For technical reasons, if there are exactly three kinds of neutrinos, as the Standard Model of Particle Physics provides, the effective number of neutrino species Neff that we expect to see in astronomy measurements is slightly more than 3. A new paper calculates the expected value to record high precision.
Towards a precision calculation ofin the Standard Model II: Neutrino decoupling in the presence of flavour oscillations and finite-temperature QED
We present in this work a new calculation of the standard-model benchmark value for the effective number of neutrinos,, that quantifies the cosmological neutrino-to-photon energy densities. The calculation takes into account neutrino flavour oscillations, finite-temperature effects in the quantum electrodynamics plasma to , where is the elementary electric charge, and a full evaluation of the neutrino--neutrino collision integral. We provide furthermore a detailed assessment of the uncertainties in the benchmark value, through testing the value's dependence on (i) optional approximate modelling of the weak collision integrals, (ii) measurement errors in the physical parameters of the weak sector, and (iii) numerical convergence, particularly in relation to momentum discretisation. Our new, recommended standard-model benchmark is , where the nominal uncertainty is attributed predominantly to errors incurred in the numerical solution procedure, augmented by measurement errors in the solar mixing angle .