On a Knot Model of Mesons and Baryons

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 π mesons. We show that the π mesons are modeled by the prime knot 41 (which is assigned with the prime number 3). We show that the knot model of the π meson gives the strong interaction for the formation of the π meson and the weak decay π → μ + νμ. We give a mass machanism for the generation of the masses of the π meson, π meson, the muon μ and the muon neutrino νμ. We then extend the knot model to the K 0 and K mesons. We show that the K and K mesons are modeled by the prime knot 61 (which is assigned with the prime number 11) while the anti-particles K and K− are modeled by the mirror image of 61. We show that the strange degree of freedom of the strange quark is from the linking of knots of the K mesons. This linking gives the strong interaction for the associated production of elementary particles with strangeness. We then extend the knot model to the basic mesons η, ρ, ω,K∗, η′, and φ. These mesons are modeled by the prime knots 62,63,63,71,72,72 respectively where 62, 63, 71, 72 are assigned with the prime numbers 13, 17, 19, 23 respectively. We then extend the knot model to the basic baryons p, n,Λ, Σ,Ξ; ∆,Σ∗,Ξ∗, Ω− and Λ∗. We show that these baryons are modeled by the prime knots 62, 62,71,71,71; 71, 71, 71,72 and 71 respectively where 62,71,72 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 a meson or a baryon is modeled by a representation of the form W (K)Z where W (K) denotes a quantum knot and the components of the complex vector Z represent quarks. This is as the strong interaction for forming the meson or the baryon. Then two components zi, i = 1, 2 of Z may be separated such that they are still attached to W (K) in the form that they are attached to W (K) at two different positions of the quantum knot W (K). This process of separation is identified as the weak interaction of the two quarks (or leptons) represented by zi, i = 1, 2 of Z. We show that the existing quark model is as a part of this knot model. Thus this knot model is consistent with the existing quark model. PACS numbers: 12.40.-y, 12.40.Yx, 12.10.Dm, 12.60.-i.