Quark Model Approach Research Articles

Investigation on the stabilities of doubly heavy tetraquark states

In our recent work [S. Noh and W. Park, Nonrelativistic quark model analysis of Tcc, ], the mass and binding energy of Tcc are found to be 3873 MeV and −2 MeV, respectively, which align with the observations reported at LHCb [R. Aaij (LHCb Collaboration), Observation of an exotic narrow doubly charmed tetraquark, ]. Based on our latest quark model approach, we extend our search for other potentially stable configurations of doubly heavy tetraquarks using our nonrelativistic quark model described in Noh and Park, [Nonrelativistic quark model analysis of Tcc, ]. Our numerical calculations indicate that the u¯s¯cb configuration is deeply bound. However, the u¯d¯cb configuration with the isospin symmetry in the light quark sector is relatively less bound. In this study, we emphasize a compulsory aspect for requiring a complete set of three-dimensional harmonic oscillator bases through the discussion of the u¯s¯cb configuration and investigate the essential differences between the u¯s¯cb and u¯d¯cb configurations. Published by the American Physical Society 2024

Production of single-charmed baryons in a quark model approach

The production of single-charmed baryons $\Lambda_c^+ \Lambda_c^-$, $\Lambda_c^+ \Sigma_c^-$+h.c. and $\Sigma_c^+ \Sigma_c^-$ in $p\bar p$ collisions is studied in the framework of a constituent quark model which has satisfactorily described the $N\bar N$ system and the strangeness production $p\bar p\to \Lambda\bar \Lambda$, $\Lambda\bar\Sigma$ and $\Sigma\bar\Sigma$ processes. Predictions on the total cross sections are analyzed for different approaches to the underlying $n\bar n\to c\bar c$ process, mediated by one gluon annihilation diagrams. The results indicate that the cross section is of the order of $1$ nb between $10-14$ GeV for $\Lambda_c^+\Lambda_c^-$ and $\Lambda_c^+ \Sigma_c^-$ channels, and around $0.01-0.1$ nb for $\Sigma_c^+\Sigma_c^-$. This estimations can be relevant for their future search in facilities like $\bar{P}$ANDA.

Mass spectrum of triply heavy baryon in the hypercentral quark model

In this study, we consider baryons as three-body bound systems according to hypercentral constituent quark model in configuration space and solve three-body Klein–Gordon equation. Then we analyze perturbative spin-dependent and isospin-dependent interaction effects. To find the analytical solution, we used screened potential and calculate the eigenfunctions and eigenvalues of triply heavy baryons by using Nikiforov–Uvarov method. We compute the ground and excited state masses of triply heavy baryons with quantum numbers [Formula: see text], [Formula: see text], [Formula: see text] via constituent quark model approach.

Decuplet baryons in nuclear and hyperonic medium

Masses and the magnetic moments of baryon decuplet are evaluated in the symmetric nuclear and hyperonic matter at finite temperature using a chiral SU(3) quark mean field model approach. The decuplet baryon masses considerably decrease with the rise in the baryonic density of the medium. With the increase in strangeness (more number of hyperons as compared to nucleons) fraction, the non-strange baryons show an increase in their masses, whereas the strange baryons show a decrease. The contributions coming from the valence quarks, quark sea and the orbital angular momentum of the quark sea have been considered to calculate net magnetic moment. The magnetic moments of decuplet baryons are found to show a considerable increase with the baryonic density of the medium since constituent quark magnetic moment and the quark spin polarizations show significant variation in the nuclear medium especially in the low temperature and baryonic density regime. The increase is however quantitatively less as compared to the case of octet baryon members. With the inclusion of hyperons along with nucleons, the non-strange baryons show a decrease in the magnitude of their effective magnetic moments, whereas the strange baryons show an increase. The strangeness fraction of the medium is found to largely affect the valence quark magnetic moment and quark sea magnetic moment of the baryons.

