Neutrino non-standard interactions meet precision measurements of $N_{\mathrm{eff}}$

Abstract

The number of relativistic species, $N_{\mathrm{eff}}$, has been precisely calculated in the standard model, and would be measured to the percent level by CMB-S4 in future. Neutral-current non-standard interactions would affect neutrino decoupling in the early Universe, thus modifying $N_{\mathrm{eff}}$. We parameterize those operators up to dimension-7 in the effective field theory framework, and then provide a complete, generic and analytical dictionary for the collision term integrals. From precision measurements of $N_{\mathrm{eff}}$, the most stringent constraint is obtained for the dimension-6 vector-type neutrino-electron operator, whose scale is constrained to be above about 195 (331) GeV from Planck (CMB-S4). We find our results complementary to other experiments like neutrino coherent scattering, neutrino oscillation, collider, and neutrino deep inelastic scattering experiments.

Minor changes. Match the published version. To appear in JHEP

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