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

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.

The ‘t Hooft Coupling and Baryon Mass Splitting in the Large-N_c Quark Model

We study the ＇t Hooft coupling gt and the mass splitting of the ground-state baryons in terms of the large Noinspired quark model, by which the Hartree wavefunctions of light quarks are obtained. By fitting the spectra of decuplet and octet baryons, we obtain the ＇t Hooft coupling gt to be around 1.57. We generalize the scenario to the case of heavy baryons, such as Ac, gt values which does not deviate much from 1.57, as well as to the case of mesons with 9t far from that for baryons. The consequence is discussed.

QQqq Four-Quark Bound States in Chiral SU(3) Quark Model

The possibility of QQqq heavy-light four-quark bound states has been analyzed by means of the chiral SU(3) quark model,where Q is the heavy quark (c or b) and q is the light quark (u,d,or s).We obtain a bound state for the bbnn configuration with quantum number J^R=1^+,I=0 and for the ccnn(J^R=1+,I=0) configuration,which is not bound but slightly above the D~*D~* threshold (n is u or d quark).Meanwhile,we also conclude that a weakly bound state in bbnn system can also be found without considering the chiral quark interactions between the two light quarks, yet its binding energy is weaker than that with the chiral quark interactions.

Chiral SU(3) Quark Model Study of Tetraquark States: cn■/cs

魅力奇怪的家庭 D sJ (2317), D sJ (2460), 和 D 有令人吃惊的性质的 s (2632), ，正在质问现在的模型。许多理论解释被奉献给这个问题。大多数作者建议他们不是常规 c 夸克模型状态，但是可能是 P 波浪 c 的四夸克的状态和一个四夸克的状态。在这个工作，我们跟随 four-quark-state 图画，并且学习 cn/cs 状态的群众(n 是 u 或 d 夸克) 在 chiral 苏(3 ) 夸克模型。数字结果表演有旋转同等值 J P = 0 + 可能不是 D s (2632) 。同时，我们也结束那 D sJ (2317 ) 和 D sJ (2460 ) 不能作为纯四夸克的状态被解释。

Charmonium Spectrum and Their Transitions in Relativistic Quark Models

用为夸克的现象学的相对论的泛音模型(RHM ) ，我们获得了 S 波浪 charmonium 状态的群众。在调查使用的完整的 Hamiltonian 有 Lorentz 分级的正向量监禁潜力，与限制的那一起 gluon 交换潜力(COGEP ) 。与为扎根的状态和放射状地激动的状态的试验性的群众的一个好协议被获得因为三位字节和汗衫 S 挥动介子。计算费用半径，介子腐烂常数， leptonic 腐烂宽度，二光子腐烂宽度，和放射的 M1 腐烂宽度在对试验性的结果的好同意。

Low-Energy Kπ Phase Shifts in Chiral SU（3） Quark Model

The low-energy region kaon-pion S- and P-wave phase shifts with isospin I = 1/2 and I = 3/2 are dynamically studied in the chiral SU(3) quark model by solving a resonating group method equation. The model parameters are taken to be the values fitted by the energies of the baryon ground states and the kaon-nucleon elastic scattering phase shifts of different partial waves. As a preliminary study the s-channel q(-q) annihilation interactions are not included since they only act in the very short range and are subsequently assumed to be unimportant in the low-energy domain. The numerical results are in qualitative agreement with the experimental data.

Study of Ratio of Proton Momentum Distributions with a Chiral Quark Model

The ratio between the anomalous magnetic moments of proton and neutron has recently been suggested to be connected to the ratio of proton momentum fractions carried by the valence quarks inside it. This moment fraction ratio is respectively evaluated by using constituent quark model and chiral quark model in order to check meson cloud effect. Our results show that the meson cloud effect is remarkable to the ratio of the proton momentum fractions, and therefore, this ratiois a sensitive test for the meson cloud effect as well as for the SU(6) symmetry breaking effect.

