Pion radii in the nonlocal chiral quark model

The electromagnetic radius of a charged pion and the transition radius of a neutral pion are calculated in the framework of the nonlocal chiral quark model. It is shown in this model that the vector meson contributions to the pion radii are noticeably suppressed in comparison with a similar contribution in the local Nambu-Jona-Lasinio model. The form factor for the process is calculated for -1 GeV²< q ² < 1.6 GeV². Our results are in satisfactory agreement with experimental data.Received: 28 November 2003, Published online: 13 July 2004PACS: 14.40.-n Mesons - 11.10.Lm Nonlinear or nonlocal theories and models - 12.39.Ki Relativistic quark model     

Low energy theorems in a nonlocal chiral quark model at finite temperature

We solve the Dyson equation and the Bethe-Salpeter equation for a nonlocal effective quark interaction kernel which is instantaneous and separable. The momentum-dependent dynamical quark mass, the scalar and pseudoscalar meson masses, the pion decay constant and the quark meson coupling constant are calculated at finite temperature in the Hartree approximation for the quark self energy. We obtain relations between these quantities, which coincide to leading order in the current quark mass (m ₀/Δm) with the basic low energy theorems: the Goldstone theorem, the Gell-Mann-Oakes-Renner relation and the Goldberger-Treimann relation at finite temperature. A formula for the σ?π mass gap is obtained which exhibits an additional contribution from the momentum dependence of the quark mass.     

Forward-like functions for dual parametrization of GPDs from the nonlocal chiral quark model

We derive the set of inversion relations allowing to establish the link between the dual parametrization of GPDs and a broad class of phenomenological models for GPDs. As an example we consider the results of the calculation of the pion GPD in the nonlocal chiral quark model (NlCQM) to recover the set of forward-like functions Q _2ν representing this GPD in the framework of dual parametrization. We also argue that the Abel tomography method overlooks possible δ -function-like contributions to the GPD quintessence function which make explicit contribution to the D form factor.     

H-particle in a chiral quark model

In this paper we discuss the binding energy of the H-particle using a chiral quark model, where pion exchange plays an important role to reproduce the mass difference between the nucleon and Δ resonance. Since the main source for the bound H-particle is believed to be the color magnetic interaction, which gives the nucleon and Δ mass difference, it is very interesting to investigate whether the chiral quark model gives rise to the bound H-particle or not. We employ an extended resonating group method in order to take into account the possibility of a change of baryon wave functions when two baryons interact with each other. We found that a change of baryon size together with the Hamiltonian which consists of gluon, pseudoscalar meson and sigma meson exchange potentials gives rise to the bound H-particle. The binding energy is found to be about 25 MeV in a hybrid chiral quark model. Differences between the ordinary gluon dominant model and chiral quark models are also investigated. It is found that a pure chiral model has no bound state when the widely used sigma-quark coupling strength is employed.     

Pion radiative weak decays in nonlocal chiral quark models

We analyze the radiative pion decay π⁺→e⁺νeγ${\pi }^{+}\to e^{+}{\nu }_e\gamma$ within nonlocal chiral quark models that include wave function renormalization. In this framework we calculate the vector and axial-vector form factors FV$F_V$ and FA$F_A$ at q²=0$q^2=0$ — where q²$q^2$ is the e⁺νe$e^{+}{\nu }_e$ squared invariant mass — and the slope a   of FV(q²)$F_V(q^2)$ at q²→0$q^2\to 0$. The calculations are carried out considering different nonlocal form factors, in particular those taken from lattice QCD evaluations, showing a reasonable agreement with the corresponding experimental data. The comparison of our results with those obtained in the (local) NJL model and the relation of FV$F_V$ and a   with the form factor in π⁰→γ^?γ${\pi }^0\to {\gamma }^{?}\gamma$ decays are discussed.     

