Chiral Quark Model Research Articles

Spectrum of the excitedN*andΔ*baryons in a relativistic chiral quark model

The spectrum of the SU(2) flavor baryons is studied in the frame of a relativistic chiral quark potential model based on the one-pion and one-gluon exchange mechanisms. It is argued that the ${N}^{*}$ and ${\mathrm{\ensuremath{\Delta}}}^{*}$ resonances strongly coupled to the $\ensuremath{\pi}N$ channel are identified with the orbital configurations $(1{S}_{1/2}{)}^{2}(nlj)$ with a single valence quark in the excited state ($nlj$). With the obtained selection rules based on the ``chiral constraint,'' we show that it is possible to construct a schematic periodic table of baryon resonances, consistent with the experimental data and yielding no ``missing resonances.'' A new original method for the treatment of the center of mass problem is suggested which is based on the separation of the three-quark Dirac Hamiltonian into the parts, corresponding to the Jacobi coordinates. The numerical estimations for the energy positions of the nucleon and delta baryons (up to and including F-wave ${N}^{*}$ and ${\mathrm{\ensuremath{\Delta}}}^{*}$ resonances), obtained within the field-theoretical framework by using time ordered perturbation theory, yield an overall good description of the experimental data at the level of the relativized constituent quark model of S. Capstick and W. Roberts without any fitting parameters. The only free parameter of the linear confinement potential was fitted previously by Th. Gutsche to reproduce the axial charge of the nucleon. The ground state $\mathrm{\ensuremath{\Delta}}(1232)$ is well reproduced. However, nucleon ground state and most of the radially excited baryon resonances (including Roper) are overestimated. On the contrary, the first band of the orbitally excited baryon resonances with a negative parity are underestimated. At the same time, the second band of the orbitally excited ${\mathrm{\ensuremath{\Delta}}}^{*}$ states with the negative parity are mostly overestimated, while the ${N}^{*}$ states are close to the experimental boxes. The theoretical estimations of the energy levels for the positive parity baryon resonances with $\mathrm{J}=5/2$, $7/2$ are close to the experimental data. At higher energies, where the experimental data are poor, we can extend our model schematically and predict an existence of seven ${N}^{*}$ and four ${\mathrm{\ensuremath{\Delta}}}^{*}$ new states with larger spin values.

Axial-vector form factors for the low lying octet baryons in the chiral quark constituent model

We have calculated the axial-vector form factors of the low lying octet baryons ($N$, $\Sigma$, $\Xi$ and $\Lambda$) in the chiral constituent quark model ($\chi$CQM). In particular, we have studied the implications of chiral symmetry breaking and SU(3) symmetry breaking for the singlet ($g^0_{A}$) and non-singlet ($g^3_{A}$ and $g^8_{A}$) axial-vector coupling constants expressed as combinations of the spin polarizations at zero momentum transfer. The conventional dipole form of parametrization has been used to analyse the $Q^2$ dependence of the axial-vector form factors ($G^0_{A}(Q^2)$, $G^3_{A}(Q^2)$ and $G^8_{A}(Q^2)$). The total strange singlet and non-singlet contents ($G_s^0(Q^2)$, $G_s^3(Q^2)$ and $G_s^8(Q^2)$) of the nucleon determining the strange quark contribution to the nucleon spin ($\Delta s$) have also been discussed.

Isovector axial vector and pseudoscalar transition form factors ofΔin QCD

We investigate the isovector axial vector and pseudoscalar form factors of $\Delta$ baryon by employing light-cone QCD sum rules. Numerical calculations show that the form factors can be well fitted by the exponential form. We make a comparison with the predictions of Lattice QCD, Chiral Perturbation Theory and Quark Model.

Unpolarized transverse momentum-dependent densities based on the modified chiral quark model

We investigate the transverse momentum-dependent (TMD) quark and gluon distribution functions in the modified chiral quark model (χQM). Calculations of the TMD quark and gluon densities, using the modified χQM, are carried out for the first time in this article. For this propose, we first formulate the TMD interactions that occur in the χQM at low Q 2 scale (Q 2 = 0.35 GeV2) and then obtain the TMD parton distributions inside the proton, considering these interactions. To this end, we need to compute the TMD bare quark distributions. These TMD bare densities are calculated using the solution of the Dirac equation with a squared radial symmetry potential. It is shown that our results present appropriate behavior, which is expected for the TMD parton distributions.

