New analyses of event shape observables in electron-positron annihilation and the determination of αs running behavior in perturbative domain

Abstract

In this paper, we give comprehensive analyses for event shape observables in electron-positron annihilation by using the Principle of Maximum Conformality (PMC) which is a rigorous scale-setting method to eliminate the renormalization scheme and scale ambiguities in perturbative QCD predictions. Conventionally the renormalization scale and theoretical uncertainties in event shape observables are often evaluated by setting the scale to the center-of-mass energy $$ \sqrt{s} $$ s . The event shape distributions using this conventional scale setting are plagued by the large renormalization scale uncertainty and underestimate the experimental data. Moreover, since the renormalization scale is simply fixed to the center-of-mass energy $$ \sqrt{s} $$ s , only one value of the coupling αs at the single scale $$ \sqrt{s} $$ s can be extracted. In contrast, the PMC renormalization scales are determined by absorbing the nonconformal β contributions that govern the behavior of the running coupling via the Renormalization Group Equation (RGE). The resulting PMC scales change with event shape kinematics, reflecting the virtuality of the underlying quark and gluon subprocess. The PMC scales thus yield the correct physical behavior of the scale and the PMC predictions agree with precise event shape distributions measured at the LEP experiment. More importantly, we can precisely determine the running of the QCD coupling constant αs(Q2) over a wide range of Q2 in perturbative domain from event shape distributions measured at a single center-of-mass energy $$ \sqrt{s} $$ s .

Elimination of QCD Renormalization Scale and Scheme Ambiguities

“…Up to now, the PMC approach has been successfully applied to many physical processes (see, e.g., [13,14,23] for reviews), including the Higgs boson production at the LHC, the Higgs boson decays to γγ, gg, and b b processes, the top-quark pair production at the LHC and Tevatron and its decay process [24], the semihard processes based on the BFKL approach [20,[25][26][27], the electron-positron annihilation to hadrons [10,11,13], the hadronic Z 0 boson decays, the event shapes in electron-positron annihilation [17,28], the electroweak parameter ρ [29,30], the Υ(1S) leptonic decay [31,32], and the charmonium production [33][34][35]. In addition, the PMC provides a possible solution to the B → ππ puzzle [36] and the γγ * → η c puzzle [37].…”

“…Comprehensive PMC analysis for event shapes in e + e − annihilation and a novel method for the precise determination of the QCD running coupling α s (Q 2 ) are shown in Refs. [28,51]. Interested readers may turn to these studies for more details.…”

Infinite-order scale-setting using the principle of maximum conformality: A remarkably efficient method for eliminating renormalization scale ambiguities for perturbative QCD

“…[41,42]) have recently shown a direct improvement of theoretical predictions. The recently developed Infinite-Order Scale-Setting using the Principle of Maximum Conformality (PMC ∞ ) has been shown to significantly reduce the theoretical errors in Event Shape Variable distributions, highly improving also the fit with the experimental data [39,[43][44][45]. An improved theoretical prediction on with respect to the world average has also been shown in Refs.…”