Direct comparison of sterile neutrino constraints from cosmological data, ${\nu }_e$ disappearance data and ${\nu }_{\mu }\to {\nu }_e$ appearance data in a $3+1$ model

Abstract

We present a quantitative, direct comparison of constraints on sterile neutrinos derived from neutrino oscillation experiments and from Planck data, interpreted assuming standard cosmological evolution. We extend a $1+1$ model, which is used to compare exclusions contours at the 95% CL derived from Planck data to those from ${\nu }_e$-disappearance measurements, to a $3+1$ model. This allows us to compare the Planck constraints with those obtained through ${\nu }_{\mu }\to {\nu }_e$ appearance searches, which are sensitive to more than one active-sterile mixing angle. We find that the cosmological data fully exclude the allowed regions published by the LSND, MiniBooNE and Neutrino-4 collaborations, and those from the gallium and rector anomalies, at the 95% CL. Compared to the exclusion regions from the Daya Bay ${\nu }_e$-disappearance search, the Planck data are more strongly excluding above $|\Delta m_{41}^2|\approx 0.1{\mathrm{eV}}^2$ and $m_{\mathrm{eff}}^{\mathrm{sterile}}\approx 0.2\mathrm{eV}$, with the Daya Bay exclusion being stronger below these values. Compared to the combined Daya Bay/Bugey/MINOS exclusion region on ${\nu }_{\mu }\to {\nu }_e$ appearance, the Planck data is more strongly excluding above $\Delta m_{41}^2\approx 5\times 10^{-2}{\mathrm{eV}}^2$, with the exclusion strengths of the Planck data and the Daya Bay/Bugey/MINOS combination becoming comparable below this value.

Comments: 9 pages, 4 figures, accepted by Eur. Phys. J. C