Search Results (62)

The chiral quark soliton model (CQSM) is an effective quark model of baryons maximally taking account of the most important feature of low-energy QCD, i.e., the spontaneous chiral symmetry breaking of the QCD vacuum and the associated appearance of Nambu–Goldstone pions. It shares many common features with the famous Skyrme model in that the baryons are viewed as rotating hedgehog objects in both models. Despite many similarities, it turned out that the CQSM can give more realistic predictions on most baryon observables. Above all, a decisive advantage of the CQSM over the Skyrme-like models is that it can handle non-local quark–quark correlations in baryons, which is absolutely impossible within the framework of effective meson theories. This feature is decisively important for making theoretical predictions on the quark distribution functions inside the nucleon, which are defined as nucleon matrix elements of bilinear quark operators with light-cone separation. In the present paper, we try to elucidate why and how the CQSM can give successful predictions for a variety of types of nucleon quark distribution functions, especially for the flavor asymmetry of the unpolarized and longitudinally polarized sea-quark (anti-quark) distribution functions in the nucleon. Full article

We investigate finite-size effects in the T–$\mu$ phase diagram of magnetized quark matter within the framework of a nonlocal extension of the Polyakov–Nambu–Jona-Lasinio (PNJL) model. Finite-size corrections are incorporated through the multiple reflection expansion (MRE) formalism, which describes a spherical quark droplet of radius R and modifies the density of states by including surface and curvature contributions. We consider two-flavor quark matter at finite temperature and chemical potential in the presence of a uniform magnetic field with strengths ranging from $eB=0$ to 1 ${\mathrm{GeV}}^2$, and droplet radii from $R=3$ fm to the bulk limit. The nonlocal PNJL (nlPNJL) model naturally reproduces both magnetic catalysis at low temperatures and inverse magnetic catalysis near the chiral transition, in agreement with lattice QCD results. We analyze the chiral condensate, the traced Polyakov loop, the normalized quark condensate, and the corresponding susceptibilities. We find that finite-size effects do not modify the overall structure of the phase diagram, and that the coincidence of the chiral restoration and deconfinement transitions persists for all magnetic field strengths and system sizes explored, within the present implementation in which finite-size corrections are restricted to the fermionic sector. However, the critical end point (CEP) is notably shifted as a function of both magnetic field strength and system size: It moves toward higher chemical potentials and lower temperatures as system size decreases, an effect that is significantly amplified by strong magnetic fields. Our results have potential implications for the physics of phase conversion in compact stars and for the interpretation of relativistic heavy-ion collision experiments. Full article

We present a novel proposal for the effective Lagrangian of the low-energy Yang–Mills quantum field theory. The proposed effective Lagrangian exhibits the spontaneous BRST symmetry breaking. We build on the Fujikawa model that we couple to the Yang–Mills elementary field sector, motivated by the analogy with Chiral Quark Model. We interpret the Fujikawa fields as effective fields, composites of the elementary gluon and ghost fields. In order to justify the existence of two massless Nambu–Goldstone modes among the Fujikawa fields, we require not only the BRST but also the anti-BRST invariance of the effective Lagrangian, with both being spontaneously broken. The most striking consequence of that is the emergence of the effective gluon and ghost masses. We reproduce the Curci–Ferrari model as a special case of our effective model upon the spontaneous BRST symmetry breaking. In order to reproduce also the non-nilpotent modified-BRST symmetry, characteristic for the Curci–Ferrari model, we modify our effective Lagrangian to be invariant with respect to the extended-BRST symmetry, which mixes the elementary and Fujikawa field sectors, and which is nilpotent. The Curci–Ferrari model is reproduced by the elementary field sector of the resulting Lagrangian. The remaining Fujikawa-field-dependent terms guarantee the underlying nilpotent extended-BRST symmetry, which is now hidden in the sense of the spontaneous symmetry breaking. Full article

