QCD Calculations of Pion Electromagnetic and Transition Form Factors

Its value depends on the shape of φπ(x). In particular, using the asymptotic form[2, 1] φ as π (x) = 6fπx(1 − x) one obtains I0 = 3fπ which gives the F as γγ∗π0(Q ) = 4πfπ/Q 2 prediction for the large-Q behavior[1]. Brodsky and Lepage[1] proposed the interpolation formula F γγ∗π0(Q ) = 1/[πfπ(1 + Q2/s0)] which reproduces, for s0 = 4π f π , both the Q 2 = 0 value and the high-Q behavior. The same result follows from the model[3] based on local quark-hadron duality, in which Fγγ∗π0(Q ) is obtained by calculating the amplitude of the transition of the pion into a q̄q pair with the invariant mass s, with subsequent integration over the pion duality interval 0 < s < s0. Adding the one-loop pQCD corrections[4, 5] and assuming the asymptotic distribution amplitude (DA) one obtains F γγ∗π0(Q ) ∣