Chiral Quark Model Research Articles

Confining density functional approach for color superconducting quark matter and mesonic correlations

We present a novel relativistic density-functional approach to modeling quark matter with a mechanism to mimic confinement. The quasiparticle treatment of quarks provides their suppression due to large quark selfenergy already at the mean-field level. We demonstrate that our approach is equivalent to a chiral quark model with medium-dependent couplings. The dynamical restoration of the chiral symmetry is ensured by construction of the density functional. Beyond the mean field, quark correlations in the pseudoscalar channel are described within the Gaussian approximation. This explicitly introduces pionic states into the model. Their contribution to the thermodynamic potential is analyzed within the Beth–Uhlenbeck framework. The modification of the meson mass spectrum in the vicinity of thee (de)confinement transition is interpreted as the Mott transition. Supplemented with the vector repulsion and diquark pairing the model is applied to construct a hybrid quark-hadron EoS of cold compact-star matter. We study the connection of such a hybrid EoS with the stellar mass-radius relation and tidal deformability. The model results are compared to various observational constraints including the NICER radius measurement of PSR J0740+6620 and the tidal deformability constraint from GW170817. The model is shown to be consistent with the constraints, still allowing for further improvement by adjusting the vector repulsion and diquark pairing couplings.

Generalized parton distributions and spin structures of light mesons from a light-front Hamiltonian approach

We present the generalized parton distributions (GPDs) for the valence quarks of the pion and the kaon in both momentum space and position space within the basis light-front quantization framework. These GPDs are obtained from the eigenvectors of a light-front effective Hamiltonian consisting of the holographic quantum chromodynamics (QCD) confinement potential, a complementary longitudinal confinement potential, and the color-singlet Nambu-Jona--Lasinio interactions for the valence quarks of mesons. We then calculate the generalized form factors of the pion and the kaon from the moments of these GPDs. Combining the tensor form factors with the electromagnetic form factors, we subsequently evaluate the impact parameter dependent probability density of transversely polarized quarks inside the pion and the kaon. The numerical results for the generalized form factors, corresponding charges, as well as those for the probability densities and the transverse shift of the polarized densities are consistent with lattice QCD simulations and with chiral quark models.

Toward discovering low-lying P-wave excited Σ c baryon states * *Supported by the National Natural Science Foundation of China (U1832173, 11775078) and Scientific and Technological Innovation Programs of Higher Education Institutions of Shanxi Province, China (2020L0617)

In this study, by combining the equal spacing rule with recent observations of and baryons, we predict the spectrum of the low-lying -mode -wave excited states. Furthermore, their strong decay properties are predicted using the chiral quark model and the nature of is investigated by analyzing the invariant mass spectrum. The structure observed in the mass spectrum was found to potentially arise from two overlapping -wave resonances, and . These resonances have similar decay widths of MeV and predominantly decay into the channel. The state is likely to be a very narrow state with a width of MeV, with its decays almost saturated by the channel. Additionally, evidence of the resonance as a very narrow peak may be seen in the invariant mass spectrum. The other two -wave states, and , are relatively narrow states with similar widths of MeV and predominantly decay into and , respectively. This study can provide useful references for discovering these low-lying -wave states in forthcoming experiments.

Strange hidden-charm tetraquarks in constituent quark model

In the framework of the chiral quark model (ChQM), we systematically investigate the strange hidden-charm tetraquark systems cs{bar{c}}{bar{u}} with two structures: q{bar{q}}-q{bar{q}} and qq-{bar{q}}{bar{q}}. The bound-state calculation shows that there is no any bound state in present work, which excludes the molecular state explanation (D^{0}D_{s}^{*-}/D^{*0}D_{s}^{-}/D^{*0}D_{s}^{*-}) of the reported Z_{cs}(3985)^{-} or Z_{cs}(4000)^{+}. However, the effective potentials for the cs-{bar{c}}{bar{u}} systems show the possibility of some resonance states. By applying a stabilization calculation and coupling all channels of both two structures, two new resonance states are obtained, which are the IJ^{P}=frac{1}{2} 0^{+} state with the energy around 4111–4116 MeV and the IJ^{P} =frac{1}{2} 1^{+} state with energy around 4113–4119 MeV, respectively. Both of them are worthy of search in future experiments. Our results show that the coupling calculation between the bound channels and open channels is indispensable to provide the necessary information for experiments to search for exotic hadron states.

