Determination of pion distribution amplitudes from the electromagnetic form factor with the data-driven dispersion relation

We study the pion electromagnetic form factor in the modulus squared dispersion relation, and do the model independent extraction of the most important nonperturbative parameters in pion light-cone distribution amplitude. The motivation of this work is the recent measurement of timelike form factor in the resonant regions, which makes up the piece lacking solid QCD-based calculation. With the perturbative QCD calculation up to next-to-leading-order QCD corrections and twist four level of meson distribution amplitudes, we obtain the chiral mass of pion meson as $m_0^\pi(1 \, {\rm GeV}) = 1.31^{+0.27}_{-0.30} \, {\rm GeV}$. More accuracy measurement of the timelike form factor are desirable to help us to determine the lowest gegenbauer moments in pion distribution amplitudes with the data-driven dispersion relation method developed in this work.