Nonrelativistic Quark Model Research Articles

Higher fully charmed tetraquarks: Radial excitations and P -wave states

We systematically calculate the mass spectrum of the higher excited fully-charmed tetraquark $cc\bar c\bar c$ states including the S-wave radial excitations and the P-wave states with a nonrelativistic quark model. The quark model is composed of a vector one-gluon-exchange (OGE) and a scalar linear confinement interaction with the parameters determined by the charmonium spectrum. In the calculation, we consider both the $3_c-\bar 3_c$ and the $6_c-\bar{6}_c$ color representations. For the $cc\bar c\bar c $ state, the $6_c-\bar 6_c$ component is located lower than the $\bar 3_c-3_c$ one because of the stronger attractive interactions between the diquark and antidiquark. We focus on two excited modes and their properties for the P-wave tetraquarks. The mass splitting for the $\rho$-mode excitations with different color configurations is large. The low-lying $6_c-\bar 6_c$ $\rho$-mode component helps to explain the small mass gap between the ground S-wave and the P-wave tetraquark states. The recently observed $X(6900)$ state may be the candidate of the first radially excited tetraquarks with $J^{PC}=0^{++}$ or $2^{++}$, or the $1^{+-}$ or $2^{-+}$ P-wave states based on the mass spectrum. Moreover, the lowest $T_c$ states with the exotic $J^{PC}$ quantum numbers $0^{--}$ and $1^{-+}$ may decay into the P-wave $\eta_c J/\psi$ and di-$J/\psi$ modes, respectively. The future experimental search of these $T_c$ states will enrich the hadronic spectrum.

Non-relativistic quark model under external magnetic and Aharanov–Bohm (AB) fields in the presence of temperature-dependent confined Cornell potential

The dissociation of quarkonia in a thermal QCD medium in the background of Aharanov–Bohm (AB) and strong magnetic fields was investigated. For this purpose, the Schrödinger equation with charged quarkonium in the Cornell potential under the influence of the AB flux and an external magnetic fields directed along the z-axis was employed. Using the Nikiforov–Uvarov (NU) method, the energy eigenvalue was obtained. The effects of temperature, AB flux, and external magnetic field were studied. The study shows that the dissociation energies of the 1S states of charmonium and bottomonium decrease with increasing temperature, AB flux, and external magnetic field. In addition, the quarkonium melts faster in a hot medium in the presence of an AB flux and an external magnetic field. We found that charmonium melts at 13.79 [Formula: see text] and bottomonium melts at 99.48 [Formula: see text]. A comparison was conducted with other studies. Thus, the present non-relativistic model provides satisfactory results for the dissociation binding energy in a hot medium when the AB flux and external magnetic fields are included.

Doubly heavy tetraquarks, qq′Q¯Q′¯ , in a nonrelativistic quark model with a complete set of harmonic oscillator bases

We improve our previous variational method based nonrelativistic quark model by introducing a complete set of three-dimensional harmonic oscillator bases as the spatial part of the total wave function. To assess the validity of our approach, we compare the binding energy thus calculated with the exact value for the hydrogen model. After fitting to the masses of the ground state hadrons, we apply our new method to analyzing the doubly heavy tetraquark states $q{q}^{\ensuremath{'}}\overline{Q}\overline{{Q}^{\ensuremath{'}}}$ and compare the results for the binding energies to results in other works. We also calculate the ground state masses of ${T}_{sc}(ud\overline{s}\overline{c})$ and ${T}_{sb}(ud\overline{s}\overline{b})$ with $(I,S)=(0,1),(0,2)$. We find that ${T}_{bb}(ud\overline{b}\overline{b})$ and $us\overline{b}\overline{b}$, both with $(I,S)=(0,1)$, are stable against the two lowest threshold meson states with binding energies $\ensuremath{-}145$ and $\ensuremath{-}42\text{ }\text{ }\mathrm{MeV}$, respectively. We further find that ${T}_{cb}(ud\overline{c}\overline{b})$ is near the lowest threshold. The spatial sizes for the tetraquarks are also discussed.