Asymmetric sea quark and gluon densities, based on the polarized chiral quark model

We investigate the polarized structure of the proton based on the modified chiral quark model (). We calculate the polarized quark, antiquark and gluon densities inside the proton at low Q2 values using the . We then evolve these densities to high energy scales. The polarized antiquark and gluon distributions are obtained using the . These distributions can be calculated in our model, considering the gluon cloud which surrounds the bare quarks. This is a new feature which was not taken into account previously in the polarized . Using the ‘Pauli-blocking’ ansatz, we are able to extract asymmetric antiquark densities which are flavor dependent. It is shown that our results are in good agreement with the experimental data and also compatible with the different fitting parameterizations. What makes our results more distinctive is that all initial parton densities are obtained via a completely theoretical framework in which we do not need to resort to any specific parameterizations.

Importance of asymptotic freedom for the pseudocritical temperature in magnetized quark matter

Although asymptotic freedom is an essential feature of QCD, it is absent in effective chiral quark models like the Nambu--Jona-Lasinio and linear sigma models. In this work we advocate that asymptotic freedom plays a key role in the recently observed discrepancies between results of lattice QCD simulations and quark models regarding the behavior of the pseudocritical temperature ${T}_{pc}$ for chiral-symmetry restoration in the presence of a magnetic field $B$. We show that the lattice predictions that ${T}_{pc}$ decreases with $B$ can be reproduced within the Nambu--Jona-Lasinio model if the coupling constant $G$ of the model decreases with $B$ and the temperature. Without aiming at numerical precision, we support our claim by considering a simple ansatz for $G$ that mimics the asymptotic-freedom behavior of the QCD coupling constant $1/{\ensuremath{\alpha}}_{s}\ensuremath{\sim}ln(eB/{\ensuremath{\Lambda}}_{\text{QCD}}^{2})$ for large values of $B$.

The bound state problem

We use a diagrammatic method to derive the Faddeev equations of the coupled NΛΛ–ΞNN system and apply them to the bound-state problem of the channel. We use as input the nucleon–nucleon, nucleon–hyperon and hyperon–hyperon interactions obtained from a chiral constituent quark model. We explore different parametrizations of the quark–quark interacting potential. While the system alone is unbound, the full coupled channel problem NΛΛ–ΞNN may present a three-baryon bound state just below threshold. Different from double- hypernuclei with four nucleons or more, where the Pauli principle acts strongly because there is no room for more that four nucleons in S wave, in H the full interaction can act in S wave.

Multiquark contributions to charm baryon spectroscopy

We study possible multiquark contributions to the charm baryon spectrum by considering higher order Fock space components. For this purpose we perform two different calculations. In a first approach we do a coupled-channel calculation of the $ND$ system looking for molecular states. In a second step we allow for the coupling to a heavy baryon--light meson two-hadron system looking for compact exotic five--quark structures. Both calculations have been done within the framework of a chiral constituent quark model. The model, tuned in the description of the baryon and meson spectra as well as the $NN$ interaction, provides parameter-free predictions for charm $+1$ molecular or compact two-hadron systems. Unlike the $N \bar D$ system, no sharp quark-Pauli effects are found. However, the existence of different two-hadron thresholds for the five-quark system will make the coupled-channel dynamics relevant. Only a few channels are candidates to lodge molecular or compact hadrons with a five-quark structure, being specially relevant the $(T)J^P=(0)1/2^-$ and $(T)J^P=(2)5/2^-$ channels. The identification of molecular states and/or compact hadrons with multiquark components either with or without exotic quantum numbers is a challenge of different collaborations like $\bar {\rm P}$ANDA, LHCb, ExHIC or J-PARC.

