Melić, Blaženka; Nižić, Bene; PassekKumerički, Kornelija
(2002)
BrodskyLepageMackenzie scale for the pion transition form factor.
Physical Review D, 65
(5).
053020105302033.
ISSN 05562821
Abstract
The nexttoleading order (NLO) BrodskyLepageMackenzie (BLM) scale for the pion transition form factor is determined. To achieve that, a consistent calculation up to n(f)proportional nexttonexttoleading order contributions to both the hardscattering amplitude and the perturbatively calculable part of the pion distribution amplitude is performed. By combining and matching the results obtained for these two amplitudes, a proper cancellation of collinear singularities is established and the gamma(s) ambiguity problem (related to the use of the dimensional regularization method) is resolved by using the naivegamma(s) as well as the 't HooftVeltman (HV) schemes. It is demonstrated that the prediction for the pion transition form factor is independent of the factorization scale mu(F)(2) at every order in the strong coupling constant, making it possible to use the simplest choice mu(F)(2) = Q(2) at the intermediate steps of the calculation. Assuming the pion asymptotic distribution amplitude and working in the (MS) over bar scheme, we find the BLM scale to be mu(K)(2) = mu(BLM)(2)approximate toQ(2)/9. Based an the same distribution, the complete NLO prediction for the pion transition form factor is calculated in the alpha(V) definition of the QCD coupling renormalized at mu(R)(2) = mu(V)(2) = e(5/3) mu(BLM)(2)approximate toQ(2)/2. It is in good agreement with the presently available experimental data.
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