Hidden-charm tetraquarks with strangeness in the chiral quark model

The hidden-charm tetraquarks with strangeness, $c\bar{c}s\bar{q}$ $(q=u,\,d)$, in $J^P=0^+$, $1^+$ and $2^+$ are systematically investigated in the framework of real- and complex-scaling range of a chiral quark model, whose parameters have been fixed in advance describing hadron, hadron-hadron and multiquark phenomenology. Each tetraquark configuration, compatible with the quantum numbers studied, is taken into account; this includes meson-meson, diquark-antidiquark and K-type arrangements of quarks with all possible color wave functions in four-body sector. Among the different numerical techniques to solve the Schr\"odinger-like 4-body bound state equation, we use a variational method in which the trial wave function is expanded in complex-range Gaussian basis functions, which is characterized by its simplicity and flexibility. This theoretical framework has already been used to study different kinds of multiquark systems, such as the hidden-charm pentaquarks, $P^+_c$, and doubly-charmed tetraquarks, $T^+_{cc}$. The recently reported $Z_{cs}$ states by the BESIII and LHCb collaborations are generally compatible with either compact tetraquark or hadronic molecular resonance configurations in our investigation. Moreover, several additional exotic resonances are found in the mass range between 3.8 GeV and 4.6 GeV.

Ωcc resonances with negative parity in the chiral constituent quark model

Spectrum of the low-lying $\Omega_{cc}$ resonances with negative parity, which are assumed to be dominated by $sccq\bar{q}$ pentaquark components, is investigated using the chiral constituent quark model. Energies of the $\Omega_{cc}$ resonances are obtained by considering the hyperfine interaction between quarks by exchanging Goldstone boson. Possible $sccq\bar{q}$ configurations with spin-parity $1/2^{-}$, $3/2^{-}$ and $5/2^{-}$ are taken into account. Numerical results show that the lowest $\Omega_{cc}$ resonances with negative parity may lie at $4050 \pm 100$ MeV. In addition, the transitions of the $\Omega_{cc}$ resonance to a pseudoscalar meson and a ground baryon state are also investigated within the chiral Lagrangian approach. We expect that these $\Omega_{cc}$ resonances could be observed in the $\bar{D}\Xi_{c}$ channel by future experiments.

Isospin asymmetric matter in a nonlocal chiral quark model

We analyze the features of strongly interacting matter in the presence of nonzero isospin chemical potential $\mu_I$, within a nonlocal two-flavor Polyakov-Nambu-Jona-Lasinio (PNJL) model. For a system at finite temperature $T$, we describe the behavior of various thermodynamic quantities and study the phase diagram in the $\mu_I - T$ plane. In particular, it is found that for values of $\mu_I$ larger than the pion mass and temperatures lower than a critical value of about 170 MeV the system lies in an isospin symmetry broken phase signaled by the presence of a nonzero pion condensate. Our results for the phase diagram are found to be in better agreement with those arising from lattice QCD calculations, as compared to the predictions from other theoretical approaches like the local PNJL model.

