Implications of the Super-K atmospheric, long baseline, and reactor data for the mixing angles ?13 and ?23

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Physical Review C




A three-neutrino analysis of oscillation data is performed using the recent, more finely binned Super-K oscillation data, together with the CHOOZ, K2K, and MINOS data. The solar parameters ?21 and ?12 are fixed from a recent analysis and ?32, ?13, and ?23 are varied. We utilize the full three-neutrino oscillation probability and an exact treatment of Earth’s Mikheyev-Smirnov-Wolfenstein (MSW) effect with a castle-wall density. By including terms linear in ?13 and ?:=?23??/4, we find asymmetric errors for these parameters ?13=?0.07+0.18?0.11 and ?=0.03+0.09?0.15. For ?13, we see that the lower bound is primarily set by the CHOOZ experiment while the upper bound is determined by the low energy e-like events in the Super-K atmospheric data. We find that the parameters ?13 and ? are correlated—the preferred negative value of ?13 permits the preferred value of ?23 to be in the second octant, and the true value of ?13 affects the allowed region for ?23.