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Constituent Quark Model and New Particles

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Constituent Quark Model and New Particles Constituent-Quark Model and New Particles David Akers* Lockheed Martin Corporation, Dept. 6F2P, Bldg. 660, Mail Zone 6620, 1011 Lockheed Way, Palmdale, CA 93599 *Email address: [email protected] An elementary constituent-quark (CQ) model by Mac Gregor is reviewed with currently published data from light meson spectroscopy. It was previously shown in the CQ model that there existed several mass quanta m = 70 MeV, B = 140 MeV and X = 420 MeV, which were responsible for the quantization of meson yrast levels. The existence of a 70-MeV quantum was postulated by Mac Gregor and was shown to fit the Nambu empirical mass formula mn = (n/2)137me , n a positive integer. The 70-MeV quantum can be derived in three different ways: 1) pure electric coupling, 2) pure magnetic coupling, and 3) mixed electric and magnetic charges (dyons). Schwinger first introduced dyons in a magnetic model of matter. It is shown in this paper that recent data of new light mesons fit into the CQ model (a pure electric model) without the introduction of magnetic charges. However, by introducing electric and magnetic quarks (dyons) into the CQ model, new dynamical forces can be generated by the presence of magnetic fields internal to the quarks (dyons). The laws of angular momentum and of energy conservation are valid in the presence of magnetic charge. With the introduction of the Russell-Saunders coupling scheme into the CQ model, several new meson particles are predicted to exist. The existence of the f0(560) meson is predicted and is shown to fit current experimental data from the Particle Data Group listing. The existence of meson partners or groupings is shown. PACS. 12.39.-x Phenomenological quark models - 12.40.Yx Hadron mass models and calculations - 14.80.Hv Magnetic monopoles 1 Introduction In the course of researching particle physics over several decades, Mac Gregor [1] developed a comprehensive constituent-quark (CQ) model of elementary particles. It was shown that the CQ masses were directly related to the masses of the electron, muon, and pion. A connection was later discovered between the CQ masses of Mac Gregor’s model and Nambu’s empirical mass formula mn = (n/2)137me, n a positive integer and me the mass of the electron [2]. Mac Gregor’s esoteric notation included a 70 MeV quantum, a boson excitation B with the mass of the pion at 140 MeV, a fermion excitation F with a mass of 210 MeV or twice the muon mass, and a 420 MeV excitation quantum X. The 70 MeV quantum and the 420 MeV quantum X do not correspond to any observed particles but serve as the building blocks of mesons and baryons in the CQ model. These building blocks were not introduced in an ad hoc manner but were derived from experimental systematics and angular momentum systematics of hadron spectroscopy [3- 4]. The mass regularities in meson and baryon spectra were identified independently of any theoretical viewpoint [5]. The mechanism for generating the CQ masses is discussed in Mac Gregor [1] and will be discussed further in Section 3. It is sufficient to say that we shall accept the evidence of Mac Gregor’s CQ model from its previous agreement with earlier experimental data and that we shall present further evidence from the Particle Data Group listing [6]. The experimental evidence to be presented is limited to the meson spectrum only for the purpose of our study. The common mass-band structures of the baryons were also studied and can be found in Mac Gregor’s work [1]. A sequel to the present paper on the subject of baryons can be found in Ref. [7]. In the CQ model, the mass of the resonance is determined mainly from the masses of the constituent quarks. Spin and orbital excitations can also contribute to the mass of the resonance with higher mass-states appearing at higher total angular momentum values. However, mesons with different J values appear in the same mass band in Fig. 2 of Mac 2 Gregor’s work [1]. These meson resonances appear with accurate J ~ M2 Regge trajectories for JP = 1-, 2+, and 3-. Likewise, the meson spectrum also exhibits non-Regge spacing with J ~ M for the 2+, 3-, 4+, 5- and 1+, 2-, 3+ yrast levels in Fig. 2 of Mac Gregor’s paper. The spacing of the Regge-like and non-Regge levels is in accurate 420 MeV intervals, for which Mac Gregor assigned an excitation quantum X1 = 420 MeV. The quantum X can appear with zero or non-zero units of angular momentum. Additional sets of resonances are found to depend upon their quark