A generalized 3 flavor Nambu-Jona--Lasinio Lagrangian including the explicit chiral symmetry breaking interactions which contribute at the same order in the large $1/N_c$ counting as the $U_A(1)$ t Hooft flavor determinant is considered to obtain the mixing angles in the $pi^0-eta-eta$ system and related current quark mass ratios in close agreement with phenomenological values. At the same time an accurate ordering and magnitude of the splitting of states in the low lying pseudoscalar nonet is obtained.
The claim that the light quark mass ratio (m_d - m_u)/m_s can be extracted from the decay width ratio Gamma(eta -> pi^0 pi^+ pi^-)/Gamma(eta -> eta pi^+ pi^-) is critically investigated within a U(3) chiral unitary framework. The influence of the rec
ent VES data on the eta -> eta pi^+ pi^- decay is also discussed.
We investigate the isospin symmetry breaking effects within a recently derived Nambu-Jona-Lasinio related model by fitting the measured pseudoscalar meson masses and weak decay couplings $f_pi$, $f_K$. Our model contains the next to leading order ter
ms in the $1/N_c$ expansion of the effective multi-quark Lagrangian, including the ones that break the chiral symmetry explicitly. We show the important phenomenological role of these interactions: (1) they lead to an accurate fit of the low-lying pseudoscalar nonet characteristics; (2) they account for a very good agreement of the current quark masses with the present PDG values; (3) they reduce by $40%$ the ratio $epsilon/epsilon$ of the $pi_0-eta$ and $pi_0-eta$ mixing angles, as compared to the case that contemplates explicit breaking only in the leading order, bringing it in consonance with the quoted values in the literature. The conventional NJL-type models fail in the joint description of these parameters.
We report our investigation on the doubly virtual TFFs $F_{{rm P}gamma^*}(Q^2_1,Q^2_2)$ for the ${rm P}togamma^*(q_1)gamma^*(q_2) ;({rm P}=pi^0,eta,eta)$ transitions using the light-front quark model (LFQM). Performing a LF calculation in the exactly
solvable manifestly covariant Bethe-Salpeter (BS) model as the first illustration, we used $q^+_1=0$ frame and found that both LF and manifestly covariant calculations produce exactly the same results for $F_{{rm P}gamma^*}(Q^2_1,Q^2_2)$. This confirms the absence of the LF zero mode in the doubly virtual TFFs. We then mapped this covariant BS model to the standard LFQM using the more phenomenologically accessible Gaussian wave function provided by the LFQM analysis of meson mass spectra. For the numerical analyses of $F_{{rm P}gamma^*}(Q^2_1,Q^2_2)$, we compared our LFQM results with the available experimental data and the perturbative QCD (pQCD) and the vector meson dominance (VMD) model predictions. As $(Q^2_1, Q^2_2)toinfty$, our LFQM result for doubly virtual TFF is consistent with the pQCD prediction, i.e. $F_{{rm P}gamma^*}(Q^2_1, Q^2_2)sim 1/(Q^2_1 + Q^2_2)$, while it differs far from the result of VMD model which behaves $F^{rm VMD}_{{rm P}gamma^*}(Q^2_1, Q^2_2)sim 1/(Q^2_1 Q^2_2)$. Our LFQM prediction for $F_{etagamma^*}(Q^2_1,Q^2_2)$ shows an agreement with the very recent experimental data obtained from the BaBar collaboration for the ranges of $2< Q^2_1, Q^2_1 <60$ GeV$^2$.
We investigate the $(pi^0,eta,eta)togamma^*gamma$ transitions both for the spacelike region and the timelike region using the light-front quark model (LFQM). In particular, we present the new direct method to explore the timelike region without resor
ting to mere analytic continuation from the spacelike region to the timelike region. Our direct calculation in timelike region shows the complete agreement not only with the analytic continuation result from the spacelike region but also with the result from the dispersion relation between the real and imaginary parts of the form factor. For the low energy regime, we compare our LFQM results of the transition form factors (TFFs) for the low timelike momentum transfer region and the slope parameters at $q^2=0$ with the recent experimental data from the Dalitz decays of $(pi^0,eta,eta)$. For the high energy regime, we incorporate the QCD factorization in our LFQM to examine the asymptotic behavior of TFFs both for the spacelike region and the timelike region. We compare our results with the available experimental data.
Using a sample of $1.3times 10^9$ $J/psi$ events collected with the BESIII detector, we report the first observation of $eta^{prime}topi^{+}pi^{-}pi^{+}pi^{-}$ and $eta^{prime}topi^{+}pi^{-}pi^{0}pi^{0}$. The measured branching fractions are $mathcal
{B}$($eta^{prime}topi^{+}pi^{-}pi^{+}pi^{-}$) = $(8.53pm0.69({rm stat.})pm0.64({rm syst.}))times10^{-5}$ and $mathcal{B}$($eta^{prime}topi^{+}pi^{-}pi^{0}pi^{0}$) = $(1.82pm0.35({rm stat.})pm0.18({rm syst.}))times10^{-4}$, which are consistent with theoretical predictions based on a combination of chiral perturbation theory and vector-meson dominance.