Some new applications of the Principle of maximum Conformality 具兴刚 Xing-Gang Wu 重庆大学物理系 Department of Physics, Chongging University 全国第十六届重味物理和CP破坏研讨会河南工业大学
Some new applications of the Principle of Maximum Conformality 吴兴刚 Xing-Gang Wu 重庆大学物理系 Department of Physics, Chongqing University 全国第十六届重味物理和CP破坏研讨会 河南工业大学
OUTLINE 微扰论 The principle of Maximum Conformality(PMC) Some applications Summary and Outlook
OUTLINE Summary and Outlook The principle of Maximum Conformality (PMC) Some applications 微扰论
The perturbative theory: A physical observable p could be written as the perturbative form =En P(AR)+r1a.p+1 (μ)+x2aP+2(k)+. Q s Di yts Reliable High precision a。<1 High-order prediction; Introducing renormalization scheme/scale regularization, renormalization, /scale -setting =QCDa(M2)=01181±00011 ame import Q(GeVT Up to infinite order, there is no scheme-and scale- dependence, i.e., any choice of scheme/scale should result in the same prediction. Standard Renormalization group invariance(RGI)
The perturbative theory: A physical observable could be written as the perturbative form Up to infinite order, there is no scheme- and scaledependence, i.e., any choice of scheme/scale should result in the same prediction. “Standard Renormalization group invariance (RGI)” High-order prediction; Introducing renormalization scheme/scale regularization、renormalization、scale-setting same importance 𝛼𝑠 < 1 Reliable High precision
Conventional scale-setting approach =>Choose the scale Q to be''seemingly"typical momentum transfer = Vary in a certain range, e. g [Q/2, 2Q],[Q/3, 3Q], to discuss its uncertainty Main problems of conventional scale-setting 1)Convergence depends on as-power suppression Once inconvergence appears, one cannot judge whether is its intrinsic property or caused by improper choice of scale 2) By finishing more loop-terms, the scale-dependence could be smaller, it is however caused by cancellation among different orders
Conventional scale-setting approach =>“Choose” the scale Q to be ``seemingly” typical momentum transfer =>“Vary” in a certain range, e.g. [Q/2, 2Q], [Q/3, 3Q], to discuss its uncertainty Main problems of conventional scale-setting 1) Convergence depends on s -power suppression； Once inconvergence appears, one cannot judge whether it is its intrinsic property or caused by improper choice of scale。 2) By finishing more loop-terms, the scale-dependence could be smaller, it is however caused by cancellation among different orders
Even if the prediction of quessing scale agrees with the data It, in fact, cannot answer why this is the case It is important to achieve reliable fixed-order prediction at low-order levels such as nlo and nnlo The reason for scale dependence at fixed-order? Mismatching under conventional treatment p=x0(1)aB(1)+x1(1)a3+1(1)+x2(1)aB2(1)+ p=x0(2)aB(2)+x1(2)a31(2)+x2(2)a32(42)+ Directly replacing H1->H2=> Mismatching of coefficients and alphas values = one reason for large scale uncertainty
Even if the prediction of guessing scale agrees with the data. It, in fact, cannot answer why this is the case It is important to achieve reliable fixed-order prediction at low-order levels, such as NLO and NNLO ? The reason for scale dependence at fixed-order ? Mismatching under conventional treatment Directly replacing 1 -> 2 => Mismatching of coefficients and alphas values => one reason for large scale uncertainty