Testing Leptogenesis via CP asymmetries in Lepton-Number-Violating $W$ Decays at Colliders

In principle, searches for CP asymmetries in rare $W$-boson decays can test low-scale leptogenesis in the GeV-scale type-I seesaw with three quasi-degenerate-in-mass heavy right-handed neutrinos. To investigate this, we focus on the lepton-number-violating heavy-neutrino-mediated decay $W^{\pm }\to e^{\pm }{e}^{\pm }(\bar{q}{q}^{\mathrm{\prime }}{)}^{\mp }$, with $(\bar{q}{q}^{\mathrm{\prime }}{)}^{+}=(\bar{d}u{)}^{+}$ and $(\bar{q}{q}^{\mathrm{\prime }}{)}^{-}=(\bar{u}d{)}^{-}$. We determine the minimum branching ratio required for a CP asymmetry to be observable at colliders with a given statistical significance. We then perform a numerical scan of the presently-allowed parameter space, also solving the density matrix equations for low-scale leptogenesis, and identify regions where, simultaneously, the present baryon asymmetry of the Universe can be achieved and the collider CP asymmetry for the considered decay is observable at HL-LHC and FCC-hh. We find that these regions are sizeable. A future observation of a CP asymmetry in $W^{\pm }\to e^{\pm }{e}^{\pm }(\bar{q}{q}^{\mathrm{\prime }}{)}^{\mp }$ within the regions identified here would provide evidence in favour of low-scale leptogenesis as the origin of the matter-antimatter asymmetry of the Universe.