Chiral Quark Model Research Articles

Dynamical study of $T_{ss}$ systems at a chiral quark model

Abstract Since the discovery of $T_{cc}$ by LHCb, there has been considerable interest in $T_{cc}$ and its heavy-flavor partners. However, the study of its strange partner $T_{ss}$ has been largely overlooked. Within the framework of the chiral quark model, we conducted a systematic study of the bound states of $T_{ss}$ utilizing the Gaussian Expansion Method. Considering all physical channels with $01^{+}$, including molecular and diquark structures. Our calculations revealed that upon considering the coupling between diquarks and molecular states, we identified a deep bound state with a bounding energy of 60 MeV, primarily composed of $K K^{*}$. Using the $^3P_0$ model, we calculated the decay width of $K^{*}$ within the $KK^{*}$ bound state, which is approximated as the decay width of the bound state in the $T_{ss}$ system. The results indicate that due to the effect of binding energy, the decay width of $K^{*}$ in $KK^{*}$ is approximately $3$ MeV smaller than that of $K^{*}$ in vacuum. Additionally, resonance state calculations were performed. Utilizing the real-scaling method, we searched for possible resonance states in the $T_{ss}$ sysytem. Due to the strong attraction in the $[K^{*}]_8[K^{*}]_8$ configuration, four resonance states were found in the vicinity of $2.2$-$2.8$ GeV, predominantly featuring hidden-color structures, and their decay widths are all less than $10$ MeV. We strongly recommend experimental efforts to search for the resonance states in the $T_{ss}$ system predicted by our calculations.

Dynamical study of D*DK and D*DD¯ systems at quark level

Inspired by the recent report from the LHCb Collaboration on Tcc, which can be interpreted as a molecular DD*, we investigated two trimeson systems of the Tcc partner with IJP=01− in the framework of a chiral quark model. In the first case, because of the attraction between D* and D¯, we explored the existence of bound states in the system D*DD¯, which is obtained by adding D¯ into the molecular bound state Tcc (DD*). Similarly, in the second case, we explored whether there is a bound state in the D*DK system, which is obtained by adding K into the Tcc, given the attraction between D and K. The results show that both of them are bound states, in which the binding energy of the molecular state DD*K is relatively small, only 0.4±0.4 MeV, while the binding energy of DD*D¯ is up to 1.6±0.3 MeV. According to the calculation results of the root-square-mean distances, the spatial structure of the two systems shows the obvious (DD*)−(D¯/K) structure, in which D is close to D* while DD* as a whole is relatively distant from the third hadron (D¯/K), which are similar to the nucleon-electron structure. As a result, we strongly recommend that these bound states DD*D¯ and DD*K are searched for experimentally. Published by the American Physical Society 2024

Exotic Qqq¯q¯ states in the chiral quark model

In the framework of the chiral quark model, we investigate the Qqq¯q¯ (Q=c, b and q=u, d) tetraquark system with two structures: Qq¯−qq¯ and Qq−q¯q¯. The bound-state calculation shows that for the single channel, there is no evidence for any bound state below the minimum threshold in both cqq¯q¯ and bqq¯q¯ systems. However, after coupling all channels of two structures, we obtain a bound state below the minimum threshold in the cqq¯q¯ system with the energy of 1998 MeV, and the quantum number is IJP=120+. Meanwhile, in the bqq¯q¯ system, two bound states with energies of 5414 MeV and 5456 MeV are obtained, and the quantum numbers are IJP=120+ and IJP=121+, respectively. Besides, we also employ the real-scaling method to search for resonance states in the cqq¯q¯ and bqq¯q¯ systems. Unfortunately, no genuine resonance states were obtained in both systems. We suggest future experiments to search for these three possible bound states. Published by the American Physical Society 2024

Equivalence among color-singlet, color-octet, and diquark structures in a chiral quark model

Since the quark model was put forward, theoretical researchers have always attached great importance to the study of hidden color channels (including color octets and diquark structure). Because of the influence of color van der Waals forces, the hidden color channel itself has strong attraction, which provides a dynamic mechanism for the formation of a resonance state or bound state. In this paper, taking the Tcc system as an example, under the framework of the Gaussian expansion method, a set of relatively complete color singlets (that is, the ground state of the color singlet plus its corresponding higher-order component) is used to replace the contribution of the color octet. Similarly, we endeavor to replace the diquark structure with a relatively complete set of molecular states, encompassing both the ground state and excited states. Our results demonstrate that the color-octet structure can be effectively replaced by a set of relatively complete color-singlet bases, while the diquark structure cannot be entirely substituted by an equivalently comprehensive set of molecular state bases. Published by the American Physical Society 2024

