The Principle Of Maximum Conformality And Its Application To The High Energy Physics Processes

As is well know, the physical predictions of the p QCD theory, calculated up to all orders, are surely independent of the choice of renormalization scale and renormalization scheme due to the renormalization group invariance. However, there are renormalization scale and renormalization scheme ambiguities at any finite order calculation and it constitutes one of the source of important error for the experimental analysis and p QCD prediction. The elimination of the renormalization scale and renormalization scheme ambiguitie so as to obtain the more accurate QCD predictions is a key problem for the p QCD theory.The principle of maximum conformality(PMC) has been designed for eliminating the renormalization scale and renormalization scheme ambiguities via a systematic way. The PMC provides the underlying principle for BLM. The main idea of PMC lies in that all the nonconformal terms in perturbative QCD series are summed into the running coupling to form the optimal renormalization scale. The PMC prediction consistent with the renormalization group invariance and satisfies all self-consistency conditions for setting the renormalization scale. After PMC scale setting, all non-conformal terms are summed into the running coupling so that the remaining terms in the perturbative series are identical to that of a conformal theory. Moreover, the divergent “renormalon” series( !)n n i sn b a does not appear in the conformal series and the convergence of the series can be greatly improved in principle. Thus, one obtains a scale-and scheme-independent prediction at any finite order by using the PMC.In the present paper, we apply the PMC method to set the optimal renormalization scale of the various QCD high energy physics processes:(I) Higgs decay channels, H ®bb and H ®gg up to four loop level, and H ®gg up the three loop level, respectively, these Higgs decay channels play an important role for the Higgs physics;(II) The 0Z boson decay including the nonsinglet, vector-singlet, and axial-singlet part up to four loop level;(III) top-quark pair production cross section up to two loop level and its charge asymmetry at the LHC;(VI) The double charmonium production processes, /()( 0,1, 2)c Je e J y y cJ+ -+ ®ï¿  + =;(III) The electroweak parameter r up to four loop level. In contrast to the conventional practice of simple guessing the renormalization scale, the prodiction under the PMC method have the advantages as follow:(I) the renormalization scale and renormalization scheme ambiguities are removed, there is residual scale dependence due to unknown higher order b- terms, which however is highly suppressed.(II) we finally obtain the conformal perturbative series for the various QCD processes. Due to the divergent “renormalon” series disappear and the convergence of the p QCD conformal series can be greatly improved in principle. In the 0CN ® Abelian limit, the PMC method agrees with the Gell-Mann-Low scale setting.(III) we obtain the more precise p QCD prodictions, which are in better agreement with the experimental results. The PMC recults not only increase the precision of QCD tests, but also increase the sensitivity of the collider experiments to new physics beyond the standard model.