Pion-assisted charmed dibaryon candidate

The ${\mathrm{\ensuremath{\Lambda}}}_{c}(2286)N$ system is studied in a chiral constituent quark model, and the resulting $s$-wave interaction is used in separable form within three-body models of the $\ensuremath{\pi}{\mathrm{\ensuremath{\Lambda}}}_{c}N$ system with quantum numbers $(C,I,{J}^{P})=(+1,\frac{3}{2},{2}^{+})$. Separable interactions are also used for the dominant $p$-wave pion-baryon channels dominated by the $\mathrm{\ensuremath{\Delta}}(1232)$ and ${\mathrm{\ensuremath{\Sigma}}}_{c}(2520)$ resonances. Faddeev equations with relativistic kinematics are solved on the real axis to search for bound states and in the complex plane to search for three-body resonances. Some of the models considered generate a very narrow bound state, requiring isospin violation for its strong decay. Other models lead to a narrow resonance ($\mathrm{\ensuremath{\Gamma}}\ensuremath{\lesssim}0.4\text{ }\text{ }\mathrm{MeV}$) for a resonance mass below the ${\mathrm{\ensuremath{\Sigma}}}_{c}(2455)N$ threshold. This would be the lowest-lying $C=+1$ dibaryon, with mass estimated as $\ensuremath{\approx}3370\ifmmode\pm\else\textpm\fi{}15\text{ }\text{ }\mathrm{MeV}$.

The unobservable axial-pion mixing in QCD and near-conformal dynamics

We study a chiral quark model of π, σ, ρ, and a 1 mesons in the large-N c limit. We show that the quadratic a 1 − π mixing can be set to zero at zero momentum, thus protecting the g σππ and g ρππ couplings from being contaminated by the corresponding vertices with one or both pions replaced by the axial-vector meson. We further require the chiral-quark Lagrangian to feature an approximate classical scale invariance, the latter being only broken by dimension-two mass terms, and that the longitudinal vector meson scattering amplitudes grow at most like s, where √s is the center-of-mass energy. This allows us to accurately predict the correct value of g σππ , g ρππ , and the a 1 decay constant $$f_{a_1 }$$ . We further show that strongly coupled theories with near-conformal dynamics are expected to feature an approximate custodial chiral symmetry, with interesting phenomenological consequences.

Generalized Beth–Uhlenbeck approach to mesons and diquarks in hot, dense quark matter

An important first step in the program of hadronization of chiral quark models is the bosonization in meson and diquark channels. This procedure is presented at finite temperatures and chemical potentials for the SU(2) flavor case of the NJL model with special emphasis on the mixing between scalar meson and scalar diquark modes which occurs in the 2SC color superconducting phase. The thermodynamic potential is obtained in the Gaussian approximation for the meson and diquark fields and it is given in the Beth–Uhlenbeck form. This allows a detailed discussion of bound state dissociation in hot, dense matter (Mott effect) in terms of the in-medium scattering phase shift of two-particle correlations. It is shown for the case without meson–diquark mixing that the phase shift can be separated into a continuum and a resonance part. In the latter, the Mott transition manifests itself by a change of the phase shift at threshold by π in accordance with Levinson’s theorem, when a bound state transforms to a resonance in the scattering continuum. The consequences for the contribution of pionic correlations to the pressure are discussed by evaluating the Beth–Uhlenbeck equation of state in different approximations. A similar discussion is performed for the scalar diquark channel in the normal phase. Further developments and applications of the developed approach are outlined.

A dynamical mass and confinement in nucleon model

A possible dynamical softening of the Chiral bag is studied in connection with the chiral quark model and the Nambu–Jona–Lasinio (NJL) model. It is demonstrated that the bag functions constructed by the pion degrees is able to confine quark through generation of the rising effective mass of valence quark due to the pion dressing and break chiral symmetry dynamically. The tendency of the bag functions toward the MIT bag is illustrated in the large-n limit for a solitonic configuration of the chiral field Un(r) for which U1(r) is the Skyrmion profile. The mass running with the length scale agrees with that of the NJL Model for n ≥ 2.