The charged $Z_c$ and $Z_b$ structures in a constituent quark model approach

The nature of the recently discovered Z_cZc and Z_bZb structures is intriguing. Their charge forces its minimal quark content to be Q\bar Q q\bar qQQ‾qq‾ (where Q=\{c,b\}Q={c,b} and q=\{u,d\}q={u,d}). In this work we perform a molecular coupled-channels calculation of the I^G(J^{PC})=1^+(1^{+-})IG(JPC)=1+(1+−) charm and bottom sectors in the framework of a constituent quark model which satisfactorily describes a wide range of properties of (non-)conventional hadrons containing heavy quarks. All the relevant channels are included for each sector, i.e.: The D^{(\ast)}\bar D^{\ast}+h.c.D(*)D‾*+h.c., \pi J/\psiπJ/ψ and \rho\eta_cρηc channels for the Z_cZc and B^{(\ast)}B^{\ast}B(*)B* and \Upsilon(nS)\piΥ(nS)π (n=1,2,3n=1,2,3) channels for the Z_bZb analysis. Possible structures of these resonances will be discussed.

Diffractive incoherent vector meson production off protons: a quark model approach to gluon fluctuation effects

Fluctuations play an important role in diffractive production of vector mesons. It was in particular recently suggested, based on the Impact-Parameter dependent Saturation model (IPSat), that geometrical fluctuations triggered by the motion of the constituent quarks within the protons could explain incoherent diffractive processes observed at HERA. We propose a variant of the IPSat model which includes spatial and symmetry correlations between constituent quarks, thereby reducing the number of parameters needed to describe diffractive vector meson production to a single one, the size of the gluon cloud around each valence quark. The application to J/varPsi , rho and phi diffractive electron and photon production cross sections reveal the important role of geometrical fluctuations in incoherent channels, while other sources of fluctuations are needed to fully account for electroproduction of light mesons, as well as photo production of J/varPsi mesons at small momentum transfer.

A Potential Model Approach in the Study of Static and Dynamic Properties of Heavy-Light Quark-Antiquark Systems

We report some approximate analytic form of meson wave function constructed upon solving Schrodinger equation with linear plus Coulomb type Cornell potential. With this wave function, we study Isgur-Wise function and its derivatives for heavy-light mesons in the infinite heavy quark mass limit. We also explore the elastic form factors, charge radii and decay constants of pseudoscalar mesons in this QCD inspired quark model approach.

Neutral pion photoproduction on the nucleon in a chiral quark model

A chiral quark-model approach is adopted to study the $\gamma p\rightarrow \pi^0p$ and $\gamma n\rightarrow \pi^0 n$ reactions. Good descriptions of the total and differential cross sections and single-polarization observables are obtained from the pion production threshold up to the second resonance region. It is found that (i) the $n=0$ shell resonance $\Delta(1232)P_{33}$, the $n=1$ shell resonances $N(1535)S_{11}$ and $N(1520)D_{13}$, and the $n=2$ shell resonance $N(1720)P_{13}$ play crucial roles in these two processes. They are responsible for the first, second and third bump structures in the cross sections, respectively. (ii) Furthermore, obvious evidences of $N(1650)S_{11}$ and $\Delta(1620)S_{31}$ are also found in the reactions. They notably affect the cross sections and the polarization observables from the second resonance region to the third resonance region. (iii) The $u$-channel background plays a crucial role in the reactions. It has strong interferences with the $s$-channel resonances. (iv) The $t$-channel background seems to be needed in the reactions. Including the $t$-channel vector-meson exchange contribution, the descriptions in the energy region $E_\gamma= 600\sim 900$ MeV are improved significantly. The helicity amplitudes of the main resonances, $\Delta(1232)P_{33}$, $N(1535)S_{11}$, $N(1520)D_{13}$, $N(1720)P_{13}$, $N(1650)S_{11}$ and $\Delta(1620)S_{31}$, are extracted and compared with the results from other groups.

Unpolarized transverse momentum dependent parton distribution functions beyond leading twist in quark models

Higher-twist transverse momentum dependent parton distribution functions (TMDs) are a valuable probe of the quark-gluon dynamics in the nucleon, and play a vital role for the explanation of sizable azimuthal asymmetries in hadron production from unpolarized and polarized deep-inelastic lepton-nucleon scattering observed in experiments at CERN, DESY and Jefferson Lab. The associated observables are challenging to interpret, and still await a complete theoretical explanation, which makes guidance from models valuable. In this work we establish the formalism to describe unpolarized higher-twist TMDs in the light-front framework based on a Fock-space expansion of the nucleon state in terms of free on-shell parton states. We derive general expressions and present numerical results in a practical realization of this picture provided by the light-front constituent quark model. We review several other popular quark model approaches including free quark ensemble, bag, spectator and chiral quark-soliton model. We discuss how higher-twist TMDs are described in these models, and obtain results for several TMDs not discussed previously in literature. This study contributes to the understanding of non-perturbative properties of subleading twist TMDs. The results from the light-front constituent quark model are also compared to available phenomenological information, showing a satisfactory agreement.

