Nonrelativistic Constituent Quark Model Research Articles

Study of weak radiative decays of D0→Vγ

The weak radiative decay of D0→Vγ with V=K¯0, and ϕ, ρ0, and ω, is systematically studied in the vector meson dominance model. It allows us to distinguish the short-distance mechanisms which can be described by the tree-level transitions in the nonrelativistic constituent quark model, and the long-distance mechanisms which are related to the final-state interactions (FSIs). We find that the FSI effects play a crucial role in D0→Vγ and the SU(3) flavor symmetry can provide a natural constraint on the relative phase between the short and long-distance transition amplitudes. Our analysis suggests that the D-meson weak radiative decays can serve as a good case for investigating the nonperturbative QCD mechanisms at the charm quark mass region. Published by the American Physical Society 2024

Pion parton distribution functions with the nonrelativistic constituent quark model

We calculate the valence quark distribution functions of the π meson using the non-relativistic chiral constituent quark model. The π wave function is obtained by solving the two-body Schrödinger equation within the framework of constituent quark model. We transform the π wave function from the rest frame to the light cone or infinite momentum frame based on the Lorentz boost. The valence quark distributions at the initial evolution scale are obtained. The QCD evolution is given with the DGLAP equations with parton-parton recombination corrections. With tuning the valence up (down) quark mass to 70 MeV, the calculated valence up quark distributions at Q2=20 GeV2 are in good agreement with the E615 experimental data. The structure functions F2π(x,Q2) of pion are also calculated which consist with the H1 experimental data. The proposed mechanisms here could be also used to study other hadrons.

Mass spectrum and decays of the first radial excitation axial vector meson nonet

In this work, the mass spectrum of the first radial excitation axial vector meson nonet is considered in the framework of the nonrelativistic constituent quark model and Regge phenomenology. After that, we investigate the strong decay characteristics of these states within the [Formula: see text] model. The results are compared to values from other phenomenological models, and they may be beneficial in the prospective search for [Formula: see text] meson nonets.

Spectroscopy of Ωccc and Ωbbb baryons

In this paper, we study the properties of triply charm and triply bottom baryon. The mass spectra of these baryons are calculated in nonrelativistic constituent quark model with Coulomb plus screened potential. Several states [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] of the [Formula: see text] and [Formula: see text] baryons with quantum number [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are determined. Regge trajectories are also plotted to determine the quantum number of baryons. Moreover, the magnetic moments are calculated for [Formula: see text].

Electron-based Constituent Quark Model

The empirically introduced Electron-based Constituent Quark Model (ECQM) is considered from the symmetry motivated point of view, including the 3:1 ratio between the electron mass me and the QED correction MH∘(α/2π)2 to the scalar mass. Common parameters Mq=me(α/2π)−1=441MeV, 391 MeV in ECQM and NRCQM (Nonrelativistic Constituent Quark Model) and 16me=δ are used in the description existing empirical data.

Toward the discovery of novel Bc states: Radiative and hadronic transitions

The properties of the $B_c$-meson family ($c\bar b$) are still not well determined experimentally because the specific mechanisms of formation and decay remain poorly understood. Unlike heavy quarkonia, i.e. the hidden heavy quark-antiquark sectors of charmonium ($c\bar c$) and bottomonium ($b\bar b$), the $B_c$-mesons cannot annihilate into gluons and they are, consequently, more stable. The excited $B_c$ states, lying below the lowest strong-decay $BD$-threshold, can only undergo through radiative decays and hadronic transitions to the $B_c$ ground state, which then decays weakly. As a result of this, a rich spectrum of narrow excited states below the $BD$-threshold appear, whose total widths are two orders of magnitude smaller than those of the excited levels of charmonium and bottomonium. In a different article, we determined bottom-charmed meson masses using a non-relativistic constituent quark model which has been applied to a wide range of hadron physical observables, and thus the model parameters are completely constrained. Herein, continuing to our study of the $B_c$ sector, we calculate the relevant radiative decay widths and hadronic transition rates between $c\bar b$ states which are below $BD$-threshold. This shall provide the most promising signals for discovering excited $B_c$ states that are below the lowest strong-decay $BD$-threshold. Finally, our results are compared with other models to measure the reliability of the predictions and point out differences.

