Finding a way to determine the pion distribution amplitude from the experimental data

Abstract

It is believed that one can extract more accurate information of the pion distribution amplitude from the pion-photon transition form factor (TFF) 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.