Low-energyK−p→Ληreaction and the negative parityΛresonances

The reaction $K^-p\rightarrow\Lambda\eta$ at low energies is studied with a chiral quark model approach. Good descriptions of the existing experimental data are obtained. It is found that $\Lambda(1670)$ dominates the reaction around threshold. Furthermore, $u$- and $t$-channel backgrounds play crucial roles in this reaction as well. The contributions from the $D$-wave state $\Lambda(1690)$ are negligibly small for its tiny coupling to $\eta\Lambda$. To understand the strong coupling properties of the low-lying negative parity $\Lambda$ resonances extracted from the $\bar{K}N$ scattering, we further study their strong decays. It is found that these resonances are most likely mixed states between different configurations. Considering these low-lying negative parity $\Lambda$ resonances as mixed three-quark states, we can reasonably understand both their strong decay properties from Particle Data Group and their strong coupling properties extracted from the $\bar{K}N$ scattering. As a byproduct, we also predict the strong decay properties of the missing $D$-wave state $|\Lambda\frac{3}{2}^-\ >_3$ with a mass of $\sim1.8$ GeV. We suggest our experimental colleagues search it in the $\Sigma(1385)\pi$ and $\Sigma\pi$ channels.

Low-energy reactionsK−p→Σ0π0,Λπ0,K¯0nand the strangenessS=−1hyperons

A combined study of the reactions ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\Sigma}}^{0}{\ensuremath{\pi}}^{0}$, $\ensuremath{\Lambda}{\ensuremath{\pi}}^{0}$, and ${\overline{K}}^{0}n$ at low energies is carried out with a chiral quark-model approach. Good descriptions of the experimental observations are obtained. The roles of the low-lying strangeness $S=\ensuremath{-}1$ hyperon resonances in these processes are carefully analyzed. We find that (i) in the ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\Sigma}}^{0}{\ensuremath{\pi}}^{0}$ process, both $\ensuremath{\Lambda}(1405){S}_{01}$ and $\ensuremath{\Lambda}(1520){D}_{03}$ play dominant roles. Significant contributions of $\ensuremath{\Lambda}(1670){S}_{01}$ and $\ensuremath{\Lambda}(1690){D}_{03}$ could be seen around their threshold; (ii) in the ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\Lambda}{\ensuremath{\pi}}^{0}$ process, some obvious evidence of $\ensuremath{\Sigma}(1775){D}_{15}$ and $\ensuremath{\Sigma}(1750){S}_{11}$ could be found. Some hints of $\ensuremath{\Sigma}(1620){S}_{11}$ might exist in the reaction as well. $\ensuremath{\Sigma}(1750){S}_{11}$ and $\ensuremath{\Sigma}(1620){S}_{11}$ should correspond to the representations $[70{,}^{4}8]{S}_{11}$ and $[70{,}^{2}8]{S}_{11}$, respectively; (iii) in the ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\overline{K}}^{0}n$ process, the dominant resonances are $\ensuremath{\Lambda}(1405)$ and $\ensuremath{\Lambda}(1520)$. Some evidence of $\ensuremath{\Lambda}(1690){D}_{03}$, $\ensuremath{\Sigma}(1670){D}_{13}$, and $\ensuremath{\Sigma}(1775){D}_{15}$ could be seen as well. A weak coupling of $\ensuremath{\Lambda}(1670){S}_{01}$ to $\overline{K}N$ should be needed in the reactions ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\Sigma}}^{0}{\ensuremath{\pi}}^{0}$ and ${\overline{K}}^{0}n$. Furthermore, by analyzing these reactions, we also find that the $u$-, $t$-channel backgrounds and $s$-channel Born term play crucial roles in the reactions: (i) The angle distributions of ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\Sigma}}^{0}{\ensuremath{\pi}}^{0}$ are very sensitive to the $u$-, $t$-channel backgrounds and $s$-channel $\ensuremath{\Lambda}$ pole; (ii) the reaction ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\Lambda}{\ensuremath{\pi}}^{0}$ is dominated by the $u$-, $t$-channel backgrounds and the ground $P$-wave state $\ensuremath{\Sigma}(1385){P}_{13}$; (iii) while the reaction ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\overline{K}}^{0}n$ is governed by the $t$-channel background, and $\ensuremath{\Sigma}(1385){P}_{13}$ also plays an important role in this reaction.

