Tao Huang, Xing-Gang Wu, Tao Zhong
It is believed that the pion-photon transition form factor (TFF) should get more information on the pion distribution amplitude (DA) due to the single pion in this process. However the BABAR and Belle data of the pion-photon TFF have a big difference for $Q^2\in [15,40]$ GeV$^2$, and at present, the pion DA can not be definitely determined from the pion-photon TFF. it is crucial to find the right pion DA behavior and to determine which data is more reliable. In this letter, we perform a combined analysis of the most existing data of the processes involving pion by using a general model for the pion wavefunction/DA. Such a DA model can mimic all the existed pion DA behaviors, whose parameters can be fixed by the constraints from the processes $\pi^0\to\gamma\gamma$, $\pi\to\mu\nu$, $B\to\pi l \nu$, and etc. Especially, we examine the $B \rightarrow \pi$ transition form factors that provides another constraint to the parameter $B$ in our DA model, which results in $B \in[0.00,0.29]$. This inversely shows that the predicted curve for the pion-photon TFF is between the BABAR and Belle data in the region $Q^2\in$ $[15,40]$ GeV$^2$. It will be tested by coming more accurate data at large $Q^2$ region, and the definite behavior of pion DA can be concluded finally.
View original:
http://arxiv.org/abs/1303.2301
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