An estimate of dibaryon production in the process of at anda facility* *Supported by the National Natural Science Foundation of China (11475192), the Sino-German CRC 110 "Symmetries and the Emergence of Structure in QCD" project by NSFC (12070131001), the Key Research Program of Frontier Sciences, CAS (Y7292610K1), and the National Key Research and Development Program of China (2020YFA0406300), IHEP Innovation

Although was first observed by WASA@COSY, its existence has yet to be further confirmed in different types of processes at other facilities. In this work, the possible production of the single dibaryon state in the process of in a future experiment at the anda facility is estimated. Following the method used in our previous study (Chin. Phys. C 46, 023105), a phenomenological Lagrangian approach is employed to study the single production. Based on the conclusions obtained by the non-relativistic constituent quark model, the cross section of the reaction via the intermediate state is estimated, which is in the order of . It is shown that the dominant contribution comes from the diagram with the subprocess. However, it is difficult to measure owing to the large background. Further, although the cross section of the diagram with the subprocess is small, i.e., only approximately of the total cross section or even smaller, the corresponding number of events is still sufficiently large and can be measured at anda because the outgoing and come from the same source .

Spectroscopic Properties of Light Baryon

Hadron Spectroscopy provides a realm to study the internal quark dynamics within the hadrons through phenomenological, theoretical as well as experimental approaches. In the present article, an attempt has been made to exploit the nucleon N resonances using a non-relativistic hypercentral Constituent Quark Model (hCQM). The properties are studied based on the linear nature of confining part of the potential. The 1S-5S, 1P-3P, 1D-2D and 1F states mostly with four star labelled resonances are explored again with the separation of charge states using different constituent quark masses. Also, Regge trajectories for some obtained states are plotted for examining the linear nature.

Hyperon weak radiative decay * *Supported by the National Natural Science Foundation of China (11425525, 11521505), DFG and NSFC funds to the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD” (NSFC) (11261130311), Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030302), National Key Basic Research Program of China (2015CB856700); Q.W. is also supported by the research

We revisit the hyperon weak radiative decays in the framework of the non-relativistic constituent quark model. This study confirms the nonlocal feature of the hyperon weak radiative transition operators, which are dominated by the pole terms, and an overall self-consistent description of the available experimental data for the Cabibbo-favored hyperon weak radiative decays is presented. It provides a natural mechanism for evading the Hara theorem, where sizeable parity-violating contributions can come from the intermediate orbital excitations. Cancellations between pole terms also explain the significant SU(3) flavor symmetry breaking manifested by the experimental data. We also discuss several interesting selection rules arising from either the electromagnetic or the weak interaction vertices. These features suggest nontrivial relations among various hyperon decays.

Triply charmed and bottom baryons in a constituent quark model

In this work, we study the mass spectrum of the $\Omega_{ccc}$ and $\Omega_{bbb}$ baryons up to the $N=2$ shell within a nonrelativistic constituent quark model (NRCQM). The model parameters are adopted from the determinations by fitting the charmonium and bottomonium spectra in our previous works. The masses of the $\Omega_{ccc}$ and $\Omega_{bbb}$ baryon states predicted in present work reasonably agree with the results obtained with the Lattice QCD calculations. Furthermore, to provide more knowledge of the $\Omega_{ccc}$ and $\Omega_{bbb}$ states, we evaluate their radiative decays with the available masses and wave functions from the potential model.

Ω baryon spectrum and their decays in a constituent quark model

Combining the recent developments of the observations of $\mathrm{\ensuremath{\Omega}}$ sates we calculate the $\mathrm{\ensuremath{\Omega}}$ spectrum up to the $N=2$ shell within a nonrelativistic constituent quark potential model. Furthermore, the strong and radiative decay properties for the $\mathrm{\ensuremath{\Omega}}$ resonances within the $N=2$ shell are evaluated by using the masses and wave functions obtained from the potential model. It is found that the newly observed $\mathrm{\ensuremath{\Omega}}(2012)$ resonance is most likely to be the spin-parity ${J}^{P}=3/{2}^{\ensuremath{-}}$ $1P$-wave state $\mathrm{\ensuremath{\Omega}}({1}^{2}{P}_{3/{2}^{\ensuremath{-}}})$, it also has a large potential to be observed in the $\mathrm{\ensuremath{\Omega}}(1672)\ensuremath{\gamma}$ channel. Our calculation shows that the $1P$-, $1D$-, and $2S$-wave $\mathrm{\ensuremath{\Omega}}$ baryons have a relatively narrow decay width of less than 50 MeV. Based on the obtained decay properties and mass spectrum, we further suggest optimum channels and mass regions to find the missing $\mathrm{\ensuremath{\Omega}}$ resonances via the strong and/or radiative decay processes.

