$B-L$ violating nucleon decays as a probe of leptoquarks and implications for baryogenesis

We study the effective $B-L$ violating couplings for scalar and vector leptoquarks which can naturally induce dimension seven $B-L$ violating operators leading to very interesting nucleon decay modes such as $n \rightarrow e^- \pi^+, e^-K^+,\mu^- \pi^+, \mu^-K^+$ and $p \rightarrow \nu \pi^+$. This opens a new window to probe the nature and couplings of the scalar and vector leptoquarks in an ultraviolet model independent way which can provide an orthogonal probe for scalar and vector leptoquark solutions to the recent anomalous $B$-decay data. Furthermore, we also discuss how these $B-L$ violating interactions can also pave a new way to understand the origin of matter-antimatter asymmetry of the Universe.