Doubly virtual (π0,η,η′) →γ∗γ∗ transition form factors in the light-front quark model

We report our investigation on the doubly virtual transition form factors (TFFs) FPγ∗(Q12,Q22) for the P→γ∗(q1)γ∗(q2)(P=π0,η,η′) 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 use the q1+=0 frame and find that both LF and manifestly covariant calculations produce exactly the same results for FPγ∗(Q12,Q22). This confirms the absence of the LF zero mode in the doubly virtual TFFs. We then map 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 FPγ∗(Q12,Q22), we compare our LFQM results with the available experimental data and the perturbative QCD (pQCD) and vector meson dominance (VMD) model predictions. As (Q12,Q22)→, our LFQM result for doubly virtual TFF is consistent with the pQCD prediction, i.e., FPγ∗(Q12,Q22)∼1/(Q12+Q22), while it differs greatly from the result of the VMD model, which behaves as FPγ∗VMD(Q12,Q22)∼1/(Q12Q22). Our LFQM prediction for Fη′γ∗(Q12,Q22) shows an agreement with the very recent experimental data obtained from the BABAR Collaboration for the ranges of 2<(Q12,Q22)<60 GeV2.