A New Quantum Number Triangular Array That Defines the Internal Organization of Valence Quarks, the Hadron Quark Model, and the CKM Matrix

Donald William Chakeres,Richard Vento

doi:10.4236/jmp.2016.71016

Abstract

Purpose: The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants, including the quarks, are associated with partial harmonic fractional exponents, , of a fundamental frequency, vF. The model has shown that the properties of the quarks are based on a progression of prime number composites. They also fall on three separate power law lines related to integer factors of the Y-intercept, , of a fundamental electromagnetic line which is scaled by the Rydberg constant, R and Planck’s constant. The quark lines are scaled by the quantum number factors {1, 2, 3}, and their Y-intercepts are referred to as nbem. The goal is to present a new proto-quark model in a six-quark inverted triangular array that defines the global organization of the valence quarks, which determines the hadronic quantum numbers, the standard hadron quark model, and the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Methods: The charm, bottom, top quarks are associated with power law line Y-intercept, nbem equal to 1; the strange and down quarks with nbem equal to 2; and the up quark with nbem equal to 3. An inverted equilateral triangular array with three rows arranged from upper row (triangle base) to bottom row (triangle vertex), is associated respectively with nbem numbers 1, 2, and 3. The novelty of our perspective thus defines a new global valence quark organization which supersedes the Standard hadron composite quark model. The quarks are ordered via relative mass, partial fractions, and nbem quantum number. The top row of our inverted triangle includes the c, b, and t quarks from left to right; the middle row depicts the d and s quarks; and the bottom row, the up quark. Results: Our array depicts a quantum generator of the global organization of the valence quarks defining the composite quark model. The vertices of the triangular array are the up quarks, the midpoints are the down quarks. All weak transitions are from a corner to a midpoint or vice versa. The standard 3 by 3 CKM matrix is generated from the new quark triangle with each up type quark (u, c, and t) transforming to each down type (d, s, and b), with their experimental flavor transition magnitudes given. Conclusion: A new quark quantum number, nbem, is an important discovery that generates a new proto-valence quark triangle that secondarily generates the composite quark model and the CKM matrix.

Highlights

This paper focuses on the fundamental origin of the valence quark internal organization encompassing the properties of an up type or down type quark, the three generations, their relative mass scaling, and fractional charges that secondarily generate the existing composite quark model
We propose a new proto quark model triangular array of the six valence quarks based on their nbem integers, and depicted in a standard isosceles triangular quark array identical to that of essentially all other quark model arrays [10]
This paper demonstrates a unique triangular valence quark array utilizing a new quantum number series

Summary

Introduction

The quark model has been a great success of the Standard Model (SM) and particle physics [1]-[12]. It is a classification scheme for composite hadrons in terms of multiple valence quarks. These are associated with quantum numbers such as isospin, J, parity, and charge of the hadrons. The quark model underlies the Eightfold Way. The composite hadrons are defined by equilateral triangular arrays where there is a valence quark at each corner of a single triangle. The existing model only defines the organization of the composite quarks within the hadrons not between the quarks themselves. This includes their relative mass, charge, and whether they are up type or down type quarks

Methods

Results

Conclusion