Beautiful Majorana Higgses at Colliders

We investigate a novel collider signature within the minimal Left-Right Symmetric Model, featuring a Higgs sector composed of a bi-doublet and two triplets. Our study focuses on a region of the parameter space where the $SU(2)_R$ charged gauge boson $W_R$ lies in the multi-TeV regime (3-100 TeV) and the additional Higgs states play a significant role. In this scenario, a heavy neutral Higgs boson $\Delta$ with a dominant $SU(2)_R$ triplet component can be produced in association with either a Standard Model Higgs boson or a massive weak boson. The subsequent decay of the heavy Higgs into Majorana neutrinos $N$ results in displaced lepton signatures, providing a striking manifestation of lepton number violation. Additionally, we explore how the production of $b$-jets in these processes can enhance hadron-collider sensitivity to such signals. A particularly compelling channel, $pp \to b \bar b NN$, offers the exciting possibility of simultaneously probing the spontaneous mass origin of both Dirac fermions and Majorana states. Based on an optimised event selection strategy and state-of-the-art Monte Carlo simulations, we outline the expected reach at the HL-LHC and future colliders. Our findings demonstrate that this channel probes a region of parameter space where the neutral Higgs triplet and heavy neutrino masses are relatively light ($m_\Delta \lesssim 250$ GeV, $m_N \lesssim 80$ GeV), indirectly constraining the $W_R$ boson to the deep multi-TeV domain, with sensitivity extending up to 70-80 TeV, effectively turning the LHC into a precision machine.