Flavour interferometry in Reissner-Nordstrom background

TL;DR

This work analyzes flavour oscillations of neutrino-like particles in a curved spacetime described by the Reissner-Nordström metric, focusing on gravitational lensing by a charged compact object. It derives the phase along RN geodesics in the ultra-relativistic limit, employing a weak-field expansion with an analytic-continuation prescription to regulate divergences, and computes the four-flavour interference pattern for two intersecting geodesics. A key result is the emergence of two oscillation lengths, one radial and one orthoradial, whose phase factors depend on $m_1^2$ and $m_2^2$, with the RN charge shifting the pattern relative to Schwarzschild. The framework, valid for fermions as well, highlights the importance of coherence and suggests that gravitational lensing-induced flavour interference could, in principle, yield independent measurements of the eigen-masses from astrophysical neutrino signals.

Abstract

We derive the phase acquired by a neutral scalar particle propagating along Reissner-Nordstrom geodesics. Considering two flavours propagating on different trajectories which intersect, we plot the interference pattern induced by gravitational lensing from the charged compact object. Although the effect of the charge is subdominant in the metric, it proves to be significant in the phase, and shifts the interference pattern, compared to the Schwarzschild case. This pattern is characterised by two oscillation lengths which, if known, would allow the determination of both eigen masses independently.

Figures (8)

• Figure 1: The source is located at the point $A$, at the distance $r_A$ from the compact object, and the detector is located at the point $B$, at the distance $r_B$ from the compact object. $b$ is the impact parameter and the closest approach distance is denoted by $r_0$.
• Figure 2: Four phases interfere at the intersection point after scattering: two flavours on each trajectory.
• Figure 3: Oscillation probability for a nearly maximal charge $r_Q=0.49r_S$ and a mass difference of $1\%$.
• Figure 4: Difference of oscillation probability $\Delta P_{f\to f'}$ (charged minus uncharged) for a mass difference of $1\%$.
• Figure 5: Oscillation probability for a nearly maximal charge $r_Q=0.49r_S$ and a mass difference of $0.1\%$.