Quark Model Analysis of the Weinberg Operator Contribution to the Nucleon EDM

The Weinberg operator (chromo-electric dipole moment of gluon) is a CP violating quantity generated in many candidates of new physics beyond the standard model, and it contributes to observables such as the electric dipole moments (EDM) of the neutron or atoms which are currently measured in experiments. In this proceedings contribution, we report on our result of the evaluation of the Weinberg operator contribution to the nucleon EDM in the nonrelativistic quark model using the Gaussian expansion method.

The Genuine Resonance of Full-Charm Tetraquarks

In this work, the genuine resonance states of full-charm tetraquark systems with quantum numbers JPC=0++,1+−,2++ are searched in a nonrelativistic chiral quark model with the help of the Gaussian Expansion Method. In this calculation, two structures, meson-meson and diquark–antidiquark, as well as their mixing with all possible color-spin configurations, are considered. The results show that no bound states can be formed. However, resonances are possible because of the color structure. The genuine resonances are identified by the stabilization method (real scaling method). Several resonances for the full-charm system are proposed, and some of them are reasonable candidates for the full-charm states recently reported by LHCb.

Relativistic corrections to decays of heavy baryons in the quark model

We investigate relativistic corrections of an order $1/{m}^{2}$, where $m$ is the constituent quark mass, to heavy baryon decays by emitting one pseudoscalar meson in the quark model. This work is motivated by shortcomings in the previous studies in the nonrelativistic quark model for decays of the Roper-like states, such as ${\mathrm{\ensuremath{\Lambda}}}_{c}(2765)$. We find that the relativistic corrections due to the internal motion of quarks are essential ingredients in improving their decay properties, such that the decay widths are significantly increased. In addition, such corrections can explain a phenomenological suppression of the quark axial-vector coupling constant ${g}_{A}^{q}$ for the ${\mathrm{\ensuremath{\Sigma}}}_{c}(2455)$ and ${\mathrm{\ensuremath{\Sigma}}}_{c}(2520)$ decays.

Magnetic Moments and Decay Rates for Double Heavy Baryons in the Non-Relativistic Quark Model

Magnetic Moments and Decay Rates for Double Heavy Baryons in the Non-Relativistic Quark Model

Effect of relativistic kinematics on the stability of multiquarks

We discuss whether the bound nature of multiquark states in quark models could benefit from relativistic effects on the kinetic energy operator. For mesons and baryons, relativistic corrections to the kinetic energy lead to lower energies, and thus call for a retuning of the parameters of the model. For multiquark states, as well as their respective thresholds, a comparison is made of the results obtained with non-relativistic and relativistic kinetic energy. It is found that the binding energy is lower in the relativistic case. In particular, $QQ\bar q\bar q$ tetraquarks with double heavy flavor become stable for a larger ratio of the heavy to light quark masses; and the all-heavy tetraquarks $QQ\bar Q\bar Q$ that are not stable in standard non-relativistic quark models remain unstable when a relativistic form of kinetic energy is adopted

Weinberg operator contribution to the nucleon electric dipole moment in the quark model

We evaluate the contribution of the CP violating gluon chromo-electric dipole moment (the so-called Weinberg operator, denoted as $w$) to the electric dipole moment (EDM) of nucleons in the nonrelativistic quark model. The CP-odd interquark potential is modeled by the perturbative one-loop level gluon exchange generated by the Weinberg operator with massive quarks and gluons. The nucleon EDM is obtained by solving the nonrelativistic Schr\"{o}dinger equation of the three-quark system using the Gaussian expansion method. It is found that the resulting nucleon EDM, which may reasonably be considered as the irreducible contribution, is smaller than the one obtained after $\gamma_5$-rotating the anomalous magnetic moment using the CP-odd mass calculated with QCD sum rules. We estimate the total contribution to be $d_n = w \times 20 \, e \, {\rm MeV}$ and $d_p = - w \times 18 \, e \, {\rm MeV}$ with 60% of theoretical uncertainty.

