Abstract
It is noted that the low-energy behavior of the pion-photon transition form factor $F_{\pi\gamma}(Q^2)$ is sensitive to the transverse distribution of the pion wavefunction, and its high-energy behavior is sensitive to the longitudinal one. Thus a careful study on $F_{\pi\gamma}(Q^2)$ can provide helpful information on the pion wavefunction precisely. In this paper, we present a combined analysis of the data on $F_{\pi\gamma}(Q^2)$ reported by the CELLO, the CLEO, the BABAR and the BELLE collaborations. It is performed by using the method of least squares. By using the combined measurements of BELLE and CLEO Collaborations, the pion wavefunction longitudinal and transverse behavior can be fixed to a certain degree, i.e. we obtain $\beta \in [0.691,0.757] \rm GeV$ and $B \in [0.00,0.235]$ for $P_{\chi^2} \geq 90\%$, where $\beta$ and $B$ are two parameters of a convenient pion wavefunction model whose distribution amplitude can mimic the various longitudinal behavior under proper choice of parameters. We observe that the CELLO, CLEO and BELLE data are consistent with each other, all of which prefers the asymptotic-like distribution amplitude; while the BABAR data prefers a more broad distribution amplitude, such as the CZ-like one.
Highlights
When Q2 ∼ a few GeV2, one should take the k⊥terms into account so as to achieve a reliable prediction of Fπγ (Q2) [7,8,9,10,11,12,13,14,15]
When Q2 is large enough, the k⊥terms become less important, and the transition form factor (TFF) Fπγ (Q2) shall be dominated by the longitudinal behavior of the pion wave function,which is related to the pion distribution amplitude (DA)
We shall study the pion–photon TFF Fπγ (Q2) by using a convenient pion wave function model. This pion wave function is constructed from the revised lightcone harmonic oscillator model and its DA can conveniently mimic the asymptotic-like to more broad longitudinal behavior via proper choices of input parameters
Summary
When Q2 ∼ a few GeV2, one should take the k⊥terms into account so as to achieve a reliable prediction of Fπγ (Q2) [7,8,9,10,11,12,13,14,15]. We shall study the pion–photon TFF Fπγ (Q2) by using a convenient pion wave function model. This pion wave function is constructed from the revised lightcone harmonic oscillator model and its DA can conveniently mimic the asymptotic-like to more broad longitudinal behavior via proper choices of input parameters. We perform a combined analysis of the experimental data reported by the CELLO, the CLEO, the BABAR and the BELLE Collaborations, with an attempt to extract useful information of the pion wave function. A combined analysis for the experimental data reported by the CELLO, the CLEO, the BABAR, and the BELLE Collaborations is presented in Sect.
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