## What is/are Chiral Quark?

Chiral Quark - We investigate the pentaquark system $qqqs\overline{q}$ in a framework of chiral quark model.^{[1]}The prototype test case studied is the chiral nucleon-meson model, with added comments on the chiral quark-meson model.

^{[2]}Depending on the contributions to the Landau levels, we conclude that the chiral magnetic field enhances the chiral quark condensates and hence the chiral QCD phase–diagram, i.

^{[3]}We review the current status of the research on effective nonlocal NJL-like chiral quark models with separable interactions, focusing on the application of this approach to the description of the properties of hadronic and quark matter under extreme conditions.

^{[4]}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 $$IJ^P=\frac{1}{2}(\frac{1}{2})^-$$ I J P = 1 2 ( 1 2 ) - , $$\frac{1}{2}(\frac{3}{2})^-$$ 1 2 ( 3 2 ) - , $$\frac{1}{2}(\frac{5}{2})^-$$ 1 2 ( 5 2 ) - , $$\frac{3}{2}(\frac{1}{2})^-$$ 3 2 ( 1 2 ) - , $$\frac{3}{2}(\frac{3}{2})^-$$ 3 2 ( 3 2 ) - and $$\frac{3}{2}(\frac{5}{2})^-$$ 3 2 ( 5 2 ) -.

^{[5]}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.

^{[6]}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.

^{[7]}We also reflect on previous calculations on quark distributions in chiral quark soliton models and attempt to put them into perspective.

^{[8]}We investigate the strong force fields and stabilities of the nucleon and the singly heavy baryon ${\mathrm{\ensuremath{\Sigma}}}_{c}$ within the framework of the chiral quark-soliton model.

^{[9]}China Stimulated by the newly observed charged hidden-charm state Zcs(3985) − by BESIII Collaboration, Zcs(4000) , Zcs(4220) + and the excited B s states by LHCb Collaboration, a full calculation including masses and decay widths is emerged in the chiral quark model.

^{[10]}The chiral quark-meson coupling (CQMC) models are applied to revisiting static properties of spherical nuclei in comparison with the results from the conventional quantum hadrodynamics (QHD)-like models as well as the available experimental data.

^{[11]}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.

^{[12]}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.

^{[13]}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.

^{[14]}We conduct a dynamical calculation of pentaquark systems with quark contents $sssu\overline{u}$ in the framework of two quark models: the chiral quark model (ChQM) and quark delocalization color screening model (QDCSM).

^{[15]}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.

^{[16]}The charge ${Q}_{U}$ of chiral quarks and leptons is a combination of $Q$, $B$, ${L}_{i}$, and ${T}_{3L}$ with the axial ${F}_{A}$.

^{[17]}To this end, we calculate the sea quark and gluon distribution functions of these mesons applying the modified chiral quark model ( $ \chi QM$χQM.

^{[18]}Specifically, we calculate the frequency peak f p e a k redshifted at today time and the fractional energy density Ω g w h 2 in light of equation-of-state improved by the finite quark (baryon) chemical potential (we consider an effective three flavor chiral quarks model of QCD).

^{[19]}Inspired by the recent observation of exotic resonances $X(4140)$, $X(4274)$, $X(4350)$, $X(4500)$ and $X(4700)$ reported by several experiment collaborations, we investigated the four-quark system $cs\bar c\bar s$ with quantum numbers $J^{PC}=1^{++}$ and $0^{++}$ in the framework of the chiral quark model.

^{[20]}In the framework of a nonrelativistic chiral quark model, we continue to study the mass spectra of the fully-heavy $bb\bar{c}\bar{c}$ and $bc\bar{b}\bar{c}$ tetraquarks.

^{[21]}The light-by-light contribution from the axial-vector (AV) mesons exchanges to the muon anomalous magnetic moment is estimated in the framework of the nonlocal chiral quark model.

^{[22]}The strong decays of the low-lying $\lambda$-mode $\Lambda_b(1D,2S)$ and $\Sigma_b(2S)$ states are studied in a chiral quark model.

