The doubly virtual $({\pi }^0,\eta ,{\eta }^{\prime })\to {\gamma }^{\ast }{\gamma }^{\ast }$ transition form factors in the light-front quark model

Abstract

We report our investigation on the doubly virtual TFFs $F_{\mathrm{P}{\gamma }^{\ast }}(Q_1^2,Q_2^2)$ for the $\mathrm{P}\to {\gamma }^{\ast }(q_1){\gamma }^{\ast }(q_2)(\mathrm{P}={\pi }^0,\eta ,{\eta }^{\prime })$ 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 $F_{\mathrm{P}{\gamma }^{\ast }}(Q_1^2,Q_2^2)$. 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 $F_{\mathrm{P}{\gamma }^{\ast }}(Q_1^2,Q_2^2)$, we compared our LFQM results with the available experimental data and the perturbative QCD (pQCD) and the vector meson dominance (VMD) model predictions. As $(Q_1^2,Q_2^2)\to \infty$, our LFQM result for doubly virtual TFF is consistent with the pQCD prediction, i.e. $F_{\mathrm{P}{\gamma }^{\ast }}(Q_1^2,Q_2^2)\sim 1/(Q_1^2+Q_2^2)$, while it differs far from the result of VMD model which behaves $F_{\mathrm{P}{\gamma }^{\ast }}^{\mathrm{VMD}}(Q_1^2,Q_2^2)\sim 1/(Q_1^2{Q}_2^2)$. Our LFQM prediction for $F_{{\eta }^{\prime }{\gamma }^{\ast }}(Q_1^2,Q_2^2)$ shows an agreement with the very recent experimental data obtained from the BaBar collaboration for the ranges of $2<Q_1^2,Q_1^2<60$ GeV${}^2$.

7 pages, 6 figures. Slight change of title, Correct some typos; version to appear in Phys. Rev.D. arXiv admin note: substantial text overlap with arXiv:1708.00736

References in corpus (14)

• Decay constants and radiative decays of heavy mesons in light-front quark model
• Study of the electromagnetic transition form-factors in η-> μ^+μ^-γand ω-> μ^+μ^-π^0 decays with NA60
• Measurement of the pseudoscalar mixing angle and ${\eta }^{\prime }$ gluonium content with KLOE detector
• Distribution amplitudes and decay constants for $(\pi ,K,\rho ,K^{\ast })$ mesons in light-front quark model
• Lattice calculation of the pion transition form factor ${\pi }^0\to {\gamma }^{\ast }{\gamma }^{\ast }$
• Semileptonic and radiative decays of the B_c meson in light-front quark model
• Observation of the Dalitz Decay ${\eta }^{\prime }\to \gamma e^{+}{e}^{-}$
• Consistency of the light-front quark model with chiral symmetry in the pseudoscalar meson analysis
• Measurement of the ${\pi }^0$ electromagnetic transition form factor slope
• Measurement of the pi^0 -> e^+e^-gamma Dalitz decay at the Mainz Microtron
• Complete structure dependent analysis of the decay $P\to l^{+}{l}^{-}$
• Spacelike and timelike form factors for the $({\pi }^0,\eta ,{\eta }^{\prime })\to {\gamma }^{\ast }\gamma$ transitions in the light-front quark model
• Two-particle twist-3 distribution amplitudes of the pion and kaon in the light-front quark model
• Twist-3 Distribution Amplitudes of Pion in the Light-Front Quark Model

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