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A large primordial lepton asymmetry is capable of explaining the baryonasymmetry of the Universe (BAU) through suppression of the electroweaksphaleron rates (``sphaleron freeze-in") which can lead to a first-order cosmicQCD transition with an observable gravitational wave (GW) signal. Withnext-to-leading order dimensional reduction and the exact 1-loop fluctuationdeterminant, we accurately compute the lepton asymmetry needed to realize thisparadigm, finding it to be an order of magnitude smaller than previousestimates. Further, we apply an improved QCD equation of state capable ofdescribing the phase transition line together with the critical endpointleading to better agreement with lattice and functional QCD results. Based onthis, we identify the range of lepton flavor asymmetries inducing a first-ordercosmic QCD transition. We then extract the parameters relevant to theprediction of GW signal from a first-order cosmic QCD transition. Our resultshowcases the possibility of probing the sphaleron freeze-in paradigm as anexplanation of BAU by future gravitational wave experiments like $\mu$Ares.

Sphaleron freeze-in baryogenesis with gravitational waves from the QCD transition