Neutrino amplitude decomposition: Toward observing the atmospheric - solar wave interference

TL;DR

This paper develops a method to decompose neutrino oscillation amplitudes into atmospheric and solar components in matter, enabling better observation of their interference, which is crucial for understanding lepton flavor structure.

Contribution

It introduces a novel amplitude decomposition method in matter environments, extending previous vacuum techniques to facilitate interference analysis.

Findings

Derived formulas for amplitude decomposition in matter frameworks

Analyzed properties of decomposed probabilities in neutrino oscillations

Compared decomposition behavior between different neutrino transition channels

Abstract

Observation of the interference between the atmospheric and solar oscillation waves with the correct magnitude would provide another manifestation of the three-generation structure of leptons. As a prerequisite for such analyses we develop a method for decomposing the oscillation $S$ matrix into the atmospheric and solar amplitudes. Though the similar method was recently proposed successfully in vacuum, once an extension into the matter environment is attempted, it poses highly nontrivial problems. Even for an infinitesimal matter potential, inherent mixture of the atmospheric and solar oscillation waves occurs, rendering a simple extension of the vacuum definition untenable. We utilize general kinematic structure as well as analyses of the five perturbative frameworks, in which the nature of matter-dressed atmospheric and solar oscillations are known, to understand the origin of the trouble, how to deal with the difficulty, and to grasp the principle of decomposition. Then, we derive the amplitude decomposition formulas in these frameworks, and discuss properties of the decomposed probabilities. We mostly discuss the $\nu_{\mu} \rightarrow \nu_{e}$ channel, but a comparison with the $\nu_{\mu} \rightarrow \nu_{\tau}$ channel reveals an interesting difference.