Nucleon Form Factors and N-△ Transitions in a Hypercentral Constituent Quark Model with Meson Cloud

我们学习核子形式因素和核子 -- Δ(1232 ) 在亢奋的中央成分夸克的一个框架的转变当模特儿。介子介子云效果明确地被考虑。我们介子遮蔽的结果表演实质地作出贡献到核子形式因素以及到他合法地Δ(的振幅 1232 ) ，并且它与试验性的测量相比给一个改进协议。

Quark Model Approach to the Charge Dependent N-N Interaction

The N-N 1S0 scattering length differences ΔαCSB and ΔαCIH of the charge symmetrybreaking and charge independence breaking are calculated by a resonating group method with aquark cluster model.By adding the QED-QCD interference effect to the quark mass differenceand the electromagnetic interaction,the ΔαCSH and ΔαCIH can be reproduced with modelparameters constrained by the hadron isomultiplet masses.

Radiative decays D*(s)→ D(s)γ in covariant confined quark model

Radiative decays D((s))*→D((s))γare revisited in light of new experimental data from the BaBar and BESⅢCollaborations.The radiative couplings gD*Dγencoding nonperturbative QCD effects are calculated in the framework of the covariant confined quark model developed by us.We compare our results with other theoretical studies and experimental data.The couplings(in GeV-1)|g(D*+D+γ)|=0.45(9)and|g(D*0D0γ)|=1.72(34)calculated in our model agree with the corresponding experimental data|g(D*+D+γ)|=0.47(7)and|g(D*0D0γ)|=1.77(16).The most interesting case is the decay Ds*→Dsγ,for which a recent prediction based on light-cone sum rules at next-to-leading order|gDs*Dsγ|=0.60(19)deviates from the first(and only to date)lattice QCD result|gDs*Dsγ|=0.11(2)at nearly3σ.Our calculation yields|gDs*Dsγ|=0.29(6),which falls somehow between the two mentioned results,although it is larger than those predicted in other studies using quark models or QCD sum rules.

The■Q(q=u,d;Q=c,b)tetraquark system in a chiral quark model

The S-wave■tetraquarks,with spin-parities■,and 2+,in both isoscalar and isovector sectors,are systematically studied using a chiral quark model.The meson-meson,diquark-antidiquark,and K-type arrangements of quarks and all possible color wave functions are comprehensively considered.The four-body system is solved using the Gaussian expansion method,a highly efficient computational approach.Additonally,a complex-scaling formulation of the problem is established to disentangle bound,resonance,and scattering states.This theoretical framework has already been successfully applied in various tetra-and penta-quark systems.For the complete coupled channel and within the complex-range formulation,several narrow resonances of■systems are obtained,in each allowed■-channel,within the energy regions of■GeV and 5.7-6.7GeV,respectively.The predicted exotic states,which indicate a richer color structure when going towards multiquark systems beyond mesons and baryons,are expected to be confirmed in future high-energy particle and nuclear experiments.

Double-heavy tetraquarks with strangeness in the chiral quark model

Recently,some progress has been made in the experiments on double-heavy tetraquarks,such as T_(cc)reported by the LHCb Collaboration and Xccssreported by the Belle Collaboration.Coming on the heels of our previous work about T_(cc) and T_(bb), we present a study on the bound and resonance states of their companions,QQqs(Q=c,b;q=u,s) tetraquarks with strange flavor in the chiral quark model.Two pictures,meson-meson and diquark-antidiquark ones,and their couplings were considered in our calculations.Isospin violation was neglected herein.Our numerical analysis indicated that the states ccus with 1/2(1^(+)) ald bbus with 1/2(1^(+)) are the most promising stable states against strong interactions.Besides,we found several resonance states for the double-heavy strange tetraquarks with the real scaling method.