Form factors of the nucleon axial current

A symmetry-preserving Poincaré-covariant quark+diquark Faddeev equation treatment of the nucleon is used to deliver parameter-free predictions for the nucleon's axial and induced pseudoscalar form factors, GA and GP, respectively. The result for GA can reliably be represented by a dipole form factor characterised by an axial charge gA=GA(0)=1.25(3) and a mass-scale MA=1.23(3)mN, where mN is the nucleon mass; and regarding GP, the induced pseudoscalar charge gp⁎=8.80(23), the ratio gp⁎/gA=7.04(22), and the pion pole dominance Ansatz is found to provide a reliable estimate of the directly computed result. The ratio of flavour-separated quark axial charges is also calculated: gAd/gAu=−0.16(2). This value expresses a marked suppression of the size of the d-quark component relative to that found in nonrelativistic quark models and owes to the presence of strong diquark correlations in the nucleon Faddeev wave function – both scalar and axial-vector, with the scalar diquark being dominant. The predicted form for GA should provide a sound foundation for analyses of the neutrino-nucleus and antineutrino-nucleus cross-sections that are relevant to modern accelerator neutrino experiments.

Investigation of multi-quark systems

In this study, the researcher decided to study Tetraquark and Pentaquark systems. We introduce the Pentaquark system as a meson-baryon system and Tetraquark as a diquark-antidiquark system. A diquark consists of two quarks. The interaction potential between these particles is considered as a combination of two color charge potentials and the confinement potential is considered as harmonic and linear sentences. Solve the Schrodinger equation by considering the effects of spin-spin, isospin- isospin, spin-isospin, and then obtain the mass of the diquark and the heavy tetraquuarks with charm quarks and bottom. These calculations are calculated using the approach of diquark - antidiquark within the framework of the non-relativistic quark model. In the following, we calculate the mass of Pentaquark systems in the same way.

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.

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.

Decay Properties of Conventional and Hybrid $$\boldsymbol{B}_{\boldsymbol{c}}$$ Mesons

Spectrum, radial wave functions at origin, decay constants, weak decay widths, life-time, and branching ratios for radially excited conventional and hybrid $$B_{c}$$ mesons are derived within non-relativistic quark model framework employing Schrodinger equation by shooting method. Calculated results are compared with available theoretical results and experimental observations. This work may help in identifying the new discovered $$B_{c}$$ meson states at CDF, LHCb, and ATLAS.

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.

NLO QCD corrections to heavy baryon fragmentation functions through quark-diquark model

At very high transverse momenta, the dominant mechanism for heavy hadron production is fragmentation. In this work, we first use the nonrelativistic quark model to compute the heavy baryon fragmentation functions at lowest order of perturbative QCD and then we apply the approximative quark-diquark model for the same fragmentation process. Diquark model enables one to analyze the two-stage fragmentation of a heavy quark into a heavy diquark followed by the fragmentation of produced diquark into outgoing heavy baryon. An acceptable agreement is found between the results obtained through both approaches. Relying on the diquark model, we extend our computation to next-to-leading order accuracy at perturbative QCD.

Comment on “The effect of spin and tensor interactions on heavy-light mesons in the nonrelativistic quark model” by M. Abu-Shadya and Sh. Y. Ezz-Alarab

We analyze the solution of the Schrodinger equation with a quark–antiquark potential obtained in a paper published recently in this journal. The authors derived their results in a rather arbitrary way from an ansatz that is not square integrable and used them to fit experimental data.

Properties of $$\boldsymbol{B}_{\boldsymbol{c}}$$ Mesons and Variational Constraints on Their Masses

Spectrum, radii, radial wave functions at origin, decay constants and momentum widths for radial and orbital excited $B_c$ mesons are derived within non-relativistic quark model framework through finding numerical solution of the Schrodinger equation by shooting method. Masses of orbitally excited states are derived with a more simpler method that is developed by combining the uncertainty and variational principles. Masses of $B_c$ mesons are also calculated by using Momentum widths. Besides calculations, theoretical results are compared with the experimental observations which have implications for scalar form factors and leptonic decays of $B_c$ mesons.

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.

Mass and decay properties of double heavy baryons with a phenomenological potential model

We consider baryons in a nonrelativistic quark model, find the wave function and masses of the baryons with two heavy quarks including Xi _{bc}(bcu), Xi _{cc}(ccu), Xi _{bb}(bbu), Omega _{bb}(bbs), Omega _{bc}(bcs) and {Omega _{cc}}(ccs). We calculate magnetic moments of these baryons. Using transition magnetic moments, we obtain the radiative decay widths for double heavy baryons. Then we calculate some of the semileptonic decay widths of these baryons. Our results are compared with other theoretical predictions.