Testing leptogenesis at the LHC and future muon colliders: a $Z^{\mathrm{\prime }}$ scenario

If the masses of at least two generations of right-handed neutrinos (RHNs) are near-degenerate, the scale of leptogenesis can be as low as $\sim$ 100 GeV. In this work, we study probing such resonant leptogenesis in the $B-L$ model at the LHC and future multi-TeV muon colliders via the process $Z’\to NN\to\ell^\pm\ell^\pm+{\rm jets}$,with$Z’$the$U(1)_{B-L}$gaugebosonand$N$ the RHN. The same-sign dilepton feature of the signal makes it almost background-free, while the event number difference between positive and negative leptons is a hint for $CP$ violation, which is a key ingredient of leptogenesis. We found that resonant leptogenesis can be tested at the HL-LHC for $M_{Z^{\mathrm{\prime }}}$ up to 12 TeV, while at a 10 (30) TeV muon collider the reach can be up to $M_{Z^{\mathrm{\prime }}}\sim 28(100)$ TeV via the off-shell production of $Z^{\mathrm{\prime }}$.