Newtonian Self-Gravitation in the Neutral Meson System

TL;DR

This paper explores the implications of the Schrödinger-Newton equation for high-energy meson-antimeson systems, revealing how nonlinear gravity effects influence flavor oscillations without damping, depending on wave-function relations.

Contribution

It provides a novel analysis of nonlinear gravitational effects on meson systems, highlighting the dependence on wave-function relations and contrasting with collapse models.

Findings

Nonlinear gravity affects flavor oscillations.

No damping change unlike collapse models.

Behavior depends on wave-function shape and relation.

Abstract

We derive the effect of the Schr\"odinger--Newton equation, which can be considered as a non-relativistic limit of classical gravity, for a composite quantum system in the regime of high energies. Such meson-antimeson systems exhibit very unique properties, e.g. distinct masses due to strong and electroweak interactions. We find conceptually different physical scenarios due to lacking of a clear physical guiding principle which mass is the relevant one and due to the fact that it is not clear how the flavor wave-function relates to the spatial wave-function. There seems to be no principal contradiction. However, a nonlinear extension of the Schr\"odinger equation in this manner strongly depends on the relation between the flavor wave-function and spatial wave-function and its particular shape. In opposition to the Continuous Spontaneous Localization collapse models we find a change in the oscillating behavior and not in the damping of the flavor oscillation.