An Alternative Model of Particle Composition and Interactions

Scientific Paper
Title	An Alternative Model of Particle Composition and Interactions
Read in full	Link to paper
Author(s)	Jozef Kajfosz
Keywords	particle, conservation, four-component model, quark model, baryon number, strangeness, background bosons
Published	2009
No. of pages	17

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Abstract

A phenomenological model developed independently of most of the recent theoretical concepts is presented. The properties of all "ordinary" particles and anti-particles, both leptons and hadrons, are derived from only four kinds of fundamental components (4C) with "charges" ±1/2 e and ±1/2 B. These fundamental components occur always in pairs of integer Q and B values. Fermions are composed of an odd number of such pairs, and bosons of an even number of them. The number of components of each kind is strictly conserved in all interactions. Strong and electromagnetic transitions occur upon absorption of at least one E [1111] boson, and weak decays occur upon absorption of a W [2020] or anti-W [0202] boson. These spin zero, low-mass, -energy, and -momentum bosons are present in vacuum with a certain density. The conservation of the 4C components accounts (with some modifications) for the conservation of charge, baryon number, lepton number(s), strangeness and isospin. Affinity with the quark model is shown and differences between these two models are outlined. Many questions remain unaddressed and the model requires verification with experiment and intense further development.

Overview

Józef Kajfosz, a retired experimental physicist of the Institute of Nuclear Physics in Cracow and at Řež, offers what he calls a phenomenological model of particle composition built from a handful of very simple assumptions. His stated motive is dissatisfaction with the state of particle physics and "the conviction that the true story has to be simpler, more general and more beautiful," together with the judgment that minor adjustments are useless: "only a radical, challenging proposal, no matter how hopeless and unpopular at first, may possibly clear the way."

The proposal replaces six quark flavours and their colour charges with exactly four fundamental components, labelled A, B, C and D, each carrying half a unit of electric charge and half a unit of baryon number. Every particle is a bag containing some number of each, written [abcd], and the model's single dynamical law is that the count of each kind is strictly conserved in every process. Where the Standard Model treats decay as spontaneous, Kajfosz makes every transition the capture of a background boson from a population permeating the vacuum — a genuinely different physical picture, and the one from which most of his testable consequences follow. The paper closes with an unusually plain statement of its own status: it "was formulated by a physicist who is neither a theoretician nor a particle expert," and "is by now rather only a loose proposal or a very raw concept."

The argument

Four components and one conservation law

The four components A⁺⁺, B⁺⁻, C⁻⁻, D⁻⁺ carry the four sign combinations of ±½ε electric charge and ±½β baryon number. For a particle [abcd],

Q = ½(a+b−c−d),  B = ½(a−b−c+d)

The total s = a+b+c+d is always even; components come in pairs, each pair being a fermion of spin ½ℏ, so fermions have s = 2, 6, 10, … and bosons s = 4, 8, 12, …. The conservation law is simply that the sum of each of a, b, c, d over incoming particles equals the sum over outgoing ones.

That law cannot be satisfied by the observed decays alone, so a third assumption is added: neutral background bosons of negligible mass, energy and momentum participate in every process. Their compositions are E ≡ [1111], W ≡ [2020] and anti-W ≡ [0202]. E enters electromagnetic and strong processes, W or anti-W the weak ones; higher orders involve EE, WE and so on. These bosons are held to be present in the vacuum at some density, with the weak-boson density roughly ten orders of magnitude below that of E.

Fitting 92 decay modes

The assignment of compositions to known particles was made by computer search against 92 observed decay modes with their branching ratios, taken from the 2006 Particle Data Group compilation. The first pass matched 68 of 92. Kajfosz reports that all 24 failures were, without exception, decays emitting neutrinos — and that interchanging ν_μ with anti-ν_μ, or ν_e with anti-ν_e, in exactly those 24 schemes brought all 92 into agreement with the conservation law. The revised schemes are tabulated in full, so that, for example, neutron decay reads

anti-W + E + n → p + e⁻ + anti-ν_e,  [0202]+[1111]+[3021] = [3111]+[0011]+[1212]

Relation to the quark model

The correspondence with quarks is worked out explicitly. The three light quarks and antiquarks are written as linear combinations of the components — for instance u = A + ⅔B + ⅓D and d = A + C − ⅓B + ⅓D — from which the proton comes out as uud = 3A + B + C + D ≡ [3111]. The inverse transformation exists but is not unique, since the six quark compositions are interrelated by d + anti-d = u + anti-u = s + anti-s = [1111]. Applying the inverse also lets leptons be written in quark terms, which Kajfosz offers as "an attempt of a formal generalization of the quark model."

