Meson and Baryon Composition

From first principles of binary mechanics (BM) [1], eight and only eight fundamental or elementary particles were derived, each occupying a spatial object named a spot in a spot cube defined from a projection of spinor components of a pair of relativistic Dirac equations of opposite handedness to the eight vertexes of a cube quantizing space [2]. Each vertex or spot was postulated to consist of three perpendicular spot units defined from the two real components of the quantum mechanics (QM) complex wave function, further restricted to 0 or 1 allowed values, quantizing energy. Properties of the eight fundamental particles were then derived from the modulo 2 parities of the integer {x, y, z} spot coordinates in the spatial lattice, including charge, color, matter vs antimatter status, unconditional bit motion direction, handedness (left or right helicity), etc (Table 1 in [1],). These properties were used to show how most Standard Model (SM) lepton and quark particles may be compositions of the eight BM elementary particles [3]. This article adds information on some mesons and baryons, further illustrating their composition from BM particles and how the "three generations of matter" arise naturally from this analysis.

Table 1: Generation 1: Some TWO-d Mesons

Legend: Generation by number of d quarks (TWO-d). r, red; g, green; b, blue. /, antiparticle. X*, spot units in neighboring spot cubes.

Using analysis methods described previously [3], Tables 1 to 3 list some meson and selected baryon compositions, highlighting three generations of these hadron particle groups respectively, based on number of down (d) quark constituents.

Table 2: Generation 2: Some FOUR-d Mesons

Legend: Generation by number of d quarks (FOUR-d). r, red; g, green; b, blue. /, antiparticle. X*, spot units in neighboring spot cubes.

Table 3: Generation 3: Selected SIX-d Baryons

Legend: Generation by number of d quarks (SIX-d). r, red; g, green; b, blue. /, antiparticle. X*, spot units in neighboring spot cubes. Selected baryons; B and other mesons omitted.

Discussion
Properties of the eight BM fundamental particles were matched with meson and baryon properties to itemize their likely compositions. These assignments were done before the discovery of the proton (or hadron) bit cycle [4] in 2011, where the positron spot units were found to be located in three neighboring spot cubes (indicated by X* in Tables 1 to 3). In 2015, it was found that just two and only two bit cycles exist, dubbed the proton and electron bit cycles [5]. Hence, the hadron objects listed in Tables 1 to 3 may be viewed as variations in how these two bit cycles may be populated with energy (1-state bits).

The SM lepton and quark compositions [3] and the present particle compositions were all based on populating a single spot cube, with the exception of positron components in adjacent cubes (X* above). Hence, the results imply there are three and only three particle generations, because any larger particle objects would necessarily occupy multiple spot cubes. But the spot cube appears to correspond to a nucleon. Therefore, objects occupying multiple spot cubes move the analysis into the area of atomic nuclei or ions, capping the particle generation story at three and only three. The so-called pentaquark narrative might be viewed as a confirmation of this conclusion and perspective.

These composition itemizations were done in 1994. More than two decades later at present, the number of mesons which may somehow be considered to be fundamental or elementary in SM parlance has grown like rabbits [6]. From the perspective of developing BM research, most of the meson objects may be mostly representations of certain steps of a nucleon (or even a nucleus) in motion. If this is correct, the currently listed multitude of mesons might be viewed by theoreticians as rather trivial and misguided regarding search for "new fundamental particles". For example, the 48 bit loci in a spot cube (8 spots x 6 bits each), each with a 0- or 1-state possible, represent 2⁴⁸ possible system states, named bit functions as the BM replacement of the QM wave function. That is, there are about {2⁴⁸} minus {present number of documented mesons} more to go -- which is a very large number of papers to add to physics literature perhaps without any major payoff of new fundamental insights in physics.

The good news is that the entire set of 2⁴⁸ permutations can be printed out defining all possible "one-cube" particles and variations in their states, including mesons. However, serious physicists would not want to spend the rest of their lives essentially as accountants pursuing this sort of trivial book-keeping exercise. Nonetheless, at Binary Mechanics Lab, there will be a party for each predicted meson that the bean-counters report.

Perhaps the best news is a recently proposed new research program [5] in which new analytic software will be added to the Binary Mechanics Lab Simulator (BMLS) v1.38.1 to analyze BMLS outputs to identify exactly which bit functions in the proton and electron bit cycles occur with what incidence counts as a function of other variables, such as energy (1-state bit) density, applied force potential fields, etc. It is hoped that this sort of "more efficient" approach might yield more advances in nuclear physics than particle collision at facilities like CERN might accomplish in decades, if ever.

Editor's note: The meson content of Tables 1 and 2 and the now omitted B meson content in Table 3, with some minor edits, originally appeared in Table 3 of the 1994 BM paper [1].

References
[1] Keene, J. J. "Binary mechanics" J. Bin. Mech. July, 2010.
[2] Keene, J. J. "Physical interpretation of binary mechanical space" J. Bin. Mech. February, 2011.
[3] Keene, J. J. "Standard model particle composition" J. Bin. Mech. January, 2016.
[4] Keene, J. J. "The central baryon bit cycle" J. Bin. Mech. March, 2011.
[5] Keene, J. J. "Proton and electron bit cycles" J. Bin. Mech. April, 2015.
[6] Wikipedia. "List of mesons", 2016.
© 2016 James J Keene