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Mesons Modeled Using Only Electrons and Positrons with Relativistic Onium Theory Ray Fleming [email protected]

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All mesons modeled using only electrons and positrons with relativistic onium theory Ray Fleming [email protected] All mesons were investigated to determine if they can be modeled with the onium model discovered by Milne, Feynman, and Sternglass with only electrons and positrons. They discovered the relativistic positronium solution has the mass of a neutral pion and the relativistic onium mass increases in steps of me/α and me/2α per particle which is consistent with known mass quantization. Any pair of particles or resonances can orbit relativistically and particles and resonances can collocate to form increasingly complex resonances. Pions are positronium, kaons are pionium, D mesons are kaonium, and B mesons are Donium in the onium model. Baryons, which are addressed in another paper, have a non-relativistic nucleon combined with mesons. The results of this meson analysis shows that the compo- sition, charge, and mass of all mesons can be accurately modeled. Of the 220 mesons mod- eled, 170 mass estimates are within 5 MeV/c2 and masses of 111 of 121 D, B, charmonium, and bottomonium mesons are estimated to within 0.2% relative error. Since all mesons can be modeled using only electrons and positrons, quarks and quark theory are unnecessary. 1. Introduction 2. Method This paper is a report on an investigation to find Sternglass and Browne realized that a neutral pion whether mesons can be modeled as combinations of (π0), as a relativistic electron-positron pair, can orbit a only electrons and positrons using onium theory. A non-relativistic particle or resonance in what Browne companion paper on baryons is also available. The in- called a trionium compound as shown in figure 1. troduction and method are abbreviated here since there Browne also realized that onium resonances can be is a book and other papers that discuss the method in nested or collocated. A non-relativistic electron or pos- greater detail [1,2,3]. itron can combine with a π0 to form a muon or pion Milne, Feynman, and Sternglass discovered the rel- [11]. The mass estimates by Sternglass are given in ta- ativistic positronium solution where the electron and ble 1 [7]. 2 positron gain ~70 MeV/c (me/α) each giving it a mass of ~140 MeV/c2 [4,5,6,7]. This is a classical model of the neutral pion that was further refined by Sternglass. A similar derivation by Browne published in Nature is recommended reading [8]. A negative paper was pub- Fig. 1. A Browne type muon as a positron orbited by two electrons. lished where the author left out the centrifugal force term [9], but even the non-relativistic positronium so- From there it is possible to consider resonances with lution would be unstable without the centrifugal force 2, 3, 4, or more pions. For convenience they can be term countering Coulomb attraction. classified as Group 2, 3, 4, and so on, with muons The relativistic positronium solution is general as it counted as Group 1 resonances along with pions. It is applies to any pair of oppositely charged particles or possible to work toward increasing numbers of pions resonances with any mass. Unstable particle masses and masses in the model and match it with known par- are known to be quantized in factors of me/2α = 35 ticle masses, but it is also important to analyze the de- 2 2 MeV/c and me/α = 70 MeV/c [10]. Therefore, it is cay products so they are accounted for. possible to construct a particle model where all parti- A resonance’s composition is usually found in its cles are modeled using onium theory. most frequent decay modes or the ones with the most pions present. Electron-positron or proton-antiproton quantum fluctuations can be excited to form additional pions or proton-antiproton pairs, but in most cases the There is also the case where only one pion is rela- maximum number of pions in any decay mode corre- tivistic as shown in figure 3. These are referred to as lates with the resonance’s composition. Note that only KD kaons in the author’s papers since they appear to be ± electrons and protons are referred to as particles from deexcited relative to the regular kaons. A KD has an this point forward. estimated mass of 384.69 MeV/c2, however, they fre- In mesons and baryons each relativistic electron quently have more net mass in