Can the constituent quark model describe the pion?

A comparison of the nature of the pion in terms of the Bethe–Salpeter, Salpeter, and quark model approaches is presented. We show that many, but not all, properties of the pion can be captured by the constituent quark model.

η′photoproduction on the nucleon in the quark model

A chiral quark-model approach is adopted to study the $\gamma p\rightarrow \eta'p$ and $\gamma n\rightarrow \eta' n$. Good descriptions of the recent observations from CLAS and CBELSA/TAPS are obtained. Both of the processes are governed by $S_{11}(1535)$ and $u$ channel background. Strong evidence of an $n=3$ shell resonance $D_{15}(2080)$ is found in the reactions, which accounts for the bump-like structure around $W=2.1$ GeV observed in the total cross section and excitation functions at very forward angles. The $S_{11}(1920)$ seems to be needed in the reactions, with which the total cross section near threshold for the $\gamma p\rightarrow \eta' p$ is improved slightly. The polarized beam asymmetries show some sensitivities to $D_{13}(1520)$, although its effects on the differential cross sections and total cross sections are negligible. There is no obvious evidence of the $P$-, $D_{13}$-, $F$- and $G$-wave resonances with a mass around 2.0 GeV in the reactions.

ηphotoproduction on quasifree nucleons in the chiral quark model

A chiral quark-model approach is adopted to study the $\eta$ photoproduction off the quasi-free neutron and proton from a deuteron target. Good descriptions of the differential cross sections, total cross sections and beam asymmetries for these two processes are obtained in the low energy region. For $\gamma p\rightarrow \eta p$, the dominant resonances are $S_{11}(1535)$, $S_{11}(1650)$, $D_{13}(1520)$, $D_{13}(1700)$ and $P_{13}(1720)$. While for the $\gamma n\rightarrow \eta n$ process, the dominant resonances are $S_{11}(1535)$, $S_{11}(1650)$, $D_{13}(1520)$, $D_{15}(1675)$ and $P_{13}(1720)$. Furthermore, the $u$ channel backgrounds have significant contributions to the $\eta$ photoproduction processes. The configuration mixings in the $S_{11}(1535,1650)$ and $D_{13}(1520,1700)$ can be extracted, i.e. $\theta_S\simeq 26^\circ$ and $\theta_D\simeq 21^\circ$. It shows that the narrow bump-like structure around $W= 1.68$ GeV observed in $\gamma n\rightarrow \eta n$ can be naturally explained by the constructive interferences between $S_{11}(1535)$ and $S_{11}(1650)$. In contrast, the destructive interference between $S_{11}(1535)$ and $S_{11}(1650)$ produces the shallow dip around $W= 1.67$ GeV in $\gamma p\rightarrow \eta p$. The $S$ wave interfering behaviors in the proton and neutron reactions are correlated with each other in the quark model framework, and no new exotic nucleon resonances are needed in these two reactions.

UNQUENCHED QUARK MODEL DESCRIPTION OF CHARMONIUM

We show that the charmonium spectrum may be reproduced to a good precision by means of a semirelativistic quark model approach based on a universal static potential effectively incorporating effects from sea quark-antiquark pairs. Detailed predictions for upcoming data are derived.

Chiral Quark Model Approach for the Study of Baryon Resonances

We report the chiral quark model approach for the study of baryon resonances in meson photoproduction and meson-nucleon scattering processes. Focussing on the $\pi N$ and $K N$ scatterings, we show that the cross sections near threshold can be well accounted for by the chiral quark model with only few parameters. The $S$-wave dominance in both $\pi^- p\to \eta n$ and $K^- p\to \Sigma^0\pi^0$ can be well understood in the quark model framework. In particular, the quark model provides a constraint on the relative signs for resonance coupling form factors, which seems to be consistent with results from isobaric models.