^{[23]}Using vector and axial-vector correlators within finite energy sum rules with inputs from a chiral quark model, coupled to the Polyakov loop, with nonlocal vector interactions, we extend our previous work to confirm the equivalence between the continuum threshold $s_0$ and the trace of the Polyakov loop $\Phi$ as order parameters for the deconfinement transition at finite temperature $T$ and quark chemical potential $\mu$.

^{[24]}As a phenomenological study, our framework is based on SU(3) chiral quark model.

^{[25]}The quark matter equation of state is based on a nonlocal covariant chiral quark model with vector meson and diquark condensate.

^{[26]}We obtain the momentum and current mass dependence of the quark propagator and the quark-gluon vertex, and the chiral quark condensate which agrees with previous results excellently.

^{[27]}Motivated by the searching for states at LHC recently, we calculate the ground-state energies of states with quantum numbers in a nonrelativistic chiral quark model using the Gaussian expansion method.

^{[28]}In the framework of the chiral quark model along with complex scaling range, we perform a dynamical study on the low-lying $S$-wave doubly-heavy tetraquark states ($QQ\bar{q}\bar{q}$, $Q=c, b$ and $q=u, d$) with an accurate computing approach, Gaussian expansion method.

^{[29]}We investigate the electromagnetic form factors of the baryon decuplet within the framework of the $$\mathrm {SU(3)}$$SU(3) self-consistent chiral quark-soliton model, taking into account the $$1/N_c$$1/Nc rotational corrections and the effects of flavor $$\mathrm {SU(3)}$$SU(3) symmetry breaking.

^{[30]}Five-quark bound states in the hidden-charm sector were explored by us using, for the quark-quark interaction, a chiral quark model which successfully explains meson and baryon phenomenology, from the light to the heavy quark sector.

^{[31]}Motivated by the searching for $ bb\bar{b}\bar{b}$bbb¯b¯ states at LHC recently, we calculate the ground-state energies of $ bb\bar{b}\bar{b}$bbb¯b¯ states with quantum numbers $ IJ^{P}=00^{+}, 01^{+}, 02^{+}$IJP=00+,01+,02+ in a nonrelativistic chiral quark model using the Gaussian expansion method.

^{[32]}

## Nonrelativistic Chiral Quark

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.^{[1]}In the framework of a nonrelativistic chiral quark model, we continue to study the mass spectra of the fully-heavy $bb\bar{c}\bar{c}$ and $bc\bar{b}\bar{c}$ tetraquarks.

^{[2]}Motivated by the searching for states at LHC recently, we calculate the ground-state energies of states with quantum numbers in a nonrelativistic chiral quark model using the Gaussian expansion method.

^{[3]}Motivated by the searching for $ bb\bar{b}\bar{b}$bbb¯b¯ states at LHC recently, we calculate the ground-state energies of $ bb\bar{b}\bar{b}$bbb¯b¯ states with quantum numbers $ IJ^{P}=00^{+}, 01^{+}, 02^{+}$IJP=00+,01+,02+ in a nonrelativistic chiral quark model using the Gaussian expansion method.

^{[4]}

## Nonlocal Chiral Quark

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.^{[1]}The light-by-light contribution from the axial-vector (AV) mesons exchanges to the muon anomalous magnetic moment is estimated in the framework of the nonlocal chiral quark model.

^{[2]}

## chiral quark model

We investigate the pentaquark system $qqqs\overline{q}$ in a framework of chiral quark model.^{[1]}We review the current status of the research on effective nonlocal NJL-like chiral quark models with separable interactions, focusing on the application of this approach to the description of the properties of hadronic and quark matter under extreme conditions.

^{[2]}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 $$IJ^P=\frac{1}{2}(\frac{1}{2})^-$$ I J P = 1 2 ( 1 2 ) - , $$\frac{1}{2}(\frac{3}{2})^-$$ 1 2 ( 3 2 ) - , $$\frac{1}{2}(\frac{5}{2})^-$$ 1 2 ( 5 2 ) - , $$\frac{3}{2}(\frac{1}{2})^-$$ 3 2 ( 1 2 ) - , $$\frac{3}{2}(\frac{3}{2})^-$$ 3 2 ( 3 2 ) - and $$\frac{3}{2}(\frac{5}{2})^-$$ 3 2 ( 5 2 ) -.

