Assisted baryon number violation from $4k+2$ dimensions

Proton decay in six dimensions orbifolded on square $T^2/Z_2$ is highly suppressed at tree-level. This is because baryon number violating (BNV) operators containing only the zero mode of bulk fermions must satisfy the selection rule $\frac{3}{2} \Delta B \pm \frac{1}{2}\Delta L = 0 \ mod \ 4$. In this article, we show that the above relation does not prohibit mass dimension-6 BNV operators containing Kaluza Klein (KK) partners of the bulk fermions. Together with `spinless' adjoint scalar partner of hypercharge gauge boson (the Dark Matter candidate), these novel operators generate Dark Matter assisted proton decay at mass dimension-8. Here, with explicit examples of scalar and vector baryon number violating interactions, we discuss the importance of such $\Delta B=1 =\Delta L$ and $\Delta B=2=\Delta L$ operators and derive the limit on New Physics.