Transition probability of perturbative form for nu_mu -> nu_e oscillations in matter of constant density

TL;DR

This paper presents a new, clear expression for neutrino oscillation probability in constant-density matter, improving accuracy over previous formulas for terrestrial experiments.

Contribution

It introduces a perturbative formula for P(nu_mu -> nu_e) that balances simplicity with enhanced precision, building on and refining existing approaches.

Findings

Provides a more accurate oscillation probability expression.

Retains clarity of perturbative expansion in alpha.

Facilitates better predictions for terrestrial neutrino experiments.

Abstract

We give a convenient expression for the appearance probability P(nu_mu -> nu_e) describing neutrino oscillations in matter of constant density, derived using textbook quantum mechanics stratagems. Our formulation retains the clarity of an expansion in alpha = Delta m_{21}^2/Delta m_{31}^2 exhibited by the popular Cervera et al. formula [Nucl. Phys. B 579, 17 (2000)] while enabling more accurate evaluation of oscillations over terrestrial baselines.