Quarks in a polar model

TL;DR

This paper compares current-quark masses with rest masses derived from the Helmholtz equation in a polar model, suggesting a theoretical link between quark masses and mathematical roots of Bessel and Neumann functions.

Contribution

It introduces a polar model approach to relate quark masses to solutions of the Helmholtz equation, providing a novel theoretical perspective.

Findings

Current u quark mass matches the second root of the Neumann function.

Current d quark mass matches the third root of the Bessel zero function.

Results support a connection between quark masses and mathematical roots in the polar model.

Abstract

Current-quark masses are compared to the rest masses allowed by the Helmholtz equation in a polar model. Within the uncertainty of the current u quark mass determination, the current quark mass coincides with the rest mass allowed by the Helmholtz equation in the polar model in accordance with the second root of the zero Neumann function. Current d quark mass coincides with the rest mass calculated in accordance with the third root of the Bessel zero function. On the basis of a comparison of these results with the results obtained earlier for ordinary real particles u and d quarks stability is discussed.