Generalized Chiral $U(1)_{B-L}$: Towards a Less Constrained $Z'$ and Dark Matter

Abstract: Extensions of the Standard Model by a $U(1)<em>{X}$ gauge symmetry predict a new $Z&#39;$ boson, whose mass is severely constrained by high-mass dilepton resonance searches at the LHC. We show that these bounds can be relaxed by generalizing the chiral $(B-L)$ charge assignment while preserving gauge anomaly cancellation. The resulting $U(1)_X$ charges are parameterized by two independent parameters, and an appropriate choice of these parameters suppresses the $Z&#39;$ branching fraction into charged leptons, substantially weakening the dilepton constraints. The framework accommodates Dirac neutrino masses through a Dirac type-I seesaw mechanism and a stable singlet scalar DM candidate without requiring an additional discrete symmetry. We find that the modified charge assignment, although beneficial for collider phenomenology, introduces a tension between obtaining the observed relic abundance and satisfying direct detection limits when DM annihilation proceeds solely through the $Z&#39;$ portal. The inclusion of scalar-mediated annihilation channels resolves this tension and opens up a broad viable parameter space, with DM masses ranging from $M</em>{\rm DM}\simeq 60~{\rm GeV}$ to $10~{\rm TeV}$. The resulting parameter space is consistent with the observed relic density, direct detection, collider, and electroweak precision constraints, demonstrating that a generalized chiral charge structure can simultaneously accommodate a less constrained $Z&#39;$ sector, neutrino masses, and viable dark matter phenomenology.