Effect of non-zero theta(13) on the measurement of theta(23)

TL;DR

This paper analytically examines how a non-zero theta13 affects the measurement of theta23 in neutrino oscillation experiments, highlighting the importance of correct parameter conversion to avoid biased results.

Contribution

It derives the analytical relation between true and measured theta23 values considering non-zero theta13 and demonstrates its impact through simulations.

Findings

Incorrect theta23 measurement leads to biased best-fit values.

Misinterpretation causes false sensitivity to the octant of theta23.

Proper conversion is essential for accurate neutrino oscillation analysis.

Abstract

The moderately large measured value of theta13 signals a departure from the approximate two-flavour oscillation framework. As a consequence, the relation between the value of theta23 in nature, and the mixing angle measured in muon neutrino disappearance experiments is non-trivial. In this paper, we calculate this relation analytically. We also derive the correct conversion between degenerate values of theta23 in the two octants. Through simulations of a muon neutrino disappearance experiment, we show that there are observable consequences of not using the correct relation in calculating oscillation probabilities. These include a wrong best-fit value for theta23, and spurious sensitivity to the octant of theta23.