Inversion, extra charges, and the recovery of Gell-Mann–Nishijima

The particle–antiparticle operation turns out not to be simple charge reversal but [abcd] ↔ [½s−a, ½s−b, ½s−c, ½s−d]. For leptons and mesons this coincides with charge inversion; for baryons "the difference is profound." Making sense of it forces additional charges onto the components. Strangeness comes out as S_A = 0, S_B = S_C = ½, S_D = −1, hence S = ½b + ½c − d; the isospin projection as I_z = ¼a + ½b − ½c − ¼d. Any such quantity whose four component values sum to zero is automatically conserved by the component-counting law; total isospin I fails that condition and so is not guaranteed. Only three charges (Q, B and a further one he calls C) are independent, and from the resulting relations he recovers the Gell-Mann–Nishijima formula Q = I_z + ½(B + S).

Invertible pairs and two mass states

Searching for pairs of components possessing genuine antipairs yields exactly six: c ≡ CD and anti-c ≡ AB (charged), n ≡ BD and anti-n ≡ AC (neutral), b ≡ AD and anti-b ≡ BC (baryonic). The like pairs AA, BB, CC and DD are not invertible. Mesons are two such pairs, baryons three — the same combinatorics as quarks.

The obvious objection is that the same pairs then constitute both electrons and hyperons. Kajfosz answers by postulating two mass states of a pair: a light "leptonic" state of some 2.8 fm diameter, outside the range of the strong force, with only electric and baryonic charge switched on; and a heavy "hadronic" state under about 1.5 fm, inside that range, where strangeness and the other charges become active. The pair potential is imagined to have two minima. Production of heavy particles then amounts to squeezing pairs to smaller size, so that "matter could be viewed as a huge deposit of explosives. Fortunately, we lack fuses necessary to blow them up." Transitions between mass states require a W to unlock them.

Predictions, and what the model gives up

Applied to the muon, the conservation law permits far more decay modes than are observed, and Kajfosz introduces supplementary rules to prune them: an E boson cannot split arbitrarily but can only yield a gamma ray, a π⁰ or an e⁺e⁻ pair, so electromagnetic processes are confined to transitions between mass states of the same composition; and gamma rays in weak decays must come from the background boson's components rather than the decaying particle's. What survives are modes that either "imitate" the acknowledged ones — differing only in which neutrino is emitted — or have very small expected branching ratios. He states the consequence squarely: "the lepton numbers are not conserved at all in this model," but "what lepton numbers seemed to explain, the model explains in a different way," and therefore "an experimental confirmation or refutation of the predictions of this model may not be easy."

The differences from the quark model are catalogued. The Ω⁻ composition [0204] is not invertible, so its antiparticle would be illegitimate unless it absorbs an E boson and becomes a five-pair structure. A baryon [4020] with strangeness +1, called X⁺, has no quark-model counterpart except as the pentaquark uudds̄. Doubly charged Ξ⁻⁻ and anti-Ξ⁺⁺ are singled out as the best experimental test, since they are free of the invertibility problem and would be produced together in high-energy collisions. The model also allows baryons with B = ±2 and, unlike the quark model, mesons with B = ±1.

Several standing puzzles are given new readings. Proton stability follows directly from the conservation law. Strangeness violation in weak decays is only apparent, since W and anti-W themselves carry S = ±1. K⁰–anti-K⁰ mixing becomes a literal exchange reaction with the background bosons, and neutrino mixing likewise. The very small neutrino absorption cross-section follows from the need to capture a W simultaneously. And because decay is triggered rather than spontaneous, decay rates depend on the local density of background bosons — which "may not necessarily be constant, especially in a long-range, cosmic time scale," with consequences for isotopic dating.

