Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1995-05-03
Nucl.Phys.B452:188-212,1995
Physics
High Energy Physics
High Energy Physics - Phenomenology
25 pages, LaTeX. 4 figures in separate uuencoded PS file. Revisions - changes to some expressions in sections 3 & 4
Scientific paper
10.1016/0550-3213(95)00383-4
Exact large-$N_{f}$ results for the QCD Adler $D$-function and Deep Inelastic Scattering sum rules are used to resum to all orders the portion of QCD perturbative coefficients containing the highest power of $b$=$\frac{1}{6}(11N$--$2N_{f})$, for SU($N$) QCD with $N_{f}$ quark flavours. These terms correspond to renormalon singularities in the Borel plane and are expected asymptotically to dominate the coefficients to all orders in the $1/N_{f}$ expansion. Remarkably, we note that this is already apparent in comparisons with the exact next-to-leading order (NLO) and next-to-NLO (NNLO) perturbative coefficients. The ultra-violet ($UV$) and infra-red ($IR$) renormalon singularities in the Borel transform are isolated and the Borel sum (principal value regulated for $IR$) performed. Resummed results are also obtained for the Minkowski quantities related to the $D$-function, the $e^{+}e^{-}$ $R$-ratio and the analogous $\tau$-lepton decay ratio, $R_{\tau}$. The renormalization scheme dependence of these partial resummations is discussed and they are compared with the results from other groups [1--3] and with exact fixed order perturbation theory at NNLO. Prospects for improving the resummation by including more exact details of the Borel transform are considered.
Lovett-Turner C. N.
Maxwell Clerk J.
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