We present a short review dedicated to low-lying meson states. We present all meson nonets, which consist from up, down and strange light quarks. We consider the scalar nonet as a basic nonet. We work in the framework of the massless Nambu–Jona-Lasinio $U_R\left(3\right)\times U_L\left(3\right)$ quark model. The collective meson states are described through initially bare quark–antiquark pairs, whose condensates lead simultaneously to spontaneous breaking of the chiral and the flavour symmetry. After quantisation and the spontaneous breaking of the chiral symmetry, when quarks obtain constituent nonzero masses, they become dressed. We present an explanation of the inverse mass hierarchy of the low-lying nonet of the scalar mesons. The proposed explanation is based on symmetry principles. It is shown that, due to the flavour symmetry breaking, two isodoublets of $K_0^{*}\left(700\right)$ mesons play the role of Goldstone bosons. It is also proven that there exists a solution with almost degenerate masses of the $a_0\left(980\right)$ and $f_0\left(980\right)$ mesons and a zero mass of the $f_0\left(500\right)$ meson. Short description of the physical properties of other meson nonets is provided. In particular unique mass relations among the different nonets, which are experimentally confirmed, are presented. Full article

Experimentally, the $1^{+}$ state $X(3872)$ was first discovered, and subsequently, its partner state $Y(4260)$, with the same quark content $(c\overline{q}q\overline{c})$ and quantum number $1^{-}$ was also observed. Inspired by this pattern, we systematically investigate the newly discovered $1^{+}$ state $T_{cc}$ and its possible $1^{-}$ partner, the $T_{D{D}_1}$ system with the same quark content $(c\overline{q}c\overline{q})$. Within the framework of the chiral quark model, we perform a comprehensive study of the bound and resonance states of $T_{D{D}_1}$ using the Gaussian expansion method (GEM). Two quark configurations, the molecular structure and the diquark structure, are considered in our calculations. Our results indicate the existence of a shallow bound state dominated by the $D{D}_1^{*}$ channel, which is analogous to the experimentally observed $T_{cc}$, as well as two compact resonant states with narrow widths around 4.5 GeV. To avoid the influence of model parameters on the results, we additionally fitted a new set of parameters and obtained consistent conclusions. According to our calculation results, although the color-octet and diquark configurations have relatively high energies, the channel-coupling effects induced by them play a crucial role in the formation of these stable states. We strongly encourage experimental efforts to search for the stable states predicted in the $T_{D{D}_1}$ system. Full article

Inspired by the well-known experimental connections between $X\left(3872\right)$, $Z_{cs}\left(4220\right)$, and $Y\left(4620\right)$, we systematically study the recently reported strange partner of $T_{cc}$, the $1^{+}$$cc\overline{q}\overline{s}$ system, and its orbital excitation state $1^{-}$$cc\overline{q}\overline{s}$. A chiral quark model incorporating SU(3) symmetry is considered to study these two systems. To better investigate their spatial structure, we introduce a precise few-body calculation method, the Gaussian Expansion Method (GEM). In our calculations, we include all possible physical channels, including molecular states and diquark structures, and consider channel coupling effects. To identify the stable structures in the system (bound states and resonance states) we employ a powerful resonance search method, the Real-Scaling Method (RSM). According to our results, in the $1^{+}$$cc\overline{q}\overline{s}$ system, we obtain two bound states with energies of 3890 MeV and 3940 MeV, as well as two resonance states with energies of 3975 MeV and 4090 MeV. The decay channels of these two resonance states are $D{D}_s^{\ast }$ and $D^{\ast }{D}_s$, respectively. In the $1^{-}$$cc\overline{q}\overline{s}$ system, we obtain only one resonance state, with an energy of 4570 MeV, and two main decay channels: $D{D}_{s1}^{\ast }$ and $D^{\ast }{D}_{s1}^{\prime }$. We strongly suggest that experimental groups use our predictions to search for these stable structures. Full article

We perform a systematic investigation of low-lying singly charmed dibaryon systems with $J=1$, $I=0,{\displaystyle \frac{1}{2}},1,{\displaystyle \frac{3}{2}},2,{\displaystyle \frac{5}{2}}$ and strangeness $S=-1,-2,-3,-4,-5$ in the chiral quark model. According to the analysis of effective potentials, dibaryon systems characterized by lower isospin and magnitude of strangeness exhibit stronger attractive interactions, which may enhance their tendency to form bound states. Experimental efforts may therefore prioritize the search for such configurations. The bound-state calculation results indicate that we have obtained some single-channel bound states, which are $\mathrm{\Sigma }{\mathrm{\Sigma }}_c$, $\mathrm{\Sigma }{\mathrm{\Sigma }}_c^{*}$, ${\mathrm{\Sigma }}^{*}{\mathrm{\Sigma }}_c$, ${\mathrm{\Sigma }}^{*}{\mathrm{\Sigma }}_c^{*}$ with $I=0,S=-1$; ${\mathrm{\Sigma }}_c\mathrm{\Delta }$, ${\mathrm{\Sigma }}_c^{*}\mathrm{\Delta }$ with $I={\displaystyle \frac{1}{2}},S=0$; $\mathrm{\Sigma }{\mathrm{\Sigma }}_c$ with $I=1,S=-1$; ${\mathrm{\Sigma }}_c\mathrm{\Delta }$ with $I={\displaystyle \frac{3}{2}},S=0$; and ${\mathrm{\Xi }}^{*}{\mathrm{\Sigma }}_c^{*}$ with $I={\displaystyle \frac{3}{2}},S=-2$. However, these states can decay through open channels. We have listed both these single-channel bound states and their corresponding decay channels in this work for experimental reference and search. In the future, we need to study the scattering processes of the open channels further to confirm whether these states are resonance states. Full article

To investigate diquark correlation in baryons, the baryon spectra with different light–heavy quark combinations are calculated using Gaussian expansion method within both the naive quark model and the chiral quark model. By computing the diquark energies and separations between any two quarks in baryons, we analyze the diquark effect in the $ud$-q/Q, $us$-Q, $ss$-q/Q, and $QQ$-q/Q systems (where $q=u,d$, or s; $Q=c,b$). The results show that diquark correlations exist in baryons. In particular, for $qq$-Q and $QQ$-q systems, the same type of diquark exhibits nearly identical energy and size across different baryons. In the orbital ground states of baryons, scalar–isoscalar diquarks have lower energy and a smaller size compared to vector–isovector diquark, which qualifies them as “good diquarks”. In $QQ$-q systems, a larger mass of Q leads to a smaller diquark separation and a more pronounced diquark effect. In $qq$-Q systems, the separation between the two light quarks remains larger than that between a light and a heavy quark, indicating that the internal structure of such diquarks must be taken into account. A comparison between the naive quark model and the chiral quark model reveals that the introduction of meson exchange slightly increases the diquark size in most systems. Full article

In this work, we employ the nonextensive Nambu–Jona-Lasinio model to analyze the thermodynamic properties of magnetized quark matter. The nonequilibrium state is described in Tsallis distribution by a dimensionless parameter q. We find that within a reasonable temperature range, the system undergoes a crossover transition at the critical chemical potential, which is decreased by the increase of both the temperature and q value. In contrast to the enhanced stability by magnetic field in Boltzmann statistics, it is found that the stability of chiral restored matter in Tsallis statistics would be reduced by an increase of the magnetic field. Conversely, the increase of the q would enhance the stability of quark matter. Finally, we display the different magnetic effects on the stability in the chiral broken and restored regions. Full article

In this paper, I investigate the gluon distributions for the kaon and pion, as well as the improvement of the valence-quark distributions, in the framework of the gauge-invariant nonlocal chiral quark model (NL$\chi$QM), where the momentum dependence is taken into account. I then compute the gluon distributions for the kaon and pion that are dynamically generated from the splitting functions in the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) QCD evolution. In a comparison with the recent lattice QCD and JAM global analysis results, it is found that the results for the pion gluon distributions at $Q=$ 2 GeV, which is set based on the lattice QCD, have a good agreement with the recent lattice QCD data; this is followed up with the up valence-quark distribution of the pion results at $Q=$ 5.2 GeV in comparison with the reanalysis experimental data. The prediction for the kaon gluon distributions at $Q=2$ GeV is consistent with the recent lattice QCD calculation. Full article