Photon-pion transition form factor at high photon virtualities within the nonlocal chiral quark model

Recently, the BABAR collaboration reported the measurements of the photon-pion transition form factor F _πγγ*(Q ²), which are in strong contradiction to the predictions of the standard factorization approach to perturbative QCD. In the present work, based on a nonperturbative approach to the QCD vacuum and on rather universal assumptions, we show that there exist two asymptotic regimes for the pion transition form factor. One regime with the asymptotic behavior F _πγ*γ(Q ²) ∼ 1/Q ² corresponds to the result of the standard QCD factorization approach, while other violates the standard factorization and leads to asymptotic behavior as F _πγ*γ(Q ²) ∼ ln(Q ²)/Q ². Furthermore, considering specific nonlocal chiral quark models, we find the region of parameters, where the existing CELLO, CLEO and BABAR data for the pion transition form factor are successfully described.     

Pion polarizability in a chiral quark model

The pion polarizability is calculated in a chiral meson-quark model at the one-loop level. The results are in complete agreement with earlier ones obtained within a chiral meson-baryon theory. A critical discussion of a recent paper by Llanta and Tarrach is given.     

Phase diagram of neutron star quark matter in nonlocal chiral models

We analyze the phase diagram of two-flavor quark matter under neutron star constraints for a nonlocal covariant quark model within the mean-field approximation. Applications to cold compact stars are discussed.     

Quark-pion coupling constant in a chiral quark model

Incorporating chiral-symmetry to the potential model of quarks with confining potentialU(r)=1/2 (1 +γ°)ar ² with m _q =10 MeV anda=2.273 fm⁻³ that gives a reasonable quark-core contribution to μ _p , 〈r ² 〉 _p ^1/2 andg _A , the quark-pion coupling constant for quarks in a nucleon is estimated.G _qqπ ² /4π obtained between 0.4 and 0.5 is consistent with those extracted from experimental vector meson decay-width ratios by Suzuki and Bhaduri. The nucleon-pion coupling constantG _NNπ ² /4π comes out to be of the order of 13.1 in reasonable agreement with the experimental value.     

Hadron structure functions in a chiral quark model

We present a consistent regularization procedure for calculating hadron structure functions in a bosonized chiral quark model. We find that the Pauli-Villars regularization scheme is most suitable. We also summarize the phenomenology of structure functions calculated in the valence quark approximation.     

Vector and axial-vector correlators in a non-local chiral quark model

The behavior of the non-perturbative parts of the isovector-vector and isovector and isosinglet axial-vector correlators at Euclidean momenta is studied in the framework of a covariant chiral quark model with non-local quark-quark interactions. The gauge covariance is ensured with the help of the P-exponents, with the corresponding modification of the quark-current interaction vertices taken into account. The low- and high-momentum behavior of the correlators is compared with the chiral perturbation theory and with the QCD operator product expansion, respectively. The V-A combination of the correlators obtained in the model reproduces quantitatively the ALEPH and OPAL data on hadronic decays, transformed into the Euclidean domain via dispersion relations. The predictions for the electromagnetic mass difference and for the pion electric polarizability are also in agreement with the experimental values. The topological susceptibility of the vacuum is evaluated as a function of the momentum, and its first moment is predicted to be . In addition, the fulfillment of the Crewther theorem is demonstrated.Received: 9 May 2003, Revised: 22 September 2003, Published online: 4 November 2003     

K-p scattering and hyperon excitations in a chiral quark model

A chiral quark-model approach is employed to study theˉ KN scattering at low energies.The processes of Kˉp →Σ 0 π 0,Λπ 0 andˉ K 0 n at P K 800 MeV/c (i.e.the center mass energy W 1.7 GeV) are investigated.The analysis shows that the Λ(1405)S 01 dominates the processes Kˉp →Σ 0 π 0,ˉ K 0 n in the energy region considered here.Around P K 400 MeV/c,the Λ(1520)D 03 is responsible for a strong resonant peak in the cross section of Kˉp →Σ 0 π 0 andˉ K 0 n.To reproduce the data,an unexpectedly large coupling for Λ(1520)D 03 to KN is needed.In contrast,the coupling for Λ(1670)S 01 to KN appears to be weak,which could be due to configuration mixings between Λ(1405)S 01 and Λ(1670)S 01 .By analyzing Kˉ p →Λπ 0,evidences for two low mass S-wave states,Σ(1480)S 11 and Σ(1560)S 11,seem to be available.With these two states,the reaction Kˉp →ˉ K 0 n can also be described well.However,it is difficult to understand the low masses of Σ(1480)S 11 and Σ(1560)S 11 .The s-channel amplitudes for Kˉp →Λπ 0 are also larger than the naive quark model expectations.The non-resonant background contributions,i.e.t-channel and/or u-channel,also play important roles in the explanation of the angular distributions due to amplitude interferences.     