The tetraquark system in a chiral quark model* *Partially supported by the National Natural Science Foundation of China (12305093, 11535005, 11775118), the Natural Science Foundation of Zhejiang Province, China(LQ22A050004), the Ministerio Español de Ciencia e Innovación (PID2019-107844GB-C22, PID2022-140440NB-C22), the Junta de Andalucía under contract Nos. Operativo FEDER Andalucía (2014-2020 UHU-1264517, P18-FR-5057 and also PAIDI FQM-370)

The S-wave tetraquarks, with spin-parities , , and , in both isoscalar and isovector sectors, are systematically studied using a chiral quark model. The meson-meson, diquark-antidiquark, and K-type arrangements of quarks and all possible color wave functions are comprehensively considered. The four-body system is solved using the Gaussian expansion method, a highly efficient computational approach. Additonally, a complex-scaling formulation of the problem is established to disentangle bound, resonance, and scattering states. This theoretical framework has already been successfully applied in various tetra- and penta-quark systems. For the complete coupled channel and within the complex-range formulation, several narrow resonances of and systems are obtained, in each allowed -channel, within the energy regions of GeV and GeV, respectively. The predicted exotic states, which indicate a richer color structure when going towards multiquark systems beyond mesons and baryons, are expected to be confirmed in future high-energy particle and nuclear experiments.

Doubly heavy tetraquark states in the constituent quark model using diffusion Monte Carlo method

We use the diffusion Monte Carlo (DMC) method to calculate the doubly heavy tetraquark Tcc system in two kinds of constituent quark models, the pure constituent quark model AL1/AP1 and the chiral constituent quark model. When the discrete configurations are complete and no spatial clustering is predetermined, the AL1/AP1 model gives an energy of Tcc close to the DD* threshold, and the chiral constituent quark model yields a deeply bound state. We further calculate all doubly heavy tetraquark systems with JP=0+,1+,2+, and provide the binding energies of systems with bound states. The I(JP)=0(0+) bcn¯n¯, 0(1+) bbn¯n¯, 0(1+) bcn¯n¯, 12(1+) bbs¯n¯ systems have bound states in all three models. Since the DMC method has almost no restriction on the spatial part, the resulting bound states have greater binding energies than those obtained in previous works. Published by the American Physical Society 2024

Updated analyses of gluon distribution functions for the pion and kaon from the gauge-invariant nonlocal chiral quark model

In this work, we investigate the gluon distribution functions for the pion and kaon, in addition to the improved result of the valence-quark ones, in the gauge-invariant nonlocal chiral-quark model, in which the momentum dependence of the quark interactions is properly taken into account. We then analyze the gluon distribution functions, generated dynamically through the splitting functions in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi QCD evolution. By comparing with the recent lattice QCD results and Jefferson Lab angular momentum global analyses, it is found that the present numerical results for the gluon parton distribution functions for the pion exhibit a good agreement and the valence up-quark distribution results for the pion by reproducing the reanalyzed experimental data with a remarkable agreement. Our prediction on the gluon distribution functions for the kaon is also consistent with the recent lattice data for the kaon within the errors. Published by the American Physical Society 2024

Hidden-Charm Pentaquarks with Strangeness in a Chiral Quark Model

The LHCb collaboration has recently announced the discovery of two hidden-charm pentaquark states with strange quark content, Pcs(4338) and Pcs(4459); its analysis points towards having both hadrons’ isospins equal to zero and spin-parity quantum numbers 12− and 32−, respectively. Herein, we perform a systematical investigation of the qqscc¯(q=u,d) system by means of a chiral quark model, along with a highly accurate computational method, the Gaussian expansion approach combined with the complex scaling technique. baryon-meson configurations in both singlet- and hidden-color channels are considered. The Pcs(4338) and Pcs(4459) signals can be well identified as molecular bound states with dominant components ΛJ/ψ(60%) and ΞcD(23%) for the lowest-energy case and ΞcD∗(72%) for the highest-energy one. In addition, it seems that some narrow resonances can also be found in each allowed I(JP) channel in the energy region of 4.6–5.5 GeV, except for the 1(12−) channel where a shallow bound state with dominant Ξc∗D∗ structure is obtained at 4673 MeV with binding energy EB=−3 MeV. These exotic states are expected to be confirmed in future high-energy experiments.

