Study On The Pion Transition Form Factor

The form factor of the transition ργ^*→π⁰is investigated by analyzing the γγ^*→π⁰transition in the framework of the light-cone local duality QCD sum rules. Bothfinite-width (especially the momentum dependent one) and zero-width forms for thelow-energy physical absorptive part of the γγ^*→π⁰transition are considered. Thenumerical results for the transition form factor F^ρπ(Q²) in the asymptotic form, CZ, BFand BMS one of the pion distribution amplitudes (DAs) are obtained respectively, thedifference between the finite-and zero-width form is not big but still distinguishable.It is found that the results for the form factor F^ρπ(Q²) from asymptotic, CZ, BF, BMSand the flat pion DAs are compatible with the predictions of perturbative QCD. Ourresults will be helpful to distinguish the shape of the pion DA of twist-two, when theconcrete information of the experimental data for the transition ργ^*→π⁰are provided.The pion transition form factor F^γ*Ï€(q₁², q₂²) at the photon mass-shell of q₁²=q₂²=0is fixed by the axial anomaly, which may serve to be a criterion for checking theconsistency of the underlying QCD dynamics. Instead of working in the asymmetrickinematical region with one photon being real and the other one virtual, we choose towork in the symmetric kinematical region where two photons have the same virtiuali-ties. Instead of the direct extrapolation of the QCD expression to such low-energy scale,we hope to reproduce the experimental value of F^γ*Ï€(q₁²=0, q₂²=0) from light-coneQCD sum rules. The form factor of the transitions γ^*γ^*→π⁰is investigated in the framework of the zero-and finite-width light-cone local duality QCD sum rules. TheFeynman diagram technique is proposed to evaluate the low-energy absorptive part,which possesses both single-and double-pole structures as expected. The expressionof the pion transition form factor F_QCD^γ*Ï€(q₁²=t, q₂²=t) at large t is independent ofthe twist-two and twist-three pion DAs, and then a more accurate conclusion is capa-ble to reach. The influence of the light quark mass and the ωρπ coupling constant toour sum rules is considered as well. The consistency between the axial anomaly, theintermediate hadronic structure and the QCD perturbative dynamics which serve to berepresentation of the same process in different momentum region is tested to be truewithin the reasonable good region of input parameters.In addition, within the framework of the low-energy effective theory arising fromthe instanton vacuum model of QCD, the twist-four virtual photon distribution ampli-tude, g_γ3(u, P²), corresponding to the nonlocal quark-antiquark vector current is cal-culated at the low-energy scale. The coupling constant, f_γ(P²), of the quark-antiquarkvector current to the virtual photon state is also obtained. The behavior of the couplingas well as the obtained photon wave function especially at the end points is discussed.