Pseudo-Dirac Inelastic Dark Matter in the Leptophobic $U(1)_B$ Model: Confronting the LUX-ZEPLIN High-Recoil Event with Collider Searches

RESUMO

Interpreting the $248$~keV nuclear-recoil candidate reported by LUX-ZEPLIN (LZ) as an endothermic transition needs two ingredients usually put in by hand: a stable dark state, and a coherent current that is purely off diagonal. Gauging baryon number supplies both. For the minimal dark charges $B(\chi_L)=-3/2$ and $B(\chi_R)=-9/2$, the scalars that generate the dark masses leave an exact residual parity $P=(-1)^{6B}$ stabilizing the lightest state, while the same Majorana masses make the vector current transition dominated as an identity rather than a choice. At $m_\chi=1$~TeV and $\delta=300$~keV the model is over-determined: the observed LZ interval, a leading-order relic estimate and the LHC dijet limit meet at the single perturbatively acceptable point $(M_{Z_B},g_B)\simeq(1.44~\mathrm{TeV},0.233)$. That point is allowed by currently existing searches but sits just below the trigger-level dijet boundary, so it is alive and not yet decided--and a re-run of that analysis on the Run-3 data at $\sqrt s=13.6$~TeV, already on tape, will exclude it or find it. Nor is the interpretation confined to that splitting: at $\delta=200$~keV, the same construction predicts a heavier mediator at comparable coupling, $M_{Z_B}\simeq2.4$-$3.0$~TeV with $g_B\simeq0.15$-$0.34$, a range the HL-LHC dijet program will probe.