Quark Potential Model Research Articles

Fully strange tetraquark resonant states as the cousins of X(6900)

We conduct systematic calculations of the S-wave fully strange systems with “normal” (JPC=0++,1+−,2++) and “exotic” (JPC=0+−,1++,2+−) C-parities, which are the strange analog of the fully charmed tetraquark state X(6900). Within a constituent quark potential model, we employ the Gaussian expansion method to solve the four-body Schrödinger equation and the complex scaling method to identify resonant states. We obtain a series of resonant states and zero-width states in the mass range of 2.7 to 3.3 GeV, with their widths ranging from less than 1 to about 50 MeV. Their rms radii strongly indicate that they are compact tetraquark states. Among these states, the T4s,2++(2714) may be the most likely one to be observed experimentally. We urge the experimental exploration of the 2++ sss¯s¯ state around 2.7 GeV in the ϕϕ channel. Since the lowest S-wave sss¯s¯ state is around 2.7 GeV, the compact wave sss¯s¯ states are expected to be heavier. Hence, ϕ(2170) and X(2370) are unlikely to be compact tetraquark states. Published by the American Physical Society 2024

Heavy baryons in the relativized quark model with chromodynamics

Following the work of Capstick and Isgur [], we systematically study the mass spectrum of the heavy baryons in the relativized quark potential model with chromodynamics. Besides the original Godfrey-Isgur (GI) model, we also adopt a modified GI model which replaces the linear confinement by a screened one. The two models give similar results in our work. All heavy baryons observed so far can be explained as three-quark states. In particular, we identify the Ωc(3000)/Ωb(6316), Ωc(3050)/Ωb(6330), Ωc(3065)/Ωb(6340), and Ωc(3090)/Ωb(6350) states as the pλ excitations with quantum numbers 1/2−, 3/2−, 3/2−, and 5/2−. The Ωc(3120) is a 3/2− state with the pρ excitation, whose bottom partner is predicted to be Ωb(6446/6457,3/2−). The higher state Ωc(3188) is the 2sλ excitation with quantum numbers 1/2+, and Ωc(3327) is a dλ excitation with quantum numbers 3/2+ or 5/2+. Published by the American Physical Society 2024

Unified description of the Qsq¯q¯ molecular bound states, molecular resonances, and compact tetraquark states in the quark potential model

We calculate the mass spectrum of the Qsq¯q¯ (Q=c, b) tetraquark states with JP=(0,1,2)+ using the AL1 quark potential model, which successfully describes the conventional hadron spectrum. We employ the Gaussian expansion method to solve the four-body Schrödinger equation and use the complex scaling method to identify the resonances. With the notation TQs,I(J)Theo.(M), we find several near-threshold bound states and resonances, including Tcs,0(0)Theo.(2350), Tcs,0(0)Theo.(2906), Tbs,0(0)Theo.(5781), Tbs,0(1)Theo.(5840), and Tbs,0(0)Theo.(6240), which are close to the DK¯, D*K¯*, B¯K¯, B¯*K¯, and B¯*K¯* thresholds, respectively. Furthermore, their spatial structures clearly support their molecular natures. The resonance Tcs,0(0)Theo.(2906) with a mass of 2906 MeV, a width of 20 MeV, and quantum numbers I(JP)=0(0+) may serve as a good candidate for the experimental Tcs0(2900) state. We strongly urge the experimental search of the predicted states. Published by the American Physical Society 2024