The exotic hadron states in quenched and unquenched quark models

In the last two decades, a large number of exotic hadron states have been observed in experiments, which arouses great attention in the hadron physics community. In this short review, we briefly summarize progresses of our group on several exotic hadron states. Two approaches, quenched and unquenched quark models, are adopted in the calculation. The channel coupling effects, the multiquark states couple to open channels and the quark-antiquark states couple to meson-meson states, are emphasized. X(3872) is showed to be a mixture state of and in the unquenched quark model. X(2900) can be explained as a resonance state with the quantum numbers in both the quark delocalization color screening model and the chiral quark model. The reported state X(6900) can be explained as a compact resonance state with in both two quark models, and several fully heavy tetraquark states are predicated. The possible hidden-charm pentaquarks are systematically investigated in QDCSM, and seven resonance states are obtained in the corresponding baryon-meson scattering process, among which the with , with and are consistent with the experimental report of P c (4312), P c (4440), and P c (4457), respectively. More experimental data on exotic hadron states are vital for understanding exotic hadron states in quark models.

Study on Zcs and excited Bs0 states in the chiral quark model

Stimulated by the newly observed charged hidden-charm state ${Z}_{cs}(3985{)}^{\ensuremath{-}}$ by BESIII Collaboration, ${Z}_{cs}(4000{)}^{+}$, ${Z}_{cs}(4220{)}^{+}$ and the excited ${B}_{s}^{0}$ states by LHCb Collaboration, a full calculation including masses, decay widths, and the inner structures of the states has emerged in the chiral quark model. For ${Z}_{cs}$ states, we assign quantum numbers $I({J}^{P})=\frac{1}{2}({1}^{+})$ and quark composition $c\overline{c}s\overline{u}$ according to the experiment. For ${B}_{s}^{0}$ states, systematically, investigations are performed with $I({J}^{P})=0({0}^{+}),0({1}^{+}),0({2}^{+})$ in both two-body $b\overline{s}$ and four-body $b\overline{s}q\overline{q}$ ($q=u$ or $d$) systems. Each tetraquark calculation takes all structures including meson-meson, diquark-antidiquark, and all possible color configurations into account. Among the numerical techniques to solve the two-body and four-body Schr\"odinger equation, the spatial wave functions are expanded in series of Gaussian basis functions for high precision, which is the way Gaussian expansion method (GEM) so called. Our results indicate that the low-lying states of the four-quark system are all higher than the corresponding thresholds either for $c\overline{c}s\overline{u}$ or for $b\overline{s}q\overline{q}$ systems. With the help of the real scaling method, we found two molecular resonance states with masses of 4023 and 4042 MeV for the $c\overline{c}s\overline{u}$ system. The state $c\overline{c}s\overline{u}(4042)$ has a close mass and decay width with the recent observed state ${Z}_{cs}(3985{)}^{\ensuremath{-}}$. For the $b\overline{s}q\overline{q}$ system with $J=0$, some resonance states are also found. The newly observed excited ${B}_{s}^{0}$ states can be accommodated in the chiral quark model as $2S$ or $1D$ states, and the mixing with four-quark states also needs to be considered.

X(2900) in a chiral quark model * *Supported in part by the National Natural Science Foundation of China (11775118, 11535005)

Recently, the LHCb Collaboration reported their observation of the first two fully open-flavor tetraquark states named (2900) and (2900) with unknown parity. Inspired by the report, we consider all the possible four-quark candidates for X(2900), which include the molecular structure, diquark structure, and their coupling in a chiral quark model via the Gaussian expansion method. To identify the genuine resonances, the real-scaling method (stabilization method) was employed. Our results show that five possible resonances, with MeV, with MeV, with MeV, with MeV, and with MeV, originate in the system. Compared with experimental data, with MeV may be an optimal candidate. However, none of the resonances have a similar width for . Hence, further study is required.

Axial charges of the proton within an extended chiral constituent quark model

We have performed a study of the isovector, octet and singlet axial charges of the proton in an extended chiral constituent quark model, where all the possible $uudq\bar{q}$~($q=u,d,s$) five-quark Fock components in the proton wave function are taken into account. The $^3P_0$ quark-antiquark creation mechanism is assumed to account for the transition coupling between three- and five-quark components in proton, and the corresponding transition coupling strength is fixed by fitting the intrinsic sea flavor asymmetry $\bar{d}-\bar{u}$ data for proton. Accordingly, with all the parameters fixed by empirical values, the probabilities of the intrinsic five-quark Fock components in proton wave function should be $\sim30 - 50\%$, which lead to the numerical results for quark spin $\Delta u$, $\Delta d$ and $\Delta s$, as well the axial charges of proton consistent with the experimental data and predictions by other theoretical approaches.

