Invisible decays of vector Charmonia and Bottomonia to determine the Weak Mixing Angle at quarkonia scale

We compute the branching fractions of vector quarkonia ($V_Q=J\mathrm{/}\psi ,{\psi }^{\mathrm{\prime }},\mathrm{{\rm Y}}(nS)$) decays into neutrino pairs, considering both Dirac and Majorana types, within the Standard Model (SM) and beyond. The vector nature of quarkonium states yields a decay width in the SM that depends upon the weak vector coupling of the heavy quark, offering the possibility to measure the weak mixing angle at the quarkonia mass scales. If neutrinos have non-standard neutral weak couplings, this could help to distinguish the nature of neutrinos in principle.