Atmospheric, long baseline, and reactor neutrino data constraints on $\theta_{13}$

TL;DR

This study combines atmospheric, long baseline, and reactor neutrino data with advanced three-neutrino oscillation modeling to constrain the mixing angle θ13, revealing its upper bound from atmospheric data and lower bound from CHOOZ, with implications for CP conservation.

Contribution

It introduces a comprehensive three-neutrino oscillation analysis including the MSW effect, providing refined bounds on θ13 from multiple neutrino experiments and data regions.

Findings

θ13 is bounded from above by atmospheric data

CHOOZ data provides the lower bound on θ13

Linear terms in θ13 significantly affect the bounds

Abstract

A new atmospheric neutrino oscillation tool which utilizes full three neutrino oscillation probabilities and a full three neutrino treatment of the MSW effect is combined with a standard analysis of the K2K, MINOS, and CHOOZ data to examine the bounds on $\theta_{13}$ implied by existing data, including the recent, more finely binned, Super-K atmospheric data. In the region $L/E_\nu\gtrsim 10^4$ km/GeV, we have previously found that the sub-dominant expansion does not converge and that terms linear in $\theta_{13}$ can be significant. The current analysis confirms this and leads to the conclusion that $\theta_{13}$ is bounded from above by the atmospheric data while CHOOZ provides the lower bound. We trace the origin of this result to fully contained data in the previously mentioned very long baseline region, to a combination of a quadratic in $\theta_{13}$ term in ${\mathcal P}_{ee}$ and a linear term in ${\mathcal P}_{e\mu}$ and their contribution to $R_e$, a broad MSW resonance for the solar mass-squared difference at 180 MeV, and an increase in $\theta_{12}$ due to this resonant matter effect which alters the sign of the linear in $\theta_{13}$ term. Assuming CP is conserved in the lepton sector, we find $\theta_{13}=-0.07^{+0.18}_{-0.11}$, the asymmetry being a reflection of the importance of the linear in $\theta_{13}$ terms.