A new constraint on primordial lepton flavour asymmetries

A chiral chemical potential present in the early universe can source helical hypermagnetic fields through the chiral plasma instability. If these hypermagnetic fields survive until the electroweak phase transition, they source a contribution to the baryon asymmetry of the universe. In this letter, we demonstrate that lepton flavour asymmetries above $\mathrm{\mid }\mu \mathrm{\mid }\mathrm{/}T\sim 9\times {10}^{-3}$ trigger this mechanism even for vanishing total lepton number. This excludes the possibility of such large lepton flavour asymmetries present at temperatures above ${10}^6$ GeV, setting a constraint which is about two orders of magnitude stronger than the current CMB and BBN limits.