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

Understand

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.