content. For the CQ model, the constituent-quark basis states are calculated to be u(315), d(320), s(525), c(1575), and b(4725). The CQ model was postulated long before the advent of the top quark and has not been extended to the energy range for resonances involving the top quark. For purposes of our study, we limit our discussion to mesons below 2600 MeV. In addition to the excitation quantum X, there are mesons which exhibit equal spacing in the excitation quantum B = 140 MeV or the mass of the pion, as shown in Fig. 3 of Mac Gregor’s work [1]. From the analysis in Ref. [1] and from previous work [3-5], Mac Gregor concluded that the excitation quantum B served as a fundamental mass unit. In this paper, it is shown that there is exists a fine structure in one-half units of B or m = 70 MeV, separating meson band states. The mechanisms for generating this quantum m = 70 MeV will be discussed in Section 3. The evidence for this quantum is presented in Refs. [1, 3-5] and is shown in Table 1, which has the usual CQ model notation and which has the primary mesons π0(134), K±(494), and η(547) in the ground states. These mesons are listed with shell numbers (on the 70 MeV scale) in isospin space. Evidence of shell structure can be found in meson and baryon spectroscopy [8]. Earlier ideas of shell structure can be found in Ref. [9]. In Table 1, we list all the well-established 3 mesons, underlining them. The not-so-well-established resonances are also included in the CQ model. This table is an update to Table VII in Mac Gregor’s work [1] and has additional fine structure representing new states at the 1400 to 2450 MeV energy levels. These new states have m = 70 MeV regular spacings between them. This is a feature not explained in the Standard Model of elementary particle physics. It is noted that many if not all the known mesons below 2600 MeV fit into the CQ model. Moreover, in Table 2 we show a regrouping of the mesons from Table 1. On the 70-MeV scale, shell numbers are now identified in ordinary space in Table 2. In the paper by Mac Gregor [3], the 70- MeV excitation spacing can also be found for both mesons and baryons in his Fig. 8. Additional 70-MeV spacing is shown in Fig. 21 of Ref. [4]. The CQ notations for Tables 1 and 2 do not follow the rotational band rules established by Mac Gregor in Ref. [3], because we are only interested in the total CQ excitation masses for the energy levels shown in parentheses. Additional rules for hadronic binding energies and properties can be found in Ref. [4]. As shown in Tables 1 and 2, these mesons are grouped into excitation bands with different spins and isospins. For the sake of readers who may not be familiar with the notation of the CQ model, the energy bands are calculated from the total mass values as indicated by the symbols of the m, B, F and X quanta. For a notation such as X3, this represents a molecular type writing by Mac Gregor and thus has value XXX = 420 + 420 + 420 = 1260 MeV, as shown in Table 1. The superscripts to these quanta represent spin J and parity P. In studying Tables 1 and 2, we note that these mesons fit within the band structure of the CQ model, and yet there are spreads of particles within each band due to the estimates 4 for peak masses and particle widths. A comparison of the CQ model and the particles in Table 1 could be made with the Standard Model. Comparisons to meson nonet membership and to meson fits to Regge theory are possible. However, these comparisons are not in the present scope of this paper and will be presented in a later paper. In this paper, we are concerned with the groupings of the particles in Table 1 and their spreads in energy. In the next section, we introduce quarks (dyons) with electric and magnetic charges into the CQ model, which allows for new dynamical forces in the meson spectrum. These mesons are studied in the CQ model, identifying their groupings or associated states. 2 CQ Model and Russell-Saunders Coupling Mesons are composites of two quarks or quark-antiquark pairs and have been extensively studied as quarkonium and compared to nonrelativistic positronium-like bound states, which are observable as narrow resonances in electron-positron annihilation. If these quark-antiquark states are indeed comparable to atomic-like systems, then it would seem logical that the physics of the atomic scale would be applicable to the particle scale. However, the nature of the quarks would have dramatic effects as well on the physics. In the original CQ model, the quarks were of the Fermi- Yang type not the nucleon quarks of Gell-Mann and Zweig [3].
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