Finding a Way to Determine the Pion Distribution Amplitude from the Experimental Data

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 Q²∈15,40 GeV², 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. 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 π⁰→γγ, π→μν, and B→πl ν, etc. Especially, we examine the B →π transition form factors that provides another constraint to the parameter B in our DA model, which results in B∈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 Q²∈15,40 GeV². It will be tested by coming more accurate data in large Q² region, and the definite behavior of pion DA can be concluded finally.