Charmed-strange tetraquarks and their decays in the potential quark model

In the framework of a nonrelativistic potential quark model, we investigate the mass spectrum of the $1S$-wave charmed-strange tetraquark states of $cn\overline{s}\overline{n}$ and $cs\overline{n}\overline{n}$ ($n=u$ or $d$) systems. The tetraquark system is solved by a correlated Gaussian method. With the same parameters fixed by the meson spectra, we obtained the mass spectra for the $1S$-wave tetraquark states. Furthermore, based on the predicted tetraquark spectra we estimate their rearrangement decays in a quark-exchange model. We find that the rearrangement decays of the tetraquarks may be mainly driven by the spin-spin interactions. The resonances ${X}_{0}(2900{)}^{0}$ and ${T}_{c\overline{s}0}^{a}(2900{)}^{++/0}$ reported from LHCb may be assigned to be the lowest $1S$-wave tetraquark states ${\overline{T}}_{cs0}^{f}(2818)$ and ${T}_{c\overline{s}0}^{a}(2828)$ classified in the quark model, respectively. It also allows us to extract the couplings for the initial tetraquark states to their nearby $S$-wave interaction channels. We find that some of these couplings turn out to be sizeable. Following the picture of the wave function renormalization for the near-threshold strong $S$-wave interactions, the sizeable coupling strengths can be regarded as an indication of their dynamic origins as candidates for hadronic molecules. Furthermore, our predictions suggest that signals for the $1S$-wave charmed-strange tetraquark states can also be searched in the other channels, such as ${D}^{0}{K}^{+}$, ${D}^{+}{K}^{+}$, ${D}^{*+}{K}^{\ensuremath{-}}$, ${D}^{*+}{K}^{+}$, ${D}^{*0}{K}^{+}$, ${D}^{0}{\overline{K}}^{*0}$, ${D}_{s}^{+}{\ensuremath{\rho}}^{0}$, etc.

Investigations of the semileptonic decays of D and $$D_s$$ into a pseudoscalar meson using the Isgur-Wise functions

The branching ratios of the semileptonic decay widths of the charm mesons are analyzed, using three different models for the Isgur-Wise functions, such as \({D^0} \rightarrow {K^ - }{l^ + }\upsilon\), \({D^0} \rightarrow {\pi ^ - }{l^ + }\nu\), \({D_s} \rightarrow {K^0}{l^ + }\nu\) and \({D_s} \rightarrow \eta {l^ + }\nu\), where the form factors of these decays are discussed. The mass spectra of the charm mesons are obtained. We use a potential quark model and consider the non-relativistic Hamiltonian of the charm meson as a bound state of the quark-antiquark system. We take into account the harmonic-type confinement and also Hellmann potential, which is a superposition of the Coulomb and the Yukawa potential. Using the variational approach along with the harmonic oscillator wave functions, we evaluate the mass spectra of the charm mesons, the form factors and the semileptonic decay widths of \(D_{(s)}\). We present our results for masses of \(D, D_s\) and \(\eta\), the Isgur-Wise functions, the form factors of the semileptonic decays, and the branching fractions of the semileptonic decays of D and \(D_s\). Our results are motivating.

The low-lying hidden- and double-charm tetraquark states in a constituent quark model with instanton-induced interaction

Spectrum of the low-lying hidden- and double-charm tetraquark states are investigated in a nonrelativistic quark potential model, where the instanton-induced interaction is taken as the residual spin-dependent hyperfine interaction between quarks. The model parameters are fixed by fitting the spectrum of the ground hadron states. Our numerical results show that masses of several presently studied tetraquark states are close to those of the experimentally observed candidates of exotic meson, which indicates that the corresponding compact tetraquark components may take considerable probabilities in those observed exotic states.

Higher mass spectra of the fully-charmed and fully-bottom tetraquarks

In this work, we calculate the higher mass spectra for the $2S$- and $1D$-wave fully-charmed and fully-bottom tetraquark states in a nonrelativistic potential quark model. The $2S$-wave fully-charmed/bottom tetraquark states lie in the mass range of $\ensuremath{\sim}(6.9,7.1)/(19.7,19.9)\text{ }\mathrm{GeV}$, apart from the highest ${0}^{++}$ state ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7185)/{T}_{(bb\overline{b}\overline{b}){0}^{++}}(19976)$. Most of the $2S$-wave states highly overlap with the high-lying $1P$-wave states. The masses for the $1D$-wave fully-charmed/bottom tetraquark states are predicted to be in the range of $\ensuremath{\sim}(6.7,7.2)/(19.5,20.0)\text{ }\text{ }\mathrm{GeV}$. The mass range for the $D$-wave tetraquark states cover most of the mass range of the $P$-wave states and the whole mass range of the $2S$-wave states. The narrow structure $X(6900)$ recently observed at LHCb in the di-$J/\ensuremath{\psi}$ invariant mass spectrum may be caused by the $1P$-, or $2S$-, or $1D$-wave ${T}_{(cc\overline{c}\overline{c})}$ states. The vague structure $X(7200)$ may be caused by the highest $2S$-wave state ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7185)$, two low-lying $3S$-wave states ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7240)$ and ${T}_{(cc\overline{c}\overline{c}){2}^{++}}(7248)$, and/or the high-lying $1D$-wave states with masses around 7.2 GeV and ${J}^{PC}={0}^{++},{1}^{++},{2}^{++},{3}^{++}$, or ${4}^{++}$. While it is apparent that the potential quark model calculations predict more states than the structures observed in the di-$J/\ensuremath{\psi}$ invariant mass spectrum, our calculations will help further understanding of the properties of these fully-heavy tetraquark states in their strong and magnetic interactions with open channels based on explicit quark model wave functions.