Further study ofΩ^(*)|1P_(3/2^(-))within a chiral quark model

In our previous studies,we analyzed the two-body strong decays of the low-lyingΩbaryon states within a chiral quark model.The results showed that the mass,total width,and two body decayΩ(2012)→■could be well reproduced with the spin-parity J^(P)=3/2^(-)stateΩ^(*)|1P_(3/2^(-))>classified in the quark model.Stimulated by the new observations of the three-body decay processΩ(2012)^(-)→■at Belle,in the present study,we further investigate the three-body strong decayΩ^(*)|1P_(3/2^(-))>→■within the chiral quark model.It is found that theΩ^(*)|1P_(3/2^(-))>has a sizeable decay rate into the three-body final states■.When consideringΩ^(*)|1P_(3/2^(-))>as theΩ(2012)resonance,the predicted ratio■is close to the upper limit 11%measured by the Belle Collaboration in 2019;however,it is too small to be comparable to the recent measurement 0.97±0.24±0.07.In addition,the coupled-channel effects on the bare three-quark stateΩ^(*)|1P_(3/2^(-))>from nearby channels■are studied.Our theoretical results show that the coupled-channel effects onΩ^(*)|1P_(3/2^(-))>are not very large,and the molecular component is no more than 30%.To clarify the nature ofΩ(2012)resonance,precise measurements on the ratio■are needed,and further investigation on the effects of coupled channels is recommended.

Structure of the Quarks and a New Model of Protons and Neutrons: Answer to Some Open Questions

The described structural model tries to answer some open questions such as: Why do quarks not exist in the open state? Where are the antiparticles from the Big Bang?

QUARK MODEL

Revised August 2013 by C. Amsler （University of Bern）, T. DeGrand （University of Colorado, Boulder）, and B. Krusche （University of Basel）.

Quark model study of multiquark states

The six- and four-quark systems are studied in emphasized that the color confinement used in multiquark the framework of constituent quark models. It is system should be different from the one used in two- or three-quark system. For six-quark system, we look for △△ and △△ dibaryon resonances by calculating NN scattering phase shifts with explicit coupling to these dibaryon channels in quark delocalization and color screening model. The model gives a good description of low-energy NN properties and predicts IJP = 03＋ and 01＋ △△resonances, which can be promising candidates for the isoscalar ABC structure reported by the CELSIUS-WASA Collaboration. For tetraquark system, a flux-tube quark model with multi-body confinement interaction is employed to study Y（2175） as a tetraquark state. The Y（2175） with diquark-antidiquark structure has energy 2174 MeV which is very consistent with experimental data. The calculation shows that multi-body confinement potential may play a vital role in the multiquark system.

Radial excitation states of η and η′ in the chiral quark model

A chiral quark model is applied to calculate the spectra of pseudoscalar mesons η and η . By analyzing the obtained spectra, we find that the mesons η （2 1 S 0 ）, η（4 1 S 0 ）, η （3 1 S 0 ） and η （4 1 S 0 ） are the possible candidates of η（1760）, X（1835）, X（2120） and X（2370）. The strong decay widths of these pseudoscalars to all the possible two-body decay channels are calculated within the framework of the 3 P 0 model. Although the total width of η （21S0 ） is compatible with the BES Collaboration＇s experimental value for η（1760）, the partial decay width to ωω is too small, which is not consistent with the BES result. If X（1835） is interpreted as η（4 1 S 0 ）, the total decay width is compatible with the experimental data, and the main decay modes will be πa 0 （980） and πa 0 （1450）, which needs to be checked experimentally. The assignment of X（2120） and X（2370） to η （31S0 ） and η （41S0 ） is disfavored in the present calculation because of the incompatibility of the decay widths.

Light meson spectrum and their leptonic decay widths in the frame work of constituent quark models

The phenomenological non-relativistic quark model has been employed to obtain the ground state masses of light vector mesons and their radially excited states and their decay widths.The full hamiltonian used in the investigation has kinetic energy,the confinement potential and the one-gluon-exchange potential.A good agreement is obtained with the experimental masses and their leptonic decay widths.