Hadron masses from a Kaluza-Klein like Model

TL;DR

This paper develops a 10-dimensional Kaluza-Klein like model to calculate hadron masses, achieving high accuracy and providing new approximate formulas, while also exploring fundamental forces within the same framework.

Contribution

It introduces a novel 10D Kaluza-Klein like model that approximates hadron masses with high accuracy and derives formulas for mass calculations, extending beyond prior models.

Findings

Approximate formulas for hadron masses with relative errors below 5% in over half the cases.

High correlation (r=0.998) between measured and calculated hadron masses.

Calculated forces (strong, electric, weak) align with known measurements and standard model values.

Abstract

The purpose of this paper is to calculate the masses of hadrons without orbital momentum. It is hypothized the Kaluza-Klein like model does deliver results in particle physics complementing those of the Standard Model of particle physics. For this paper a Kaluza-Klein like model was developed based on the structure of the Standard Model. The model consists of 10 dimensions which are: one time, three usual macroscopic space and six compactified dimensions. Excitations - disturbances traveling with the speed of light on the 10D-spacetime - are introduced. An excitation on a compactified dimension can induce a mass in 4D-spacetime; it is accompanied by an integer, the excitation number, and has a well-defined spin. The model's parameters are determined using electron's g-factor and the measured masses of the charged leptons, the proton, the neutron, the mesons $\pi^{+}, \phi, \psi, \Upsilon$. So far, exact formulas for calculating hadron masses were not derived. The approximate formulas, however, are reported and applied to about one hundred composite particles, which are compiled within four separate tables. The comparison between the measured masses of 64 hadrons and the approximations shows relative errors below $0.05$ for 55\% and below $0.1$ in 81\% of all cases. Pearson's correlation coefficient of masses measured versus calculated is $r=0.998$. The results of another 36 hadron masses, not yet experimentally determined, are stated. For a better assessment of the presented model's validity, and in addition to the paper's original purpose, the strong, electric, and weak forces were calculated. These forces together with other derived parameters are discussed and compared with measurements or values from the standard model of particle physics.