Optimal renormalization-group improvement of the perturbative series for thee+e−annihilation cross section
Ahmady, M. R.
Chishtie, F. A.
Fariborz, A. H.
McKeon, D. G. C.
Sherry, T. N.
Steele, T. G.
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Ahmady, M. R. Chishtie, F. A.; Elias, V.; Fariborz, A. H.; McKeon, D. G. C.; Sherry, T. N.; Squires, A.; Steele, T. G. (2003). Optimal renormalization-group improvement of the perturbative series for thee+e−annihilation cross section. Physical Review D 67 (3),
Using renormalization-group methods, we derive differential equations for the all-orders summation of logarithmic corrections to the QCD series for R(s)=sigma(e(+)e(-)-->hadrons)/sigma(e(+)e(-)-->mu(+)mu(-)), as obtained from the imaginary part of the purely perturbative vector-current correlation function. We present explicit solutions for the summation of leading and up to three subsequent subleading orders of logarithms. The summations accessible from the four-loop vector correlator not only lead to a substantial reduction in sensitivity to the renormalization scale, but necessarily impose a common infrared bound on perturbative approximations to R(s), regardless of the infrared behavior of the true QCD couplant.