The strange partner of the Zc structures in a coupled-channels model

The discovery of a new charged structure in the K+ recoil-mass spectrum near the Ds−D⁎0/Ds⁎−D0 threshold, dubbed Zcs(3985)−, reinforce the idea that the structure of hadrons goes beyond the naive qqq and the qq¯ structures.The existence of this state, with quark content cc¯su¯, can be expected from the well-established Zc(3900)± and Zc(4020) states using SU(3) flavor symmetry. The Zc structures have been explained using the chiral constituent quark model in a coupled-channels calculation and, in this work, we undertake the study of the Zcs(3985)− using the same model.We are able to reproduce the K+ recoil-mass spectrum without any fine tuning of the model parameters. The study of the analytical structure of the S-matrix allows us to conclude that the structure is due to the presence of one virtual pole. A second state, the SU(3) flavor partner of the Zc(4020) is predicted at ∼4110 MeV/c2. New states in the hidden bottom strange sector are also predicted.

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.

SQq¯q¯ ( q=u , d ; Q=c , b ) tetraquarks in the chiral quark model

The low-lying $sQ\bar{q}\bar{q}$ $(q=u,\,d,\, Q=c,\,b)$ tetraquark states with $J^P=0^+$, $1^+$ and $2^+$, and in the isoscalar and isovector sectors, are systematically investigated in the framework of real- and complex-scaling range of a chiral quark model, whose parameters have been fixed in advance describing hadron, hadron-hadron and multiquark phenomenology, and thus all results presented here are pure predictions. Each tetraquark configuration, compatible with the quantum numbers studied, is taken into account; this includes meson-meson, diquark-antidiquark and K-type arrangements of quarks with all possible color wave functions in four-body sector. Among the different numerical techniques to solve the Schr\"odinger-like 4-body bound state equation, we use a variational method in which the trial wave function is expanded in complex-range Gaussian basis functions, because its simplicity and flexibility. Several compact bound states and narrow resonances are found in both charm-strange $cs\bar{q}\bar{q}$ and bottom-strange $bs\bar{q}\bar{q}$ tetraquark sectors, most of them as a product of the strong coupling between the different channels. The so-called $X_{0,1}(2900)$ signals, recently found by the LHCb collaboration, are unstable in our formalism with several candidates in the single-channel computations.

Investigation of varXi _c^0 in a chiral quark model

Recently, three new states of varXi _c^0 were observed in the invariant mass spectrum of varLambda ^+_cK^- by LHCb collaboration. In this work, we use a chiral quark model to investigate these three exited states with the help of Gaussian expansion method both in three-quark structure and in five-quark structure with all possible quantum numbers IJ^P=frac{1}{2}(frac{1}{2})^-, frac{1}{2}(frac{3}{2})^-, frac{1}{2}(frac{5}{2})^-, frac{3}{2}(frac{1}{2})^-, frac{3}{2}(frac{3}{2})^- and frac{3}{2}(frac{5}{2})^- . The calculations shows that the masses of 2S and 1D states of varXi _c are comparable to experimental results; In addition, the resonance states of five-quark configuration are possible candidates of these new states with negative parity by using the real scaling method and their decay width is also given.

Cold magnetized quark matter at finite density in a nonlocal chiral quark model

We study the behavior of two-flavor dense quark matter under the influence of an external magnetic field in the framework of a nonlocal chiral quark model with separable interactions. The nonlocality is incorporated in the model by using a Gaussian form factor. It is found that for low and moderate values of magnetic field there is a decrease of the critical chiral restoration chemical potential $$\mu _c$$ , i.e. an inverse magnetic catalysis effect is observed. For larger values of eB the behavior of $$\mu _c$$ becomes more or less flat, depending on the parametrization. Within the considered parametrization range we do not find a significant growth of the critical chemical potential for large magnetic fields, as occurs in the case of the local NJL model.

Unpolarized dihadron fragmentation functions in nonlocal chiral quark model

We have calculated the unpolarized dihadron fragmentation functions (uDiFFs) of pions and kaons using the nonlocal chiral-quark model (NLChQM) and evolved our results to the transferred momentum scale Q2=4GeV2 by the QCD evolution equations. These uDiFFs have also been computed in the Nambu–Jona-Lasinio-jet (NJL-jet) model for the sake of comparison. We find that there is substantial difference between the results of these two models. Furthermore, the DiFFs of u→π+π− and g→π+π− at Q2=109GeV2 in these two models are presented in comparison with the parametrizations fitted by the Monte Carlo event generator JETSET.

Study of qqq{bar{q}}Q pentaquark system in the chiral quark model

With the discovery of some hidden-charm pentaquark resonances by the LHCb Collaboration, investigations of pentaquark states containing heavy quarks have aroused the interest of theorists. We study herein qqq{bar{q}}Q (q = u or d, Q=c or b) pentaquark system, in the framework of the chiral quark model. In consequence, some charmed and bottomed pentaquarks are considered to exist by five-body dynamical calculations. In the charm sector, Sigma _cpi (IJ^P=0frac{1}{2}^-) and Sigma _c^*pi (IJ^P=0frac{3}{2}^-) are possible candidates of Lambda _c(2595) and Lambda _c(2625), respectively. Besides, two high-spin states, Sigma _c^*rho (IJ^P=0frac{5}{2}^-) and Delta D^*(IJ^P=1frac{5}{2}^-), are also found in the energy region of 3.2 sim 3.3 GeV. In the bottom sector, Sigma _bpi (IJ^P=0frac{1}{2}^-), Sigma _b^*pi (IJ^P=0frac{3}{2}^-) could be candidates of Lambda _b(5912) and Lambda _b(5920), respectively. And Sigma _b^*rho (IJ^P=0frac{5}{2}^-) and Delta B^*(IJ^P=1frac{5}{2}^-) are found in the energy region of 6.5 sim 6.6 GeV. Sigma _c^{(*)}pi and Sigma _b^{(*)}pi are expected as compact states, while Sigma _c^*rho , Sigma _b^*rho , Delta D^* and Delta B^* are expected as molecular states.

Coupling Hadron-Hadron Thresholds within a Chiral Quark Model Approach

Heavy hadron spectroscopy was well understood within the naive quark model until the end of the past century. However, in 2003, the X(3872) was discovered, with puzzling properties difficult to understand in the simple naive quark model picture. This state made clear that excited states of heavy mesons should be coupled to two-meson states in order to understand not only the masses but, in some cases, unexpected decay properties. In this work, we will give an overview of a way in which the naive quark model can be complemented with the coupling to two hadron thresholds. This program has been already applied to the heavy meson spectrum with the chiral quark model, and we show some examples where thresholds are of special relevance.

Historical Introduction to Chiral Quark Models

Chiral symmetry, and its dynamical breaking, has become a cornerstone in the description of the hadron’s phenomenology at low energy. The present manuscript gives a historical survey on how the quark model of hadrons has been implemented along the last decades trying to incorporate, among other important non-perturbative features of quantum chromodynamics (QCD), the dynamical chiral symmetry breaking mechanism. This effort has delivered different models such as the chiral bag model, the cloudy bag model, the chiral quark model or the chiral constituent quark model. Our main aim herein is to provide a brief introduction of the Special Issue “Advances in Chiral Quark Models” in Symmetry and contribute to the clarification of the differences among the above-mentioned models that include the adjective chiral in their nomenclature.