ηproduction off the proton in a Regge-plus-chiral quark approach

A chiral constituent quark model approach, embodying $s$- and $u$-channel exchanges, complemented with a Reggeized treatment for the $t$ channel is presented. A model is obtained allowing data for ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\eta}n$ and $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\eta}p$ to be described satisfactorily. For the latter reaction, recently released data by the CLAS and CBELSA/TAPS Collaborations in the system total energy range $1.6\ensuremath{\lesssim}W\ensuremath{\lesssim}2.8$ GeV are well reproduced by the inclusion of Reggeized trajectories instead of simple $\ensuremath{\rho}$ and $\ensuremath{\omega}$ poles. The contribution from ``missing'' resonances, with masses below 2 GeV, is found to be negligible in the considered processes.

K− p scattering and hyperon excitations in a chiral quark model

A chiral quark-model approach is employed to study the K̄N scattering at low energies. The processes of K−p → σ0π0, Λπ0 and K̄0n at PK ≤ 800 MeV/c (i.e. the center mass energy W ≤ 1.7 GeV) are investigated. The analysis shows that the Λ(1405)S01 dominates the processes K−p → σ0π0, K̄0n in the energy region considered here. Around PK ∊ 400 MeV/c, the Λ(1520)D03 is responsible for a strong resonant peak in the cross section of K−p → σ0π0 and K̄0n. To reproduce the data, an unexpectedly large coupling for Λ(1520)D03 to KN is needed. In contrast, the coupling for Λ(1670)S01 to KN appears to be weak, which could be due to configuration mixings between Λ(1405)S01 and Λ(1670)S01. By analyzing K−p → Λπ0, evidences for two low mass S-wave states, σ(1480) S11 and σ(1560) S11, seem to be available. With these two states, the reaction K−p → K̄0n can also be described well. However, it is difficult to understand the low masses of σ(1480) S11 and σ(1560) S11. The s-channel amplitudes for K−p → Λπ0 are also larger than the naive quark model expectations. The non-resonant background contributions, i.e. t-channel and/or u-channel, also play important roles in the explanation of the angular distributions due to amplitude interferences.

The ρ → γπ and ω → γπ decays in quark-model approach and estimation of coupling for pion emission by quark

In the framework of the relativistic and gauge invariant spectral integral technique, we calculate radiative decays rho(770)-> gamma pi(140) and omega(780)-> gamma pi(140) supposing all mesons (pi, rho and omega) to be quark-antiquark states. The q anti-q wave functions found for mesons and photon lead to a reasonably good description of data ($\Gamma^{(exp)}_{\rho^{\pm} \to\gamma\pi^{\pm}}=68\pm 30$ keV, $\Gamma^{(exp)}_{\rho^{0}\to\gamma\pi^0}=77\pm 28$ keV, $\Gamma^{(exp)}_{\omega\to\gamma\pi^0}=776\pm 45$ keV) that makes it possible to estimate the coupling for the bremsstrahlung emission of pion by quarks $g_\pi\equiv g_\pi (u\to d \pi)$. We have found two values for the pion bremsstrahlung coupling: $|g_\pi|=16.7 \pm 0.3 ^{+0.1}_{-2.3}$ (Solution I) and $|g_\pi|=3.0 \pm 0.3 ^{+0.1}_{-2.1}$ (Solution II). Within SU(6)-symmetry for nucleons, Solution I gives us for pi NN coupling the value $16.4 \le g_{\pi NN}^2/(4\pi) \le 23.2$ that is in qualitative agreement with the pi N scattering data, $g_{\pi NN}^2/(4\pi)\simeq 14$. For excited states, we have estimated the partial widths in Solution I as follows: $\Gamma (\rho_{2S}^\pm\to \gamma\pi)\simeq 10 - 130$ keV, $\Gamma (\rho_{2S}^0\to \gamma\pi)\simeq 10 -130$ keV, $\Gamma (\omega_{2S}\to \gamma\pi)\simeq 60 - 1080$ keV. The large uncertainties emphasise the necessity to carry out measurements of the meson radiative processes in the region of large masses.

Study of nucleon resonances in a chiral quark model via η productions

In this report we investigate η-meson productions on the proton via electromagnetic and hadron probes in a chiral quark model approach. The observables, such as, differential cross section and beam asymmetry for the two productions are calculated and compared with the experiment. The five known resonances S11(1535), S11(1650), P13(1720), D13(1520), and F15(1680) are found to be dominant in the reaction mechanisms in both channels. Significant contribution from a new S11 resonances are deduced. For the so-called “missing resonances”, no evidence is found within the investigated reactions. The partial wave amplitudes for π−p → ηn are also presented.