Uncovering a chirally suppressed mechanism of $0\nu\beta\beta$ decay with LHC searches

$\Delta L =2$ lepton number violation (LNV) at the TeV scale could provide an alternative interpretation of positive signal(s) in future neutrinoless double beta $(0\nu\beta\beta)$ decay experiments. An interesting class of models from this point of view are those that at low energies give rise to dimension-9 vector operators and a dimension-7 operator, both of whose $0\nu\beta\beta$-decay rates are "chirally suppressed". We study and compare the sensitivities of $0\nu\beta\beta$-decay experiments and LHC searches to a simplified model in this class of TeV-scale LNV that is also $SU(2)_L \times U(1)_Y$ gauge invariant. The searches for $0\nu\beta\beta$ decay, which are here diluted by a chiral suppression of the vector operators, are found to be less constraining than LHC searches whose reach is increased by the assumed kinematic accessibility of the mediator particles. For the chirally suppressed dimension-7 operator generated by TeV-scale mediators, in contrast, $0\nu\beta\beta$-decay searches place strong constraints on the size of the new Yukawa coupling. Signals of this model at the LHC and $0\nu\beta\beta$-decay experiments are entirely uncorrelated with the observed neutrinos masses, as these new sources of LNV give negligible contributions to the latter. We find the prospects for the high-luminosity LHC and ton-scale $0\nu\beta\beta$-decay experiments to uncover the chirally-suppressed mechanism with TeV-scale LNV to be promising. We also comment on the sensitivity of the $0\nu\beta\beta$-decay lifetime to certain unknown low-energy constants that in the case of dimension-9 {\it scalar} operators are expected to be large due to non-perturbative renormalization.