nucleon annihilation to an antilepton accompanied by a photon and determine tree and loop-level amplitudes for $p\to \ell^+ \gamma$ ($\ell = e, \, \mu$ ) and $n \to \bar \nu \gamma$. Our result points out factor $10^{3}$ suppression of the decay widths $\Gamma (p \to \ell^{+} \gamma)$ and $\Gamma (n \to \bar \nu \gamma)$ compared to the decay widths $\Gamma (p \to \ell^{+} \pi^{0})$ and $\Gamma (n \to \bar \nu \pi^{0})$, respectively.