Strong decays of χcJ(2P) and χcJ(3P)

In the framework of the chiral quark model, the mass spectrum of χcJ (J = 0, 1, 2, n = 1, 2, 3) is studied with the Gaussian expansion method. Using the wave functions obtained in the study of mass spectrum, the open charm two-body strong decay widths of these states are calculated by using the 3P0 model. The results show that the masses of χcJ(1P) and χc2(2P) are consistent with the experimental data. But the strong decay width of χc2(2P) is three times that of the experimental value. The decay width of χc1(2P) is sensitive to its mass. In the quark-antiquark picture, the width is about 385 MeV. However, if the channel coupling effects shift its mass to 3872 MeV, its decay width will be around 1 MeV. The possibility of assigning the state X(3872) as χc1(2P) cannot be excluded. To assign X(3915) as χc0(2P) is disfavored, due to the unmatching of decay channel. For the χcJ(3P) states, no states have been assigned. The possible candidates of χc0(3P) are X(4160) and X(4140). Their masses are close to the theoretical ones. The experimental branching ratio of X(4160), \(\Gamma (X(4160) \to D\bar D)/\Gamma (X(4160) \to D*\bar D*) < 0.09\) is compatible with that of χc0(3P), 0.07. However the broad decay width of X(4160) cannot be explained by the open charm two-body decay. To assign X(4140) as χc0(3P) is also possible, due to the compatibility of the total decay width, the further measurement of decay modes of X(4140) are expected to justify the assignment.

Pion distribution amplitude and the pion-photon transition form factor in a nonlocal chiral quark model

We study the pion Distribution Amplitude (\pi DA) in the context of a nonlocal chiral quark model. The corresponding Lagrangian reproduces the phenomenological values of the pion mass and decay constant, as well as the momentum dependence of the quark propagator obtained in lattice calculations. It is found that the obtained \pi DA has two symmetric maxima, which arise from the new contributions generated by the nonlocal character of the interactions. This \pi DA is applied to leading order and next-to-leading order calculations of the pion-photon transition form factor. Implications of the results are discussed.

Study of baryon octet electromagnetic form factors in perturbative chiral quark model

The electromagnetic properties of baryon octet are studied in the perturbative chiral quark model (PCQM). The relativistic quark wave function is extracted by fitting the theoretical results of the proton charge form factor to experimental data and the predetermined quark wave function is applied to study the electromagnetic form factors of other octet baryons as well as magnetic moments, charge and magnetic radii. The PCQM results are found, based on the predetermined quark wave function, in good agreement with experimental data.

Dynamical calculation of theΔΔdibaryon candidates

We perform a dynamical calculation of the $\Delta\Delta$ dibaryon candidates with $IJ^{P}=03^{+}$ and $IJ^{P}=30^{+}$ in the framework of two constituent quark models: the quark delocalization color screening model and the chiral quark model. Our results show that the dibaryon resonances with $IJ^{P}=03^{+}$ and $IJ^{P}=30^{+}$ can be formed in both models. The mass and width of $IJ^{P}=03^{+}$ state are smaller than that of $IJ^{P}=30^{+}$ state due to the one-gluon-exchange interaction between quarks. The resonance mass and decay width of $IJ^{P}=03^{+}$ state in both models agree with that of the recent observed resonance in the reaction $pn \rightarrow d\pi^{0}\pi^{0}$. The $IJ^{P}=30^{+}$ $\Delta\Delta$ is another dibaryon candidate with smaller binding energy and larger width. The hidden-color channel coupling is added to the chiral quark model, and we find it can lower the mass of the dibaryons by 10-20 MeV.

Asymptotic behaviour of pion-pion total cross-sections

We derive a sum rule which shows that the Froissart-Martin bound for the asymptotic behaviour of the $\pi\pi$ total cross sections at high energies, if modulated by the Lukaszuk-Martin coefficient of the leading $\log^2 s$ behaviour, cannot be an optimal bound in QCD. We next compute the total cross sections for $\pi^+ \pi^-$, $\pi^{\pm} \pi^0$ and $\pi^0 \pi^0$ scattering within the framework of the constituent chiral quark model (C$\chi$QM) in the limit of a large number of colours $\Nc$ and discuss their asymptotic behaviours. The same $\pi\pi$ cross sections are also discussed within the general framework of Large-\Nc~QCD and we show that it is possible to make an Ansatz for the isospin $I=1$ and $I=0$ spectrum which satisfy the Froissart-Martin bound with coefficients which, contrary to the Lukaszuk-Martin coefficient, are not singular in the chiral limit and have the correct Large-\Nc~counting. We finally propose a simple phenomenological model which matches the low energy behaviours of the $\sigma_{\pi^{\pm}\pi^0}^{\rm total}(s)$ cross section predicted by the C$\chi$QM with the high energy behaviour predicted by the Large-$\Nc$ Ansatz. The magnitude of these cross sections at very high energies is of the order of those observed for the $pp$ and $p{\bar p}$ scattering total cross sections.

