Nonrelativistic Quark Potential Model Research Articles

Mass spectra of doubly charmed tetraquarks Tcc

Motivated by the first observation, to the best of our knowledge, of a doubly charmed tetraquark candidate Tcc(3875)+, we perform a systematic calculation of the masses of some constituent diquarks and the doubly charmed tetraquark states from 1S to 2P excitations in a nonrelativistic constituent quark potential model. First, the mass of the charmed spin-1 diquark is predicted with ∼3500 MeV, and the masses of the light “good” (spin-0 and isospin-0) and “bad” (spin-1 and isospin-1) antidiquark are predicted with ∼670 MeV and ∼840 MeV, respectively. The mass difference between a light good and a light bad diquark is ∼170 MeV, which is consistent with previous phenomenological analyses. The interaction between the charmed diquark and the light antidiquark is then modulated by the quark-antiquark potential in the model, and the mass spectra of doubly charmed tetraquarks from 1S to 2P excitations are calculated with the obtained masses of diquarks/antidiquarks and refitted parameters from Tcc(3875)+ and X(3872). The pattern of the mass spectra of doubly charmed tetraquarks is obtained explicitly. The 1S−1P and 1S−2S mass splittings of doubly charmed tetraquarks are about 410–430 MeV and 610–650 MeV, respectively, and this mass splittings pattern is similar to that for ordinary D mesons. The mass splittings of doubly charmed tetraquarks with a good diquark is about 10–25 MeV higher than the corresponding mass splittings of doubly charmed tetraquarks with a bad diquark from 1S to 2P excitations. When Tcc(3875)+ is assumed as a IJP=01+ ground doubly charmed tetraquark with a light good antidiquark, the next P-wave excited doubly charmed tetraquarks are predicted to have masses with an average 420–430 MeV higher. A IJP=10+ ground doubly charmed tetraquark Tcc(3834) located around 3834 MeV is also expected. Published by the American Physical Society 2025

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.

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.

The light and strange baryon spectrum in a non-relativistic hypercentral quark potential model and algebraic framework

In this paper, we studied the baryon resonances spectrum within a non-relativistically quark model using a simple approach based on the Gursey-Radicati mass formula (GR). The average energy value of each SU(6) multiplet is described using the SU(6) invariant interaction given by a hypercentral potential. In this paper the hypercentral potential is composed of four components: the oscillatory potential, color charge, the intraction quark and neutral gluon and the dipole-dipole electromagnetic interaction. The results of our model (the combination of our proposed hypercentral potential and the generalized GR mass formula to the description of the spectrum) show that the light and strange baryons spectrum are in general fairly well reproduced. The overall good description of the spectrum which we obtain shows that our model can also be used to give a fair description of the energies of the excited multiplets with more than 2GeV mass and negative-parity resonance.

Characteristics of charged pions in the quark model with potential which is the sum of the Coulomb and oscillator potential

In this paper, we calculate the polarizability of the charged pions in the nonrelativistic quark potential model.

Molecular and compact four-quark states

We study charmonium (cc̄nn̄), bottomonium (bb̄nn̄) and exotic (ccn̄n̄ and bbn̄n̄) four-quark states by means of a standard non-relativistic quark potential model. We look for possible bound states. Among them we are able to distinguish between meson-meson molecules and compact four-quark states.

Radiative decays of single heavy flavour baryons

The electromagnetic transitions between ( J P = $ {\frac{{3}}{{2}}}$ + and ( J P = $ {\frac{{1}}{{2}}}$ + baryons are important decay modes to observe new hadronic states experimentally. For the estimation of these transitions widths, we employ a non-relativistic quark potential model description with color Coulomb plus linear confinement potential. Such a description has been employed to compute the ground-state masses and magnetic moments of the single heavy flavor baryons. The magnetic moments of the baryons are obtained using the spin-flavor structure of the constituting quark composition of the baryon. Here, we also define an effective constituent mass of the quarks (ecqm) by taking into account the binding effects of the quarks within the baryon. The radiative transition widths are computed in terms of the magnetic moments of the baryon and the photon energy. Our results are compared with other theoretical models.

Testing the constituent quark model in KN scattering

The kaon–nucleon S, P, D, F, G waves phase shifts have been calculated using a non-relativistic quark potential model and the resonating group method (RGM). The calculation has been performed using quark–quark potential which both includes gluon, pion and sigma exchanges and reproduces as well as possible the meson spectrum. The agreement obtained with the existing experimental phase shifts is quite poor. The results are also compared with a previous calculation based only on gluon exchanges at the quark level.

Kaon–nucleon and D–nucleon scattering in the quark model, including spin–orbit interactions

Interactions of charmed and strange mesons with baryonic matter can be calculated in the nonrelativistic quark potential model. For KN scattering data exist, and the theoretical results for S-waves are in approximate agreement with experiment. Here we apply the same model to the scattering of open-charm (D) mesons by nucleons, and give quark model predictions for DN scattering amplitudes. Spin–orbit forces in KN and DN will also be discussed.

S, P, D, F, G-waves KN phase shifts in a constituent quark model with a spin–orbit interaction

The I=1 and I=0 kaon–nucleon s, p, d, f, g-waves phase shifts have been calculated in a nonrelativistic quark potential model using the resonating group method (RGM). The interquark potential includes gluon exchanges with a spin–orbit interaction. This force has been determined to reproduce as well as possible the meson and baryon spectra. The same force is employed for the cluster and intercluster dynamics and the relative KN wave-function is calculated without any approximation. While some channels are correctly described, the theory is still unable to explain others.