Heavy baryon spectrum with chiral multiplets of scalar and vector diquarks

Chiral effective theory of scalar and vector diquarks is formulated according to the linear sigma model. The main application is to describe the ground and excited states of singly heavy baryons with a charm or bottom quark. Applying the potential quark model between the diquark and the heavy quark ($Q=c, b$), we construct a heavy-quark--diquark model. The spectra of the positive- and negative-parity states of $\Lambda_Q$, $\Sigma_Q$, $\Xi^{(')}_Q$ and $\Omega_Q$ are obtained. The masses and interaction parameters of the effective theory are fixed partly from the lattice QCD data and also from fitting low-lying heavy baryon masses. We find that the negative parity excited states of $\Xi_Q$ (flavor $\bar{\bf 3}$) are different from those of $\Lambda_Q$, because of the inverse hierarchy of the pseudoscalar diquark. On the other hand, $\Sigma_Q, \Xi'_Q$ and $\Omega_Q$ (flavor ${\bf 6}$) baryons have similar spectra. We compare our results of the heavy-quark--diquark model with experimental data as well as the quark model.

A mixing coupling scheme for spectra of singly heavy baryons with spin-1 diquarks in P-waves

A new scheme of state classification is proposed and applied to analyze masses of the heavy baryons varOmega _{Q}, varSigma _{Q} and varXi _{Q}^{prime } in P-waves. The results confirm all excited varOmega _{c} and varOmega _{b} baryons reported recently by LHCb to be bound states of a P-wave ss-diquark and a respective charm or bottom quark, and thereby predict Regge trajectories for more excited varOmega _{c} and varOmega _{b} baryons. We suggest one excited J^{P}=5/2^{-}varOmega _{b} state to be unseen by LHCb around 6352 MeV, and predict P-wave masses of all spin-partners of the odd-parity baryons varSigma _{c}(2800)/varXi _{c}^{prime }(2942) and varSigma _{b}(6097)/varXi _{b}^{prime }(6227). A computation is further given in a relativized potential quark models to explain matched values of spin couplings of all considered baryons, by which a scaling law for these spin couplings is discussed.

Fully strange tetraquark sss¯s¯ spectrum and possible experimental evidence

In this work we construct 36 tetraquark configurations for the $1S$-, $1P$-, and $2S$-wave states, and make a prediction of the mass spectrum for the tetraquark $ss\bar{s}\bar{s}$ system in the framework of a nonrelativistic potential quark model without the diquark-antidiquark approximation. The model parameters are well determined by our previous study of the strangeonium spectrum. We find that the resonances $f_0(2200)$ and $f_2(2340)$ may favor the assignments of ground states $T_{(ss\bar{s}\bar{s})0^{++}}(2218)$ and $T_{(ss\bar{s}\bar{s})2^{++}}(2378)$, respectively, and the newly observed $X(2500)$ at BESIII may be a candidate of the lowest mass $1P$-wave $0^{-+}$ state $T_{(ss\bar{s}\bar{s})0^{-+}}(2481)$. Signals for the other $0^{++}$ ground state $T_{(ss\bar{s}\bar{s})0^{++}}(2440)$ may also have been observed in the $\phi\phi$ invariant mass spectrum in $J/\psi\to\gamma\phi\phi$ at BESIII. The masses of the $J^{PC}=1^{--}$ $T_{ss\bar{s}\bar{s}}$ states are predicted to be in the range of $\sim 2.44-2.99$ GeV, which indicates that the $\phi(2170)$ resonance may not be a good candidate of the $T_{ss\bar{s}\bar{s}}$ state. This study may provide a useful guidance for searching for the $T_{ss\bar{s}\bar{s}}$ states in experiments.

