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Register a new userSpacelike and timelike form factors for the $(pi^0,eta,eta)togamma^*gamma$ transitions in the light-front quark model
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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 resorting 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.
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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$^2$.
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 light-front quark model analysis of the meson-photon transition form factor $F_{Pgamma} (Q^2)$ amenable both for the spacelike region ($Q^2 >0$) and the timelike region ($Q^2 <0$) provides a systematic twist expansion of $Q^2 F_{Pgamma} (Q^2)$ for the high $|Q^2|$ region. Investigating $F_{Pgamma} (Q^2) (P = eta_c,eta_b)$ for the entire kinematic regions of $Q^2$, we examine the twist-2 and twist-3 distribution amplitudes of $(eta_c,eta_b)$ mesons in the light-front quark model and quantify their contributions to $Q^2 F_{(eta_c,eta_b)gamma}(Q^2)$. Our numerical results for the normalized transition form factor $F_{(eta_c,eta_b)gamma}(Q^2)/F_{(eta_c,eta_b)gamma}(0)$ and the decay width $Gamma_{(eta_c,eta_b)togammagamma}$ are compared with the available data checking the sensitivity of our model to the variation of the constituent quark masses.
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 recent VES data on the eta -> eta pi^+ pi^- decay is also discussed.
The ratio R_{eta}=Gamma(eta -> pi^+pi^-gamma)/Gamma(eta -> pi^+pi^-pi^0) has been measured by analyzing 22 million phi to eta gamma decays collected by the KLOE experiment at DAPhiNE, corresponding to an integrated luminosity of 558 pb^{-1}. The eta to pi^+pi^-gamma proceeds both via the rho resonant contribution, and possibly a non-resonant direct term, connected to the box anomaly. Our result, R_{eta}= 0.1856pm 0.0005_{stat} pm 0.0028_{syst}, points out a sizable contribution of the direct term to the total width. The di-pion invariant mass for the eta -> pi^+pi^-gamma decay could be described in a model-independent approach in terms of a single free parameter, alpha. The determined value of the parameter alpha is alpha = (1.32 pm 0.08_{stat} +0.10/-0.09_{syst}pm 0.02_{theo}) GeV^{-2}
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