BLM scale for the pion transition form factor

Abstract

The NLO Brodsky-Lepage-Mackenzie (BLM) scale for the pion transition form factor has been determined. To achieve that, a consistent calculation up to nf-proportional NNLO contributions to both the hard-scattering amplitude and the perturbatively calculable part of the pion distribution amplitude has been performed. By combining and matching the results obtained for these two amplitudes, a proper cancellation of collinear singularities has been established and the gamma5 ambiguity problem (related to the use of the dimensional regularization method) has been resolved by using the naive-gamma5 as well as the 't Hooft-Veltman (HV) schemes. It has been demonstrated that the prediction for the pion transition form factor is independent of the factorization scale muF at every order in the strong coupling constant, making it possible to use the simplest choice muF^2=Q^2 at the intermediate steps of the calculation. Assuming the pion asymptotic distribution amplitude and working in the \bar{MS} scheme, we have found the BLM scale to be muR^2=muBLM^2 ~ Q^2/9. Based on the same distribution, the complete NLO prediction for the pion transition form factor has been calculated in the alphaV definition of the QCD coupling renormalized at muR^2=muV^2 = e^{5/3} muBLM^2 ~ Q^2/2. It is in good agreement with the presently available experimental data.