J/ψ-J/ψ scattering cross sections of quadratic and Cornell potentials

We study the scattering of - mesons using quadratic and Cornell potentials in our tetraquark ( ) system. The system’s wavefunction in the restricted gluonic basis, which is written by utilizing the adiabatic approximation and Hamiltonian, is used via a quark potential model. The resonating group technique is used to obtain the integral equations, which are solved to obtain the unknown inter-cluster dependence of the total wavefunction of our tetraquark system. T-Matrix elements are calculated from the solutions, and eventually, the scattering cross sections are obtained using the two potentials. We compare these cross sections and find that the magnitudes of scattering cross sections of quadratic potential are higher than the Cornell potential.

Mass spectrum and strong decays of strangeonium in a constituent quark model * *Supported by the National Natural Science Foundation of China (U1832173, 11775078, 11705056, 11405053)

In this work we calculate the mass spectrum of strangeonium up to the multiplet within a nonrelativistic linear potential quark model. Furthermore, using the obtained wave functions, we also evaluate the strong decays of the strangeonium states with the model. Based on our successful explanations of the well established states , , , , and , we further discuss the possible assignments of strangeonium-like states from experiments by combining our theoretical results with observations. It is found that some resonances, such as and , listed by the Particle Data Group, and and , newly observed by BESIII, may be interpreted as strangeonium states. The possibility of as a candidate for or cannot be excluded. We expect our results to provide useful references for looking for the missing states in future experiments.

Relativistic Friedrichs\u2013Lee model and quark-pair creation model

In this paper, we present how the Friedrichs–Lee model could be extended to the relativistic scenario and be combined with the relativistic quark pair creation model in a consistent way. This scheme could be applied to study the “unquenched” effect of the meson spectra. As an example, if the lowest J^{PC}=0^{++}(ubar{u}+dbar{d})/sqrt{2} bound state in the potential model is coupled to the pi pi continuum, two resonance poles could be found from the scattering amplitude for the continuum states. One of them could correspond to the f_0(500)/sigma and the other probably f_0(1370). This scheme might shed more light on why extra states could appear in the hadron spectrum other than the prediction of the quark potential model.

Dynamical mixing between 23S1 and 13D1 charmed mesons

In charmed $D$ and $D_s$ mesons sector, the matrix of a Hamiltonian in a quark potential model is computed in the $2^3S_1$ and $1^3D_1$ subspace. The masses of four mixed states of $2^3S_1$ and $1^3D_1$ denoted with $D^*_1(2635)$, $D^*_1(2739)$, $D^*_{s1}(2715)$ and $D^*_{s1}(2805)$ are obtained. It is an off-diagonal part of the spin-orbit tensor interaction that causes the mixing between the $2^3S_1$ and $1^3D_1$ states. The mixing angles between the $2^3S_1$ and $1^3D_1$ states are tiny. Under the mixing, a $^3P_0$ model is employed to compute the hadronic decay widths of all OZI-allowed decay channels of the four mixed states. The two light mixed states $D^*_1(2635)$ and $D^*_{s1}(2715)$ are close in mass to $D^*_J(2600)$ and $D^*_{s1}(2700)$, while the two heavy mixed states $D^*_1(2739)$ and $D^*_{s1}(2805)$ are lighter in mass than $D(2750)$ and $D^*_{s1}(2860)$. The mixing angles obtained from dynamical interaction are inconsistent with the mixing angles obtained from hadronic decay. Based on mass spectra and hadronic decay analyses, $D^*_J(2600)$, $D(2750)$, $D^*_{s1}(2700)$ and $D^*_{s1}(2860)$ are impossibly the mixed states of $2^3S_1$ and $1^3D_1$ at the small mixing angles. The inconsistence implies that $D^*_1(2760)$ and $D^*_{s1}(2860)$ have not been properly resolved from present experimental data, or there exist large unknown off-diagonal interactions that result in large mixing angles.