We review the in-medium modifications of effective masses (Lorentz scalar potentials or phenomenon of mass shift) of the heavy–heavy and heavy–light mesons in symmetric nuclear matter and their nuclear bound states. We use a combined approach with the quark–meson coupling (QMC) model and an effective Lagrangian. As demonstrated by the cases of pionic and kaonic atoms, studies of the meson–nucleus bound state can provide us with important information on chiral symmetry in a dense nuclear medium. In this review, we examine the mesons, $K,K^{\ast },D,D^{\ast },B,B^{\ast },\eta ,{\eta }^{\prime },\varphi ,{\eta }_c,J/\psi ,{\eta }_b,\mathsf{{\rm Y}}$, and $B_c$, where our emphasis is on the heavy mesons. In addition, we also present some new results for the $B_c$-nucleus bound states. Full article

We present a physics-informed Bayesian analysis of equation of state constraints using observational data for masses, radii and tidal deformability of pulsars and a generic class of hybrid neutron star equation of state with color superconducting quark matter on the basis of a recently developed nonlocal chiral quark model. The nuclear matter phase is described within a relativistic density functional model of the DD2 class and the phase transition is obtained by a Maxwell construction. We find the region in the two-dimensional parameter space spanned by the vector meson coupling and the scalar diquark coupling, where three conditions are fulfilled: (1) the Maxwell construction can be performed, (2) the maximum mass of the hybrid neutron star is not smaller than 2.0 ${\mathrm{M}}_{\odot }$ and (3) the onset density of the phase transition is not below the nuclear saturation density $n_0=0.15$ fm⁻³. The result of this study shows that the favorable neutron star equation of state has low onset masses for the occurrence of a color superconducting quark matter core between 0.5–0.7 $M_{\odot }$ and maximum masses in the range 2.15–2.22 $M_{\odot }$. In the typical mass range of 1.2–2.0 $M_{\odot }$, the radii of these stars are between 11.9 and 12.4 km, almost independent of the mass. In principle, hybrid stars would allow for larger maximum masses than provided by the hadronic reference equation of state. Full article

The aim of this work is to propose an explanation of the inverse mass hierarchy of the low-lying nonet of the scalar mesons in the framework of the massless Nambu–Jona-Lasinio $U_R\left(3\right)\times U_L\left(3\right)$ quark model. The proposed explanation is based on symmetry principles. The collective meson states are described via quark–antiquark pairs, whose condensates lead simultaneously to spontaneous breaking of chiral and flavour symmetry. It is shown that, due to flavour symmetry breaking, two iso-doublets of $K_0^{*}\left(700\right)$ mesons play the role of Goldstone bosons. It is also proven that there exists a solution with degenerate masses of the $a_0\left(980\right)$ and $f_0\left(980\right)$ mesons and a zero mass of the $f_0\left(500\right)$ meson. Full article

We investigate the time evolution of the quark condensate toward a chiral symmetry broken phase in hot and dense quark matter using a field-theoretic quark model with nonlocal chiral-invariant four-fermion coupling. By purposely selecting a parameter set in which inhomogeneous phases are energetically disfavored, we nonetheless observe the emergence of metastable patterned configurations that appear to persist for remarkably long timescales. These findings suggest that even when not fully stable, inhomogeneous phases may play a significant role in the dynamics of chiral symmetry breaking and restoration. To gain deeper insight into these phenomena, we also analyze the impact of the dimensionality of coordinate space on both the formation and stability of inhomogeneous chiral condensates. Full article

We describe the quark substructure of hadrons and the equation of state of high-density neutron star matter by using the Nambu–Jona-Lasinio (NJL) model, which is an effective quark theory based on QCD. The interaction between quarks fully respects the chiral and flavor symmetries. Guided by the success of various low-energy theorems, we assume that the explicit breaking of these symmetries occurs only via the current quark masses, and all other symmetry breakings are of dynamical nature. In order to take into account the effects of the finite quark core sizes of the baryons on the equation of state, we make use of an excluded volume framework that respects thermodynamic consistency. The effects generated by the swelling quark cores generally act repulsively and lead to an increase in the pressure with increasing baryon density. On the other hand, in neutron star matter, these effects also lead to a decrease in the density window where hyperons appear because it becomes energetically more favorable to convert the faster moving nucleons into hyperons. Our quantitative analysis shows that the net effect of the excluded volume is too small to solve the long-standing “hyperon puzzle”, which is posed by the large observed masses of neutron stars. Thus, the puzzle persists in a relativistic effective quark theory which takes into account the short-range repulsion between baryons caused by their finite and swelling quark core sizes in a phenomenological way. Full article