The scale dependence of perturbative QCD predictions for e+e− event shape moments and LHC observables

Abstract

Perturbative QCD predictions that are truncated at fixed order have an unphysical dependence on the renormalisation procedure. We investigate two methods of avoiding scale and scheme dependence in QCD predictions of physical observables: the Effective Charges (ECH) method and the Principle of Minimal Sensitivity (PMS).
The ECH method is used to avoid the renormalisation scale and scheme dependence of fixed-order predictions of event shape moments. Values of αs(MZ) are extracted from e+e− data using both ECH and the physical scale method
in the MS scheme. The ECH method at NLO is found to perform better than
standard MS perturbation theory (MS PT) when applied to means of event shapes. However ECH at NNLO functions less well than at NLO, and the ECH method also fails to describe data for higher moments of event shapes. Pad ́e Approximant methods are used to estimate missing higher orders in the perturbative expansions, a technique that works especially well for MS PT applied to the higher moments. We also examine the effect of adding non-perturbative power corrections to the perturbative approximations. It is found that power corrections are insufficient to counteract the undesirable behaviour of ECH at NNLO.
The PMS method is used to provide predictions of the b ̄b and tt ̄total cross-sections at the Tevatron and the LHC. Hadronic cross-sections depend on the factorisation scale as well as the renormalisation scale. PMS is applied by searching for stationary points on the cross-section surface in the space of the two scales. The PMS method predicts substantially larger b ̄b cross-sections than using standard diagonal scale choices. For tt ̄ production, however, there is very little difference observed between the two methods. Both produce predictions that are in good agreement with the current experimental data.