Probing the Weinberg Operator at Colliders

Motivated by searches for $0\nu \beta \beta$ decay in nuclear experiments and collider probes of lepton number violation at dimension $d\ge 7$, we investigate the sensitivity to the $d=5$ Weinberg operator using the non-resonant signature $pp\to {\mathrm{\ell }}^{\pm }{\mathrm{\ell }}^{\mathrm{\prime }\pm }jj$ at the LHC. We develop a prescription for the operator that is applicable in collisions and decays, and focus on the $\mathrm{\ell }{\mathrm{\ell }}^{\mathrm{\prime }}=\mu \mu$ channel, which is beyond the reach of nuclear decays. For a Wilson coefficient $C_5^{\mu \mu }=1$, scales as heavy as $\mathrm{\Lambda }\sim 8.3(11)$~TeV can be probed with $$\mathcal{L}$=300~{\rm fb}^{-1}~(3~{\rm ab}^{-1})$\mathrm{.}Thistranslatestoaneffective$\mu\mu$ Majorana mass of $\mathrm{\mid }{m}_{\mu \mu }\mathrm{\mid }\sim 7.3(5.4)$~GeV, and establishes a road map for testing the Weinberg operator at accelerators.