Radiative decays in charmonium beyond the p/m approximation

We analyze the theoretical description of radiative decays in charmonium. We use an elementary emission decay model to build the most general electromagnetic transition operator. We show that accurate results for the widths can be obtained from a simple quark potential model reasonably fitting the spectroscopy if the complete form of the operator is used instead of its standard p/m approximation and the experimental masses are properly implemented in the calculation.

Bottomonium spectrum in the relativistic flux tube model

The bottomonium spectrum is far from being established. The structures of higher vector states, including the $\Upsilon(10580)$, $\Upsilon(10860)$, and $\Upsilon(11020)$ states, are still in dispute. In addition, whether the $\Upsilon(10750)$ signal which was recently observed by the Belle Collaboration is a normal $b\bar{b}$ state or not should be examined. Faced with such a situation, we carried out a systematic investigation of the bottomonium spectrum in the scheme of the relativistic flux tube (RFT) model. A Chew-Frautschi like formula was derived analytically for the spin average mass of bottomonium states. We further incorporated the spin-dependent interactions and obtained a complete bottomonium spectrum. We found that the most established bottomonium states can be explained in the RFT scheme. The $\Upsilon(10750)$, $\Upsilon(10860)$, and $\Upsilon(11020)$ could be predominantly the $3^3D_1$, $5^3S_1$, and $4^3D_1$ states, respectively. Our predicted masses of $1F$ and $1G$ $b\bar{b}$ states are in agreement with the results given by the method of lattice QCD, which can be tested by experiments in future. We also compared the RFT model with the quark potential model in detail. The differences of these two kinds of models were discussed.

Quark Models of the Nucleon–Nucleon Interaction

The present chapter aims to provide a review on the relevance of quark degrees of freedom in the description of the nucleon-nucleon and, in general, of the baryon-baryon interaction. After an historical introduction, the second section of the chapter will be dedicated to the first attempts to describe the short-range part of the NN potential in the so-called quark potential models. Here the importance of the symmetries of the 6-quark system will be emphasized. Then, we will discuss the concept of the constituent quark mass as originated by the breakdown of the chiral symmetry, in line with the articles of ~\citep{MANOHAR1984189} and the Instanton Liquid Model of ~\citep{Diakonov:2002fq}, and its consequences on the quark-quark interaction due to the presence of the Goldstone boson exchanges. Once the full quark-quark interaction is established, the description of the bound states (deuteron), the scattering states of the NN system and nuclear matter in constituent quark models will be addressed. In this part a discussion of the influence of $N\Delta$, $\Delta\Delta$ or $NN^*$ components will be included. The rest of the chapter will be devoted to the extension of the model to other baryon-baryon system, namely the triton, hyperon-hyperon and nucleon-antinucleon systems, and references to other possible descriptions of the NN interaction in terms of quark degrees of freedom ( bag models). The chapter will end with a conclusion remarks where the success and limitations of the model described above will be summarized.

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.

Properties of excited charmed-bottom mesons

We calculate the spectrum of $B_c$ mesons using a non-relativistic quark potential model. Using the calculated wave functions, we compute the radiative widths of $B_c$ excited states. The strong decay widths are calculated in a modified $^3P_0$ model, assuming harmonic oscillator wave functions. The hadronic transition rates of $B_c$ mesons are calculated using the Kuang-Yan approach. These results are used to determine branching ratios of possible decay channels of several $B_c$ excited states. Calculated branching ratios are then combined with production cross section of $B_c$ states at the LHC to suggest strategies to find missing excited states of $B_c$ mesons.

Compact [formula omitted] pentaquark states predicted by a quark model

Several compact ssscc¯ pentaquark resonances are predicted in a potential quark model. The Hamiltonian is the best available one, which reproduces the masses of the low-lying charmed and strange hadrons well. Full five-body calculations are carried out by the use of the Gaussian expansion method, and the relevant baryon-meson thresholds are taken into account explicitly. Employing the real scaling method, we predict four sharp resonances, JP=1/2− (E=5180 MeV, Γ=20 MeV), 5/2− (5645 MeV, 30 MeV), 5/2− (5670 MeV, 50 MeV), and 1/2+ (5360 MeV, 80 MeV). These are the candidates of compact pentaquark resonance states from the current best quark model, which should be confirmed either by experiments or lattice QCD calculations.