Thermal twin stars within a hybrid equation of state based on a nonlocal chiral quark model compatible with modern astrophysical observations

Thermal twin stars within a hybrid equation of state based on a nonlocal chiral quark model compatible with modern astrophysical observations

Investigating Fully Strange Tetraquark System with Positive Parity in a Chiral Quark Model

Motivated by the intriguing discovery of X(6900) by the LHCb collaboration, we undertake a comprehensive study of the ss¯ss¯ tetraquark system with positive parity, employing the Gaussian expansion within the chiral quark model method. We consider two structures, the diquark–antidiquark (ss-s¯s¯) structure and meson–meson (ss¯-ss¯) structure, covering all conceivable color and spin configurations. Despite the absence of bound states in our calculations, we have identified potential resonant states with JP=0+, namely, R(0,2150) and R(0,2915), as well as a resonant state with JP=1+, denoted as R(1,2950), and a resonant state with JP=2+, denoted as R(2,2850), utilizing the real-scaling method. By comparing their energies and widths, we suggest that R(0,2915) and R(1,2950) may share characteristics with X(6900), while R(0,2150) could be a promising candidate for the experimental state f0(2100). We strongly advocate for experimental investigations to shed light on the existence and properties of these resonant states.

Intrinsic sea content of the ground state decuplet baryons in the extended chiral constituent quark model

Intrinsic sea content of the ground state decuplet baryons in the extended chiral constituent quark model

Ground states of all mesons and baryons in a quark model with hidden local symmetry

We extend the chiral quark model for u, d, c and b quarks with vector mesons, which we proposed in the previous analysis, to a model with the s quark. We include the nonet pseudo-scalar and vector mesons together with the singlet scalar meson based on the SU(3)L×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_L \ imes $$\\end{document} SU(3)R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_R$$\\end{document} chiral symmetry combined with the hidden local symmetry, which mediate force among u, d and s quarks. We fit the model parameters to the known ground state mesons and baryons. We show that the mass spectra of those hadrons are beautifully reproduced. We predict the masses of missing ground states, 1 meson and 20 baryons, which will be tested in the future experiment.

Charmoniumlike tetraquarks in a chiral quark model

The lowest-lying charmonium-like tetraquarks c{bar{c}}q{bar{q}}(q=u,,d) and c{bar{c}}s{bar{s}}, with spin-parity J^P=0^+, 1^+ and 2^+, and isospin I=0 and 1, are systematically investigated within the theoretical framework of complex-scaling range for a chiral quark model that has already been successfully applied in former studies of various tetra- and penta-quark systems. A four-body S-wave configuration which includes meson–meson, diquark–antidiquark and K-type arrangements of quarks, along with all possible color wave functions, is comprehensively considered. Several narrow resonances are obtained in each tetraquark channel when a fully coupled-channel computation is performed. We tentatively assign theoretical states to experimentally reported charmonium-like signals such as X(3872), Z_c(3900), X(3960), X(4350), X(4685) and X(4700). They can be well identified as hadronic molecules; however, other exotic components which involve, for instance, hidden-color channels or diquark–antidiquark structures play a considerable role. Meanwhile, two resonances are obtained at 4.04 GeV and 4.14 GeV which may be compatible with experimental data in the energy interval 4.0–4.2 GeV. Furthermore, the X(3940) and X(4630) may be identified as color compact tetraquark resonances. Finally, we also find few resonance states in the energy interval from 4.5 to 5.0 GeV, which would be awaiting for discovery in future experiments.

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.

Prediction of charmed-bottom pentaquarks in quark model

Inspired by the fully heavy tetraquark states reported by the LHCb, ATLAS and CMS Collaborations, we perform a systematical investigation of the low-lying fully heavy pentaquark systems composed of charm and bottom quarks (anti-quark) in the chiral quark model. With the help of the channel-coupling, we obtain several fully heavy pentaquark candidates, which are ccccbar{b} and bbbbbar{c} systems with J^P = 1/2^- and 3/2^-, cccbbar{c}, bbbcbar{b}, cccbbar{b} and bbbcbar{c} systems with J^P = 5/2^-. The binding energies of these states are all below 10 MeV and the root mean square (RMS) are around 1.8 fm, which indicates that these states are likely to be molecular states. These predicted exotic states may provide new ideas for experimental searches and we expect more experimental and theoretical researches to study and understand the fully heavy states in future.

