| A primary requirement of renormalization group invariance(RGI)is that a valid prediction for a physical observable from quantum field theory must be independent of the theoretical conventions,such as the choice of renormalization scheme and the initial choice of renormalization scale.However,the perturbative QCD(pQCD)predictions based on a truncated perturbation series do not automatically satisfy this requirement,leading to scheme-and-scale ambiguities.The conventional approach to fixed-order perturbative QCD predictions is based on an arbitrary choice of the renormalization scale,together with an arbitrary range.This ad hoc procedure based on a guessed scale assigns an arbitrary systematic error for the fixed-order pQCD predictions and reduces the predictive power of pQCD.The key to solve the renormalization scale ambiguity is to find an objective way to set the renormalization scale.The recently suggested principle of maximum conformality(PMC)has been designed for eliminating the renormalization scale and renormalization scheme ambiguities via a systematic way.The PMC is consistents with the primary requirement of RGI and satisfies all self-consistency conditions required by RG for setting the renormalization scale.The main idea of PMC lies in that all the nonconformal terms associated with coupling constant renormalization in pQCD series should be summed into the running coupling to determine the running behavior of coupling and form the optimal renormalization scale of each order.We first outline the scheme-and-scale ambiguities in fixed-order pQCD prediction and give a brief introduction about the self-consistency conditions required by RG for setting the renormalization scale,then review two systematic all-orders muti-scale approaches to QCD renormalization scale-setting based on PMC.Inspired by PMC,we provide a novel all-orders single-scale approach to QCD renormalization scale-setting(PMC-s).Using PMC-s and the recently suggested C-scheme coupling,we present a general demonstration about the scheme-independent of the PMC predictions.Based on PMC,we study the Commensurate Scale Relation(CSR)which provides a direct connection between different physical observable in QCD,such as the Crewther’s relation.We study the running behavior of the effective charge related to Bjorken sum rule by matching to the nonperturbative domain described by Light Front Holographic QCD.We then determine the the transition between the perturbative and nonperturbative domains of QCD.We also apply PMC to set the optimal renormalization scale of various high energy processes,including the annihilation of an electron and positron into hadrons,the tau decay,Higgs boson decay H→bb,the semileptonic decay of Bc meson and the leptonic decay of Y(1S)meson.We discuss the scheme dependence of fixed-order predictions via C-scheme coupling and the scheme-independence of PMC prediction through two four-loop examples,the Adler function and Rτ.In fact,the PMC residual scale dependence originated from the unknow high-order is far less than the conventional scale dependence.We provide a comparison between PMC muti-scale approach and PMC single scale approach through two four-loop examples,Re+e-and H→bb,and show the equivalency of the PMC single scale approach and the multi scale approach in the sence of perturbation.The conclusion is that the resulting PMC and PMC-s predictions are effectively the same for both total and differential observables.Thus the PMC-s approach,with its much simpler scale-setting procedure,can be adopted as a reliable substitute for the PMC multiscale approach,especially when one does not need detailed information at each order.Because of the elimination of the scheme-and-scale ambiguities,the PMC not only increase the precision of QCD tests,but also increase the sensitivity of the collider experiments to new physics beyond the standard model. |
