Pion light-cone wave function and pion distribution amplitude in the Nambu–Jona-Lasinio model

∫ dk⊥Ψπ(x,~k⊥)k 2 ⊥ = 〈~k 2 ⊥〉 = −M〈ūu〉/f 2 π for the second moment of the pion light-cone wave function, where M is the constituent quark mass and fπ is the pion decay constant. After the QCD Gegenbauer evolution of the pion distribution amplitude good end-point behavior is recovered, and a satisfactory agreement with the analysis of the experimental data from CLEO is achieved. This allows us to determine the momentum scale corresponding to our model calculation, which is close to the value Q0 = 313 MeV obtained earlier from the analogous analysis of the pion parton distribution function. The value of 〈~k ⊥〉 is, after the QCD evolution, around (400 MeV) . In addition, the model predicts a linear integral relation between the pion distribution amplitude and the parton distribution function of the pion, which holds at the leading-order QCD evolution.