Assessment

The model's real attraction is economy. Four components, one counting law and three background bosons reproduce the conservation of electric charge, baryon number and strangeness, generate the meson-as-two-fermions and baryon-as-three-fermions combinatorics without postulating it, and deliver the Gell-Mann–Nishijima relation as an algebraic consequence rather than an empirical rule. The account of apparent strangeness violation in weak decays is elegant on its own terms: if the boson whose capture triggers the decay itself carries S = ±1, then nothing is violated, only unaccounted. Recasting K⁰ mixing as an explicit exchange reaction with a vacuum population is a concrete mechanism where the standard treatment is formal. The paper is also methodologically honest in a way that is rarer than it should be: it states which quantities it abandons, it tabulates the decay modes the model wrongly permits alongside those it gets right, it names the observations that would test it, and it ends by saying the work must be evaluated by experts the author does not claim to be.

The central difficulty is the 92-of-92 fit. Twenty-four of those matches were obtained by swapping neutrino for antineutrino in the schemes that failed, and the paper presents the uniformity of the failures as support for the model. It is equally consistent with the model simply lacking the structure that distinguishes a neutrino from an antineutrino, and the distinction is not a bookkeeping convention: Davis's chlorine experiment established operationally that reactor antineutrinos do not induce the reaction that neutrinos do, and the Goldhaber measurement of neutrino helicity fixed the correlation between that label and a measurable quantity. Relabelling twenty-four decays is therefore not free, and the paper does not confront the experiments that constrain it. Kajfosz himself concedes an alternative reading in section 8(c) — that the W may act only as a catalyst for E to disintegrate — which would remove the swaps but was not pursued.

Other steps are asserted rather than derived. The two-mass-state hypothesis, with its 2.8 fm and 1.5 fm diameters and its double-minimum potential, is introduced solely to answer the objection that the same pairs cannot make both electrons and hyperons; no potential is written down and no numbers follow from it. The supplementary rules that prune the muon's permitted decays are chosen to eliminate the unwanted modes and have no independent motivation. Most tellingly, I_z is retained for hadrons, where the values agree with the multiplets, and then declared "redundant" for leptons, where it gives useless values of ±¼, ±¾ and ±5/4 — a quantity kept where it works and discarded where it does not.

The conflicts with measurement are substantial, and some are acknowledged. Section 8(f) concedes that charm and bottom cannot be expressed as charges of the components at all, and that the heavy quarks cannot be written as linear combinations of them; the top quark, the gluon and colour do not appear. More seriously, the paper's W is a spin-zero background boson of negligible mass, whereas the weak intermediate boson observed at UA1 and UA2 in 1983 and measured at LEP has a mass of about 80 GeV and spin 1 — the name is shared but nothing else is. The pentaquark uudds̄ that the model requires for its X⁺ is the same state reported in 2003 as the Θ⁺, which dedicated high-statistics searches subsequently failed to confirm; the doubly charged Ξ⁻⁻ that Kajfosz nominates as the decisive test has likewise not been observed. And the proposal that decay is triggered by boson capture makes decay rates depend on an ambient density, which conflicts with the constancy of radioactive half-lives to the precision at which they are measured, with the exponential decay law followed by muons in flight, and with the isotopic constraints from the Oklo natural reactor.

Finally, and by the author's own reckoning the crucial point, the model says nothing about mass. It assigns compositions but offers no reason why the muon weighs 207 times the electron when both are built from the pair c, or why the mass states sit where they do. Kajfosz writes that "especially its ability to explain the observed masses of particles will be crucial" — a fair statement of the gap, and one that leaves the 4C model, as he says, a raw concept rather than a theory.

See also

• Jozef Kajfosz
• Quark
• Standard Model
• Proton
• Neutron
• Electron
• Neutrino
• Muon
• Positron
• Antimatter
• Spin
• Vacuum
• Atomic Structure