Electron and its symmetry as basic elements of particle mass spectrum and discreteness in nuclear data

An analysis of empirical correlations in particle masses and nuclear data confirmed the great role of lepton masses (me, mμ), parameters of the Nonrelativistic Constituent Quark Model and the QED radiative corrections in the Standard Model development. Integer relations (1:13:16:17:18:54) between doubled value of the pion β-decay energy (close to 16me=δ=8.176 MeV), the muon mass, the pion parameters (fπ=130.7 MeV, mπ) and the NRCQM parameters ΔMΔ=147 MeV=(mΔ−mN)/2 and Mq=mΞ/3 are compared with the masses of quarks and fundamental fields and with the number of fermions in the central field. Confirmations of the period 16me were obtained from the analysis of CODATA relations (exact ratios of the masses of nucleons to the electron mass) and global analysis of nuclear data.

Constituent quark mass and spin in NRCQM model

We show that the success of the Nonrelativistic Constituent Quark Model can be associated with symmetrization, which manifests itself in the exact 3:1 ratio between the initial constituent quark mass Mq = mΞ/3=441MeV and the parameter of quark interaction ΔMΔ = (mΔ − mN)/2=147MeV. The interconnection of these parameters with the electron mass, its symmetry, the masses of the fundamental fields and the QED radiative correction is considered. The discreteness with the parameter me can be used in the study of gravitation and dark matter problems.

Electromagnetic Transition Form Factor of the Nucleon $$\Delta $$ (1232) in The Nonrelativistic Constituent Quark Model

The study of nucleon electromagnetic form factors has long been identified as a singular source of information for conception strong interactions in the extent of quark confinement. We have performed a calculation of the helicity amplitudes and the electromagnetic transition form factors of the electromagnetic excitation in $$\Delta $$(1232) resonances. In this paper, the electromagnetic interaction for N $$(938)\rightarrow \Delta (1232)$$ transitions at four-momenta transfer $$0 \le \hbox {Q2}(\hbox {GeV}^\mathrm{{2}}) \le 8$$ in the nonrelativistic constituent quark model calculated. In comparison with present experimental, relativistic and non-relativistic data, our results are in good agreement with the experimental and the other theoretical results, in particular of the medium-high $$\hbox {Q}^{2}$$ behavior.

Analyzing doubly heavy tetra- and penta-quark states by variational method

Motivated by the very recent observations of hidden charm pentaquarks Pc(4312)+, Pc(4440)+ and Pc(4457)+ of the LHCb Collaboration, we systematically study the spectra of the doubly-heavy (with or without charm/bottom numbers) pentaquarks and tetraquarks in non-relativistic constituent quark model. The model independent variational method is employed to solve the Schrödinger equation, where the test radial functions adopted are symmetric for the light quarks. In our study, the Pc(4312)+ may be assigned as the ground state with spin-parity 12− or 32−, while the Pc(4440)+ and Pc(4457)+ may be assigned as the excited states with 12−, which might all belong to the sextet with scc¯=1 and sℓ=32. It is notable that our working framework is quite similar to that of Hydrogen molecule, but with different potential structure. We also classify these pentaquarks and tetraquarks in light of the heavy quark symmetry and their decay properties are analyzed. Several promising channels for the observation of doubly-heavy pentaquarks and doubly-heavy tetraquarks in experiment are proposed.

The direct coupling of light quarks to heavy di-quarks

In the limit mQ>mQvrel>mQvrel2≫ΛQCD hadronic states with two heavy quarks Q should be describable by a version of HQET where the heavy quark is replaced by a di-quark degree of freedom. In this limit the di-quark is a small (compared with 1/ΛQCD) color anti-triplet, bound primarily by a color Coulomb potential. The excited Coulombic states and color six states are much heavier than the color anti-triplet ground state. The low lying spectrum of hadrons containing two heavy quarks is then determined by the coupling of the light quarks and gluons with momentum of order ΛQCD to this ground state di-quark. In this short paper we calculate the coefficient of leading local operator (Sv†Sv)(q¯γμvμq) that couples this color anti-triplet di-quark field Sv (with four-velocity v) directly to the light quarks q in the low energy effective theory. It is O(1/(αs(mQvrel)mQ2)). While our work is mostly of pedagogical value we make an estimate of the contribution of this operator to the masses of Ξbbq baryon and TQQq¯q¯ tetraquark using the non-relativistic constituent quark model.

