Study on the Contribution of Positronium and $\pi^{0}$ Mesons to Casimir Force

TL;DR

This paper investigates how virtual positronium and $$ mesons contribute to the Casimir force, especially at specific plate distances, providing potential corrections to existing theoretical models.

Contribution

It introduces the consideration of massive virtual particles like positronium and $$ mesons in Casimir force calculations, which has been largely overlooked.

Findings

Positronium significantly affects the Casimir force at distances around 1/m_positronium.

$$ mesons contribute notably when the separation is near 1/m_{}.

The results can improve the accuracy of theoretical Casimir force predictions.

Abstract

There is a Casimir force between two metal plates. It is generally believed that the Casimir force is mediated by virtual photons in a vacuum, which correspond to the massless intermediate particles used in our theoretical calculations. Studies have shown that not only virtual photons in a vacuum, but also other virtual particles that have masses. The lightest chargeless virtual particles with mass are positronium (1 MeV) and $\pi^{0}$ mesons (135 MeV). This paper primarily focuses on studying the corrections to the Casimir force caused by positronium and $\pi^{0}$ mesons. Especially when the distance between the two plates is on the order of $1/m_{positronium}$ , the contribution of positronium becomes significant, and on the order of $1/m_{\pi^0}$ , the contribution of the $\pi^{0}$ meson becomes significant. We hope that the calculation results can reduce the error in the theoretical calculation of the Casimir force when the distance between the plates is large and provide significant corrections when the distance is small.