On a Knot Model of Mesons and Baryons

Abstract

A quantum knot model of mesons and baryons is established. This quantum knot model is derived from a quantum gauge model which is similar to the QCD gauge model. We first establish a knot model of the $\pi$ mesons. We show that the $\pi$ mesons are modeled by the prime knot ${\bf4_1}$ (which is assigned with the prime number 3). We show that the knot model of the $\pi^+$ meson gives the strong interaction for the formation of the $\pi^+$ meson and the weak decay $\pi^+ \to \mu^+ +\nu_{\mu}$. We give a mass machanism for the generation of the masses of the $\pi^0$ meson, $\pi^+$ meson, the muon $\mu^+$ and the muon neutrino $\nu_{\mu}$. We then extend the knot model to the basic mesons $K^0, \eta, \rho, \omega, K^*, \eta^{\prime},$ and $\phi$. These mesons are modeled by the prime knots ${\bf 6_1, 6_2, 6_3, 6_3, 7_1, 7_2, 7_2}$ respectively where ${\bf 6_1, 6_2, 6_3, 7_1, 7_2}$ are assigned with the prime numbers $11, 13,17, 19, 23$ respectively. We then extend the knot model to the basic baryons $p,n, \Lambda$, $ \Sigma, \Xi$; $\Delta, \Sigma^*, \Xi^*$, $\Omega^-$ and $\Lambda^*$. We show that these baryons are modeled by the prime knots ${\bf 6_2, 6_2, 7_1, 7_1,7_1}$; ${\bf7_1, 7_1,7_1, 7_2}$ and $ {\bf7_1}$ respectively where ${\bf 6_2, 7_1, 7_2}$ are assigned with the prime numbers $13, 19, 23$ respectively. This knot model gives a unification of the electromagnetic, the weak and the strong interactions. We show that the existing quark model is as a part of this knot model.