other resonances such * ± 2 adds a mass of me/α or me/2α, so the mass can be cal- as the K (892) where they add 397.47 MeV/c . culated by summing the number of electrons in relativ- istic orbit. This mass is then added to the masses of the non-relativistic particles or resonances. Each μ± or π± contains three electrons, so a single relativistic one adds 3 x 35 MeV/c2 ≈ 105 MeV/c2 in relativistic mass Fig. 3. A KD kaon as a stationary pion orbited by a and two in relativistic orbit add ~210 MeV/c2 in rela- relativistic pion. tivistic mass. Note that K*(892)± resonances can decay to four pi- There are three-electron (eee) resonances as in fig- ons and are eKDK resonances in the onium model. The 0 * 0 ure 1, or an eπ resonance where the entire pion is in K (892) is also a KDK resonance. Research needs to orbit as in the Sternglass muon and pion. There are be conducted to explain how some KD resonances get conceivably eμ and eπ resonances that may be nonrela- their extra mass. Note that an ω is a KDKD resonance tivistic or relativistic. With two pions there can be μπ with both masses. The larger mass is used for mass es- and ππ resonances that are non-relativistic or with one timates in this paper unless otherwise stated. or both in relativistic orbit. A basic relativistic μπ res- onance is shown in figure 2 which forms a K-long. Fig. 4. A possible configuration of an η meson. Fig. 2. A K-long neutral kaon composed of a muon The η is the only well-known Group 3 meson and it and pion is a πKD resonance as illustrated in figure 4 as those masses sum to 537.04 MeV/c2 which is reasonably The masses of two charged pions plus ~210 2 2 2 close to the measured mass of 547.862 MeV/c . The η' MeV/c in relativistic mass sums to 489.22 MeV/c . with a mass of 957.78 MeV/c2 is the lowest mass group Adding a central electron brings it to 489.73 MeV/c2. 0 2 ± 5 meson as an ηKD resonance which has an estimated These are the K (497.614 MeV/c ) and K (493.677 2 2 mass of 945.33 MeV/c . In both cases the KD picks up MeV/c ) kaons [1,2]. The slight differences in mass are a significant amount of extra energy. The other basic presumed to be due to magnetic, spin, or quantum field Group 5 resonance is a πKDK resonance with an esti- effects. Note that all particle data not otherwise cited mated mass of 1017.94 MeV/c2 which is the φ with a comes from Particle Data Group (PDG) publications known mass of 1019.461 MeV/c2. [12,13]. Kaons may have 6 or 7 kaons so when two kaons combine in a relativistic orbit a total of 6, 7, 13, or 14 electrons may be relativistic. A neutral K-long kaon is shown in figure 2 as they commonly decay to a muon and a pion while K-short Fig. 5. An illustration of a ρ- meson. kaons usually decay to two pions. The different orbits of the μ and π lead to the them having different life- The last of the lower mass resonances upon which most others are built are the ρ mesons with the ρ± hav- times. But their masses are similar since there is no 2 0 ing a mass of 775.11 MeV/c . The combined masses of preferential orbital direction when two π pions are 2 combined. The charge of the muon determines if a K- a ππK, as illustrated in figure 5, is 776.75 MeV/c . long decays preferentially to matter (e-) or antimatter They have nested orbits, however the μπ orbit is likely (e+) [8,9]. This effect is responsible for all other me- the smaller of the two. The illustrations in the paper sons that have matter and antimatter variants. should be thought of as representations of the compo- sition only. The orbits are not real classical orbits, and 2 may not be in the proper size order, direction, or even a KDKD, KDK, or KK pair. The combined masses of an in the same plane. Those types of details need to be eKDKD resonance as shown in figure 6 with 980.35 worked out for each resonance. MeV/c2 in orbital mass is 1775.80 MeV/c2 which is a In many cases the mass can also change by a factor tau. This may be surprising to some, but since a tau has of ~35 MeV/c2. This may happen when a pion replaces eight known decay modes to two kaons and 30 decay a muon, or has a similar orbital shift. A KDK, or KK modes to four pions it is necessary to treat for them as resonance may contain 13, 14 or 15 relativistic elec- Group 4 mesons [9]. Both mu and tau particles are me- trons and a 4K or DD resonance usually contains 27, sons in onium theory rather than leptons further sim- 28, 29, or 30 relativistic electrons.
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