^{[3]}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.

^{[4]}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.

^{[5]}China Stimulated by the newly observed charged hidden-charm state Zcs(3985) − by BESIII Collaboration, Zcs(4000) , Zcs(4220) + and the excited B s states by LHCb Collaboration, a full calculation including masses and decay widths is emerged in the chiral quark model.

^{[6]}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.

^{[7]}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.

^{[8]}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.

^{[9]}We conduct a dynamical calculation of pentaquark systems with quark contents $sssu\overline{u}$ in the framework of two quark models: the chiral quark model (ChQM) and quark delocalization color screening model (QDCSM).

^{[10]}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.

^{[11]}To this end, we calculate the sea quark and gluon distribution functions of these mesons applying the modified chiral quark model ( $ \chi QM$χQM.

^{[12]}Inspired by the recent observation of exotic resonances $X(4140)$, $X(4274)$, $X(4350)$, $X(4500)$ and $X(4700)$ reported by several experiment collaborations, we investigated the four-quark system $cs\bar c\bar s$ with quantum numbers $J^{PC}=1^{++}$ and $0^{++}$ in the framework of the chiral quark model.

^{[13]}In the framework of a nonrelativistic chiral quark model, we continue to study the mass spectra of the fully-heavy $bb\bar{c}\bar{c}$ and $bc\bar{b}\bar{c}$ tetraquarks.

^{[14]}The light-by-light contribution from the axial-vector (AV) mesons exchanges to the muon anomalous magnetic moment is estimated in the framework of the nonlocal chiral quark model.

^{[15]}The strong decays of the low-lying $\lambda$-mode $\Lambda_b(1D,2S)$ and $\Sigma_b(2S)$ states are studied in a chiral quark model.

^{[16]}Using vector and axial-vector correlators within finite energy sum rules with inputs from a chiral quark model, coupled to the Polyakov loop, with nonlocal vector interactions, we extend our previous work to confirm the equivalence between the continuum threshold $s_0$ and the trace of the Polyakov loop $\Phi$ as order parameters for the deconfinement transition at finite temperature $T$ and quark chemical potential $\mu$.

^{[17]}As a phenomenological study, our framework is based on SU(3) chiral quark model.

^{[18]}The quark matter equation of state is based on a nonlocal covariant chiral quark model with vector meson and diquark condensate.

^{[19]}Motivated by the searching for states at LHC recently, we calculate the ground-state energies of states with quantum numbers in a nonrelativistic chiral quark model using the Gaussian expansion method.

^{[20]}In the framework of the chiral quark model along with complex scaling range, we perform a dynamical study on the low-lying $S$-wave doubly-heavy tetraquark states ($QQ\bar{q}\bar{q}$, $Q=c, b$ and $q=u, d$) with an accurate computing approach, Gaussian expansion method.

^{[21]}Five-quark bound states in the hidden-charm sector were explored by us using, for the quark-quark interaction, a chiral quark model which successfully explains meson and baryon phenomenology, from the light to the heavy quark sector.

^{[22]}Motivated by the searching for $ bb\bar{b}\bar{b}$bbb¯b¯ states at LHC recently, we calculate the ground-state energies of $ bb\bar{b}\bar{b}$bbb¯b¯ states with quantum numbers $ IJ^{P}=00^{+}, 01^{+}, 02^{+}$IJP=00+,01+,02+ in a nonrelativistic chiral quark model using the Gaussian expansion method.

^{[23]}

## chiral quark condensate

Depending on the contributions to the Landau levels, we conclude that the chiral magnetic field enhances the chiral quark condensates and hence the chiral QCD phase–diagram, i.^{[1]}We obtain the momentum and current mass dependence of the quark propagator and the quark-gluon vertex, and the chiral quark condensate which agrees with previous results excellently.

^{[2]}