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Tests of Low-Scale Leptogenesis in Charged Lepton Flavour Violation Experiments

We consider low-energy tests of low-scale leptogenesis based on the type I seesaw scenario with three right-handed singlet neutrinos $ν_{l R}$. In this scenario, successful leptogenesis is possible for quasi-degenerate in mass heavy Majorana neutrinos $N_{1,2,3}$, $M_{1,2,3}\cong M$, $|M_j - M_i|\ll M$, $i\neq j = 1,2,3$, heavy Majorana neutrino masses $M \sim (0.05 - 5\times 10^5)$ GeV, and $N_j$ charged current and neutral current weak interaction couplings as large as $\mathcal{O}(10^{-2})$. We derive the constraints on the corresponding leptogenesis parameter space from the existing data from low-energy experiments, including the limits from the experiments on $μ\rightarrow e γ$ decay and on the rate of $μ- e$ conversion in gold. We show also that the planned and upcoming experiments on charged lepton flavour violation with $μ^\pm$, MEG II on the $μ\rightarrow eγ$ decay, Mu3e on $μ\rightarrow eee$ decay, Mu2e and COMET on $μ- e$ conversion in aluminium and PRISM/PRIME on $μ- e$ conversion in titanium, can probe significant region of the viable leptogenesis parameter space, and thus have a potential for a discovery. Experiments on $τ\to eee(μμμ)$ and $τ\to e(μ)γ$ decays (e.g., BELLE II) also can probe a part of the leptogenesis parameter space, although a relatively small one.