Hadronic molecules and scattering amplitudes from the nonrelativistic quark model

This report summarizes recent calculations of low-energy hadron-hadron scattering amplitudes in the nonrelativistic quark potential model, which assume that the scattering mechanism is a single interaction (usually OGE) followed by constituent interchange. We refer to the scattering diagrams as «quark Born diagrams». For the cases chosen to isolate this mechanism,I=2ππ,I=3/2 Kπ, KN andNN, the results are usually in good agreement with experimentalS-wave scattering amplitudes given standard potential- model parameters. These calculations also lead to predictions of vector-vector bound states, one of which may be the ϑ(1710). This assignment can be tested by searches for $$K\bar K\pi \pi $$ and φπ0γ decay modes of the ϑ(1710).

Radiative decays of S-wave charmed baryons

We calculated radiative decay widths of possible radiative transitions between S-wave charmed baryons in naive static quark model and in non-relativistic quark potential model. The results obtained in these two approaches are in a fair agreement. We predict the following life time for Ωc+ and ξc′ baryons: τ(Ωc+) ≈ 10−18 s, τ(Ξc′) ≈ 10−19s.

I=3/2 K pi scattering in the nonrelativistic quark potential model.

We study $I=3/2$ elastic $K\pi $ scattering to Born order using nonrelativistic quark wavefunctions in a constituent-exchange model. This channel is ideal for the study of nonresonant meson-meson scattering amplitudes since s-channel resonances do not contribute significantly. Standard quark model parameters yield good agreement with the measured S- and P-wave phase shifts and with PCAC calculations of the scattering length. The P-wave phase shift is especially interesting because it is nonzero solely due to $SU(3)_f$ symmetry breaking effects, and is found to be in good agreement with experiment given conventional values for the strange and nonstrange constituent quark masses.

Diagrammatic approach to meson-meson scattering in the nonrelativistic quark potential model.

In this paper we use Born-order quark-exchange diagrams in a nonrelativistic potential model to describe low-energy scattering of $q\overline{q}$ mesons. A formalism for evaluating quark Born diagrams is developed, and as a first application we consider meson-meson scattering in channels in which $q\overline{q}$ annihilation is thought to be unimportant. In particular our results are relevant to $I=2 \ensuremath{\pi}\ensuremath{\pi}$ and $I=1 \mathrm{KK}$ elastic scattering. Simple rules for the Born diagrams are given, which allow the evaluation of scattering amplitudes in terms of external meson wave functions by inspection. These techniques are applied to systems having identical quarks, and ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}$, ${K}^{+}{K}^{+}$, and ${\ensuremath{\rho}}^{+}{\ensuremath{\rho}}^{+}$ elastic scattering phase shifts, cross sections, and equivalent potentials are derived as examples. The $S$-wave $I=2 \ensuremath{\pi}\ensuremath{\pi}$ phase shift for a Gaussian $q\overline{q}$ wave function with conventional quark model parameters ${\ensuremath{\alpha}}_{s}$, ${m}_{q}$, and ${\ensuremath{\beta}}_{\mathrm{SHO}}$ is found to be in good agreement with experiment and with Weinberg's PCAC (partial conservation of axial-vector current) result. At higher energies the predicted differential cross sections have the characteristic diffractive features of an exponential $t$ peak at small angles and vacuum quantum number exchange. The phase of the predicted amplitude however differs from the experimental diffractive amplitude, so these quark Born diagrams cannot be directly identified with the Pomeron of diffractive scattering phenomenology.

Charge effects in meson-nucleon coupling constants

Several quark models of charge effects in meson-nucleon coupling constants are reviewed. The emission of a meson by the electromagnetic (e.m.) interaction is calculated in a nonrelativistic quark potential model. Existing inaccuracies and errors in the perturbative calculation of the charge-independent coupling constants and of effects of the u-d mass difference in this model are corrected. We find that both e.m. and quark-mass difference effects are small, being of the order of 0.1–0.3%, except for a charge-independence breaking contribution of −1.7% from the meson mass appearing in a boson normalization factor. The perturbative one-gluon-exchange contribution to the charge-independent coupling constant is found to account for only about 60% of the magnitude of empirical coupling constants, thus indicating a need for additional mechanisms for meson emission.

To the description of hadron mass spectrum in the nonrelativistic quark potential model

The comparison of different confinement models of hadrons in non-relativistic quark potential model with the use of hyperspherical functions is carried out in the present work. Numerical values of the masses of non-strange (the lightest) hadrons belonging to the meson octet and baryon decuplet are obtained in this model. The best values of masses are obtained with the potential which incorporates the quasi-relativistic one-gluon exchange and the confinement termArn withn=2/3. The natural appearance of the Yukawa-type potential in this model is also discussed.

Criterion for a unique non-relativistic quark model

We have calculated the mean square charge radii of the neutron and proton, and compared them with the experimental values, to construct a unique non-relativistic quark potential model. It is shown for the first time that, contrary to general belief, it is possible to reproduce simultaneously the baryon mass spectrum and the electromagnetic sizes of neutron and proton using a single potential model. It was found necessary to add admixtures of excited states of the nucleon in the unperturbed ground state wavefunctions.

Consequences of a description of the nucleon and delta spectra in terms of a non-relativistic quark-potential model with oscillator variational states

General conditions are derived for matrix elements of a quark-confining potential that is assumed to yield the nucleon and delta spectra with oscillator variational states. Parameters are given for a particular functional form for the confining potential under various fitting criteria to the baryon spectra; this form is to be used in subsequent calculations of the nuclear force.