K－p scattering and hyperon excitations in a chiral quark model

A chiral quark-model approach is employed to study theˉ KN scattering at low energies.The processes of Kˉp → Σ 0 π 0,Λπ 0 andˉ K 0 n at P K 800 MeV/c （i.e.the center mass energy W 1.7 GeV） are investigated.The analysis shows that the Λ（1405）S 01 dominates the processes Kˉp → Σ 0 π 0,ˉ K 0 n in the energy region considered here.Around P K 400 MeV/c,the Λ（1520）D 03 is responsible for a strong resonant peak in the cross section of Kˉp → Σ 0 π 0 andˉ K 0 n.To reproduce the data,an unexpectedly large coupling for Λ（1520）D 03 to KN is needed.In contrast,the coupling for Λ（1670）S 01 to KN appears to be weak,which could be due to configuration mixings between Λ（1405）S 01 and Λ（1670）S 01 .By analyzing Kˉ p → Λπ 0,evidences for two low mass S-wave states,Σ（1480）S 11 and Σ（1560）S 11,seem to be available.With these two states,the reaction Kˉp →ˉ K 0 n can also be described well.However,it is difficult to understand the low masses of Σ（1480）S 11 and Σ（1560）S 11 .The s-channel amplitudes for Kˉp → Λπ 0 are also larger than the naive quark model expectations.The non-resonant background contributions,i.e.t-channel and/or u-channel,also play important roles in the explanation of the angular distributions due to amplitude interferences.     

Scalar mesons in a chiral quark model with glueball

Ground-state scalar isoscalar mesons and a scalar glueball are described in a U(3)×U(3) chiral quark model of the Nambu-Jona-Lasinio (NJL) type with 't Hooft interaction. The latter interaction produces singlet-octet mixing in the scalar and pseudoscalar sectors. The glueball is introduced into the effective meson Lagrangian as a dilaton on the base of scale invariance. The mixing of the glueball with scalar isoscalar quarkonia and amplitudes of their decays into two pseudoscalar mesons are shown to be proportional to current quark masses, vanishing in the chiral limit. Mass spectra of the scalar mesons and the glueball and their main modes of strong decay are described. Received: 14 July 2000 / Accepted: 31 July 2000     

X(2900) in a chiral quark model

Recently,the LHCb Collaboration reported their observation of the first two fully open-flavor tetraquark states named Xo(2900) and X_1(2900) with unknown parity.Inspired by the report,we consider all the possible fourquark 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,R_0(2914) with Γ=42 MeV,R1(2906) with Γ=29 MeV,R_1(2912) with Γ=10 McV,Rj(2920) with Γ=9 MeV,and R_J(2842) with Γ=24 MeV,originate in the cs■ system.Compared with experimental data,R_0(2914) with Γ=42 MeV may be an optimal X_0(2900) candidate.However,none of the resonances have a similar width for X_1(2900).Hence,further study is required.     

Nucleon structure in the perturbative chiral quark model

We give an overview of recent applications of the perturbative chiral quark model (PCQM) in the analysis of the structure of the nucleon. The PCQM is based on an effective Lagrangian, where baryons are described by relativistic valence quarks and a perturbative cloud of Goldstone bosons as required by chiral symmetry. We discuss applications to the electromagnetic properties of the nucleon, to σ-term physics, to πN scattering including radiative corrections and to the strange form factors of the nucleon.