We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham e-Theses
You are in:

RS-invariant resummations of QCD perturbation theory

Tonge, Darrell Graham (1997) RS-invariant resummations of QCD perturbation theory. Doctoral thesis, Durham University.



We propose a renormalon-inspired resummation of QCD perturbation theory based on approximating the renormalization scheme (RS) invariant effective charge (EC) beta- function coefficients by the portion containing the highest power of b = (11N'-2N(_f))/6, the first beta-function coefficient, for SU(N) QCD with N(_f) quark flavours. This can be accomplished using exact large-N(_f) all-orders results. The resulting resummation is RS-invariant and the exact next-to-leading order (NLO) and next-to-NLO (NNLO) coefficients in any RS are included. This improves on a previously employed naive leading-6 resummation which is RS-dependent. The RS-invariant resummation is used to assess the reliability of fixed-order perturbation theory for the e(^+)e(^-) R-ratio, hadronic tau-decay ratio R(_r), and Deep Inelastic Scattering (DIS) sum rules, by comparing it with the exact NNLO results in the EC RS. For R and R(_r), where large-order perturbative behaviour is dominated by a leading ultra-violet renormalon singularity, the comparison indicates fixed-order perturbation theory to be very reliable. For DIS sum rules, which have a leading infra-red renormalon singularity, the performance is rather poor. We show that QCD Minkowski observables such as the R and R(_r) are completely determined by the EC beta-function, p(x), corresponding to the Euclidean QCD vacuum polarization Adler D-function, together with the NLO perturbative coefficient of D. An efficient numerical algorithm is given for evaluating R, Rr from a weighted contour integration of D(se(^10)) around a circle in the complex squared energy .s-plane, with p(x) used to evolve in s around the contour. The difference between the R, R(_r) constructed using the NNLO and leading-b resummed versions of pi(x) provides an estimate of the uncertainty due to the uncalculated higher order corrections. We estimate that at LEP energies ideal data on the R-ratio could determine a(_s)(M(_2)(_Z)) to three-significant figures. For R(_r) we estimate a theoretical uncertainty δa(_s)(m(^2)(_r)) ~ 0.001, corresponding to δa(_s)(m(^2)(_r)) ~ 0.002. This encouragingly small uncertainty is much less than has recently been deduced from comparison with the analogous naive all-orders resummation, which we demonstrate to be extremely RS dependent and hence misleading.

Item Type:Thesis (Doctoral)
Award:Doctor of Philosophy
Thesis Date:1997
Copyright:Copyright of this thesis is held by the author
Deposited On:09 Oct 2012 11:39

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitter