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 $d\geq7$, we investigate the sensitivity to the $d=5$ Weinberg operator using the non-resonant signature $pp\to \ell^\pm \ell'^{\pm} j j$ at the LHC. We develop a prescription for the operator that is applicable in collisions and decays, and focus on the $\ell\ell'=\mu\mu$ channel, which is beyond the reach of nuclear decays. For a Wilson coefficient $C^{\mu\mu}_5=1$, scales as heavy as $\Lambda\sim 8.3~(11)$~TeV can be probed with $\mathcal{L}=300~{\rm fb}^{-1}~(3~{\rm ab}^{-1})$. This translates to an effective $\mu\mu$ Majorana mass of $\vert m_{\mu\mu}\vert\sim7.3~(5.4)$~GeV, and establishes a road map for testing the Weinberg operator at accelerators.