The longitudinal and transverse distributions of the pion wavefunction from the present experimental data on the pion-photon transition form factor

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 $\beta \in [0.691,0.757]\mathrm{GeV}$ and $B\in [0.00,0.235]$ for $P_{{\chi }^2}\ge 90\%$, 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.

7 pages, 10 figures

References in corpus (11)

• Big-Bang Nucleosynthesis
• Measurement of gamma gamma* --> pi0 transition form factor at Belle
• Comparing antithetic trends of data for the pion-photon transition form factor
• Pion transition form factor in k_T factorization
• Next-to-leading-order corrections to exclusive processes in $k_T$ factorization
• Determination of the pion distribution amplitude
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• Heavy and light meson wavefunctions
• Information on the Pion Distribution Amplitude from the Pion-Photon Transition Form Factor with the Belle and BaBar Data
• The pion distribution amplitude and the pion-photon transition form factor in a nonlocal chiral quark model
• Theoretical description and measurement of the pion-photon transition form factor

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• $\eta$-$\gamma$ and ${\eta }^{\prime }$-$\gamma$ transition form factors in a nonlocal NJL model
• Constraint of $\xi$-moments calculated with QCD sum rules on the pion distribution amplitude models
• Improved estimates of the pion-photon transition form factor in the $(1\le {\mathbf{Q}}^2\le 5)$~GeV${}^2$ range and their theoretical uncertainties
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