The modified communication between the helicity amplitudes and the electromagnetic form factor of a nucleon based on the nonrelativistic constituent quark model

In this paper, as a first step, the baryon resonance spectrum and the hyperfine structure of the baryon by using a simple approach based on the Gursey-Radicati mass formula (GR) are studied. As a second step, since the electromagnetic transition between nucleon and excited baryons has long been recognized as an important source of information for understanding strong interactions in the domain of quark confinement, we performed calculation of the helicity amplitudes and electric and magnetic transition form factors for the electromagnetic excitation of nucleon resonances in the nonrelativistic quark model. In this paper, we present a new model for the communication between the electromagnetic transition form factors and helicity amplitudes. These have shown the best communication between helicity amplitudes and electromagnetic form factors, with preservation of the unit. We present new results concerning electromagnetic form factors of the nucleon using a nonrelativistic version of the hypercentral constituent quark model and nonrelativistic current. Presenting our results in the range $ 0\leq Q^2$ (GeV2 $ \leq 5$ in comparison with the predictions obtained in other relativistic and nonrelativistic quark models, our results lead to an overall better agreement with the experimental data, especially in the medium Q2 range.

Electromagnetic Coupling of Negative Parity Nucleon Resonances N (1535) Based on Nonrelativistic Constituent Quark Model

The electromagnetic transition between the nucleon and excited baryons has long been recognized as an important source of information for understanding strong interactions in the domain of quark confinement. We study the electromagnetic properties of the excitation of the negative parity the N*(1535) resonances in the nonrelativistic constituent quark model at large momentum transfers and have performed a calculation the longitudinal and transverse helicity amplitudes. Since the helicity amplitudes depend strongly on the quark wave function in this paper, we consider the baryon as a simple, non-relativistically three-body quark model and also consider a hypercentral potential scheme for the internal baryon structure, which makes three-body forces among three quarks. Since the hyper central potential depends only on the hyper radius, therefore, the Cornell potential which is a combination of the Coulombic-like term plus a linear confining term is considered as the potential for interaction between quarks. In our work, in solving the Schrodinger equation with the Cornell potential, the Nikiforov–Uvarov method employed, and the analytic eigen-energies and eigen-functions obtained. By using the obtained eigen-functions, the transition amplitudes calculated. We show that our results in the range lead to an overall better agreement with the experimental data in comparison with the other three non-relativistic quark models.

Threshold effects in hadron spectrum: a new spectroscopy?

The exploration of energies above the open-flavor threshold in the meson spectra has led to the appearance of unexpected states difficult to accommodate in the naive picture of a bound state of a quark and an antiquark. Many of such states are located close to meson-meson thresholds, which suggests that molecular structures may be a relevant component in the total wave function of such resonances. In this work, the state of meson-meson molecules calculations is reviewed, using a nonrelativistic constituent quark model that has been applied to a wide range of hadronic observables, and therefore all model parameters are completely constrained. The model has been able to reproduce, among others, the properties of the X(3872), described as a mixture of cc and DD* states, or the spectrum of the P-wave charm-strange mesons, which are well reproduced only if DK and D*K structures are taken into account. We show that such constituent quark model, which is able to describe the ordinary heavy meson spectra, is also capable of providing a good description of many new states recently reported.

Low-lying charmed and charmed-strange baryon states

In this work, we systematically study the mass spectra and strong decays of 1P and 2S charmed and charmed-strange baryons in the framework of non-relativistic constituent quark models. With the light quark cluster–heavy quark picture, the masses are simply calculated by a potential model. The strong decays are studied by the Eichten–Hill–Quigg decay formula. Masses and decay properties of the well-established 1S and 1P states can be reproduced by our method. Sigma _c(2800)^{0,+,++} can be assigned as a Sigma _{c2}(3/2^-) or Sigma _{c2}(5/2^-) state. We prefer to interpret the signal Sigma _c(2850)^0 as a 2S(1/2^+) state although at present we cannot thoroughly exclude the possibility that this is the same state as Sigma _c(2800)^0. Lambda _c(2765)^+ or Sigma _c(2765)^+ could be explained as the Lambda _c^+(2S) state or Sigma ^+_{c1}(1/2^-) state, respectively. We propose to measure the branching ratio of mathcal {B}(Sigma _c(2455)pi )/mathcal {B}(Sigma _c(2520)pi ) in the future, which may disentangle the puzzle of this state. Our results support Xi _c(2980)^{0,+} as the first radial excited state of Xi _c(2470)^{0,+} with J^P=1/2^+. The assignment of Xi _c(2930)^0 is analogous to Sigma _c(2800)^{0,+,++}, i.e., a Xi ^prime _{c2}(3/2^-) or Xi ^prime _{c2}(5/2^-) state. In addition, we predict some typical ratios among partial decay widths, which are valuable for experimental search for these missing charmed and charmed-strange baryons.