Determination Of Two Important Standard Model Parameters (?)_t((?)_t) And α_s(M_z) By Using The Principle Of Maximum Conformality

Quantum chromodynamics(QCD),which is an important component of the Standard Model of particle physics,has been recognized as the basic theory for describing the strong interaction between quarks and gluons.In the high-energy physical processes,the strong interaction exhibits the asymptotic free property due to the higher energy scale involved,which allows one to adopt the perturbative quantum chromodynamics(pQCD)to compute the values of the observables.In pQCD higher-order computations,people need to introduce the renormalization scale for eliminating the ultraviolet divergence.According to the renormalization group invariance,the final theoretical prediction will not depend on the choice of the renormalization scale,only if one can calculate it up to a sufficiently high precision.However,due to the complexity of the higher-order diagrams calculation,people can only calculate up to the finite low-orders to obtain the renormalization scale-invariant theoretical predictions and effectively estimate the contribution of unknown higher-order terms are the important problems of the pQCD theory.Based on the renormalization group equation,the principle of maximum conformality(PMC)provides a basic method for systematically eliminating the uncertainty of the renormalization scale existing in the theoretical predictions of any finite order.The PMC uses the non-conformal β-terms in the pQCD series to determine the values of effective strong coupling constants for the high-energy physical processes,thereby the resulting theoretical predictions are independent of the choice of the renormalization scale.In this paper,the important parameters in the standard model,such as top quark mass mt(mt)and strong coupling constant αs(MZ),have been investigated in detail based on the PMC.Firstly,we compare a variety of scale-setting methods based on the principle of maximum conformality.Although they can all eliminate the conventional renormalization scale dependence,some of them can not determine the effective scale of the last order of the known expression due to the lack of higher-order information,so there will be residual scale dependence.The results show that the PMC single-scale method(PMCs)can successfully suppress the residual scale dependence existing in the previous method,which leads to an accurately theoretical prediction.Secondly,using the perturbative relationship between the quark mass of the modified minimum subtraction scheme(MS)and the quark mass of the on-shell scheme(OS),we analyze the effects of the renormalization scale and the top quark OS mass on determining the top quark MS mass.The results show that the PMCs can eliminate the conventional renormalization scale ambiguous and can estimate the contribution of a reasonable unknown high-order term,which obtains an accurate theoretical prediction mt(mt)|PMC=162.629-0.400+0.397(GeV).Subsequently,combining the four-loop perturbative calculation results of the Z boson hadronic decay width with the corresponding experimental measurement results,we consider the effects of renormalization scale and experimental error in the process of extracting the magnitude of the strong coupling constant,such as αs(MZ)|PMC=0.1180-0.0002-0.0038+0.0003+0.0039 andαs(MZ)|Conv.=0.1181+0.0116-0.00.9+0.0173+0.0038.The results show that the PMC conformal series can be used to obtain more accurate results than that of the conventional scheme.PMC can effectively eliminate the uncertainty of the renormalization scale and the renormalization scheme.Because of the elimination of the divergent renormalon terms like n!βin αsn.the convergence of the pQCD series is naturally improved,which leads to a more accurate predictions.Finally,as an extension of the PMC application,we estimate the unknown higher-order contributions of the Y(1S)leptonic decay width,Gross-Llewellyn Smith sum rule and generalized Crewther relation using the conservative way and the Pade approximation method based on the PMCs conformal series.The results show that a reasonable high-order contribution can be obtained by using the PMCs conformal series,and the theoretical predictions are closer to the experimental values.Moreover,the estimated high-order contributions are also independent of the choice of the renormalization scale.Compared to the renormalization scale-dependent conventional series,the PMC conformal series can be better used to estimate the contribution of unknown higher-order terms.In summary,our study shows that the PMCs not only eliminate the uncertainty of renormalization scale in the processes of determining the top quark mass and extracting the strong coupling constant,but also help to predict reliable higher-order contributions,which leads to the accurate predictions.It is important to accurately test the Standard Model at high energy colliders and to explore new physics beyond the Standard Model.