Form factors for semileptonicDdecays

We study the form factors for semileptonic decays of $D$-mesons. That is, we consider the matrix element of the weak left-handed quark current for the transitions $D \rightarrow P$ and $D \rightarrow V$, where $P$ and $V$ are light pseudoscalar or vector mesons, respectively. Our motivation to perform the present study of these form factors are future calculations of non-leptonic decay amplitudes. We consider the form factors within a class of chiral quark models. Especially, we study how the Large Energy Effective Theory (LEET) limit works for $D$-meson decays. Compared to previous work we also introduce light vector mesons $V = \rho, K^*,...$ within chiral quark models. In order to determine some of the parameters in our model, we use existing data and results based on some other methods like lattice calculations, light-cone sum rules, and heavy-light chiral perturbation theory. We also obtain some predictions within our framework.

Asymmetries of quark sea in nucleon

The effects of in determining the flavor structure of the octet baryons have been investigated in the chiral constituent quark model. The chiral constituent quark model is able to qualitatively generate the requisite amount of quark sea and is also known to provide a satisfactory explanation of the spin and related issues in the nonperturbative regime. The phenomenological implications of the quark sea asymmetries in the nucleon have been investigated to understand the importance of quark sea at lower values of the Bjorken scaling variable. After the first direct evidence for the point-like constituents in the nucleon, identified as the valence quarks with spin-1/2 in the naive constituent quark model (NQM) (1-3), a lot of experiments have been conducted to probe the structure of the in the deep inelastic scattering (DIS) experiments. Surprisingly, the DIS results in the early 80's (4) indicated that the valence quarks of the carry only about 30% of its spin and is referred to as the proton spin crisis in the NQM. These results provided the first evidence for the being composed of three valence quarks surrounded by an indistinct sea of quark-antiquark pairs (henceforth referred to as the sea). In the present day, the study of the composition of hadrons can be said to be primarily the study of the quark sea and gluons and is considered as one of the active areas in hadronic physics. The conventional expectation that the quark sea perhaps can be obtained through the perturbative production of the quark-antiquark pairs by gluons produces nearly equal numbers of ¯ u and ¯ d. Until early 90's a symmetric sea w.r.t. ¯ u and ¯ d was assumed, however, the famous New Muon Collaboration in 1991 (5) established the quark sea asymmetry of the unpolarized quarks in the case of nucleon by measuring ¯ d − ¯ u giving first clear evidence for the nonperturbative origin of the quark sea. This was later confirmed by the Drell-Yan experiments (6) which measured a large quark sea asymmetry ratio ¯ d/¯ u reminding us that the study of the quark sea is intrinsically a nonperturbative phenomena and it is still a big challenge to perform these calculations from the first principles of QCD. The chiral constituent quark model (CQM) (7) can yield an adequate description of the quark sea generation through the chiral fluctuations. The basic idea is based on the possibility that chiral symmetry breaking takes place at a distance scale much smaller than the confinement scale. In this region, the effective degrees of freedom are the valence quarks and the internal Goldstone bosons (GBs) which are coupled to the valence quarks (8-10) allowing a simple and intuitive method to investigate

$\Sigma_c {\bar D}$ AND $\Lambda_c {\bar D}$ STATES IN A CHIRAL QUARK MODEL

We report our recent work on a dynamical investigation of the [Formula: see text] and [Formula: see text] states in a chiral quark model. Our results show that the [Formula: see text] interaction is attractive, which consequently results in a [Formula: see text] bound state with the binding energy of about 5-42 MeV, unlike the case of [Formula: see text] state, which has a repulsive interaction and thus is unbound.