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تسجيل مستخدم جديدCalculating the pion decay constant from alpha_s(M_Z)
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We revisit the analysis of the improved ladder Schwinger-Dyson (SD) equation for the dynamical chiral symmetry breaking in QCD with emphasizing the importance of the scale ambiguity. Previous calculation done so far naively used one-loop MSbar coupling in the improved ladder SD equation without examining the scale ambiguity. As a result, the calculated pion decay constant f_pi was less than a half of its experimental value f_pi=92.4MeV once the QCD scale is fixed from the high energy coupling alpha_s(M_Z). In order to settle the ambiguity in a proper manner, we adopt here in the present paper the next-to-leading-order effective coupling instead of a naive use of the MSbar coupling. The pion decay constant f_pi is then calculated from high energy QCD coupling strength alpha_s(M_Z)=0.1172 pm 0.0020. Within the Higashijima-Miransky approximation, we obtain f_pi=85--106MeV depending on the value of alpha_s(M_Z) which agrees well with the experimentally observed value f_pi=92.4MeV. The validity of the improved ladder SD equation is therefore ascertained more firmly than considered before.
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