New determination of the branching ratio of the structure dependent radiative K+ → e+νeγ

The branching ratio of the structure dependent (SD) radiative K+→e+νeγ decay relative to that of the K+→e+νe(γ) decay including the internal bremsstrahlung (IB) process (Ke2(γ)) has been measured in the J-PARC E36 experiment using plastic scintillator/lead sandwich detectors, in contrast to the previous E36 measurement, which used a CsI(Tl) calorimeter. In the analysis, the effect of IB was also taken into account in the SD radiative decay as Ke2γ(γ)SD. By combining the new data with the previous E36 result after revision for the IB correction for Ke2γ(γ)SD, a new value Br(Ke2γ(γ)SD)/Br(Ke2(γ))=1.20±0.07 has been determined. This is consistent with a recent lattice QCD calculation, but larger than the expectation of Chiral Perturbation Theory (ChPT) at order O(p4) and the previous KLOE value. Using the method to relate form factor and branching ratio described in the KLOE paper, the present result is also consistent with the form factor prediction based on a gauged nonlocal chiral quark model, but larger than that from ChPT at order O(p6).

Axial-vector charges of the spin $$\frac{1}{2}^+$$ and spin $$\frac{3}{2}^+$$ light and charmed baryons in the SU(4) chiral quark constituent model

Following the first clear evidence of the presence of intrinsic charm contribution in the proton, the axial-vector charges of the light and charmed baryons are investigated in the framework of $SU(4)$ chiral constituent quark model after including the explicit contributions from the $u\bar u $, $d\bar d $, $s\bar s $ and $c\bar c $ fluctuations. The axial-vector charges having physical significance correspond to the generators of the $SU(4)$ group with flavor singlet $\lambda^0$, flavor isovector $\lambda^3$, flavor hypercharge $\lambda^8$ and flavor charmed $\lambda^{15}$ combinations of axial-vector current at zero momentum transfer. In contemplation to further understand the $Q^2$ dependence of these charges, we have used the conventionally established dipole form of parametrization. The baryons considered here are the spin $\frac{1}{2}^+$ and spin $\frac{3}{2}^+$ multiplets decomposed further depending on the charm content of baryons.

Relations for low-energy constants in baryon chiral perturbation theory with explicit Delta (1232) derived from the chiral quark model

We study the relations between low-energy constants in the chiral Lagrangians with Delta (1232) and those in the quark-level description model up to the third chiral order. Ten structure correspondences are involved in getting the relations. This situation is more complicated than the spin-1/2 baryon case. The obtained results may help to further investigations involving the Delta (1232) baryons.

Axial transition form factors of octet baryons in the perturbative chiral quark model

We study the axial transition form factors $G_A^{B\to B'}(Q^2)$ as well as the axial charges $g_A^{B\to B'}$ of the octet baryons in the perturbative chiral quark model~(PCQM) with including both the ground and excited states in the intermediate quark propagators. The PCQM results on the $G_A^{B\to B'}(Q^2)$ and the $g_A^{B\to B'}$ are found in good agreement with the existing experimental data and the lattice-QCD values. The study figures out that the $G_A^{B\to B'}(Q^2)$ for all transitions behave in the dipolelike form, which is dominantly caused by the three-quark core. The meson cloud with the ground-state quark propagator also plays an extremely important role but results in a flat contribution. The excited-state quark propagator contributing to the $G_A^{B\to B'}(Q^2)$ could be regarded as the higher order correction and it is very limited.

Further study of within a chiral quark model* *Supported by the National Natural Science Foundation of China (12175065, 12005060, 12075288, 11735003, 11961141012). Ju-Jun Xie is also supported by the Youth Innovation Promotion Association CAS

In our previous studies, we analyzed the two-body strong decays of the low-lying Ω baryon states within a chiral quark model. The results showed that the mass, total width, and two body decay could be well reproduced with the spin-parity state classified in the quark model. Stimulated by the new observations of the three-body decay process at Belle, in the present study, we further investigate the three-body strong decay within the chiral quark model. It is found that the has a sizeable decay rate into the three-body final states . When considering as the resonance, the predicted ratio is close to the upper limit measured by the Belle Collaboration in 2019; however, it is too small to be comparable to the recent measurement . In addition, the coupled-channel effects on the bare three-quark state from nearby channels , , and are studied. Our theoretical results show that the coupled-channel effects on are not very large, and the molecular component is no more than . To clarify the nature of resonance, precise measurements on the ratio are needed, and further investigation on the effects of coupled channels is recommended.