1,720,974 research outputs found
Thrust distribution in electron-positron annihilation using the principle of maximum conformality
No full textWe present a comprehensive and self-consistent analysis for the thrust distribution by using the principle of maximum conformality (PMC). By absorbing all nonconformal terms into the running coupling using PMC via renormalization group equation, the scale in the running coupling shows the correct physical behavior and the correct number of active flavors is determined. The resulting PMC predictions agree with the precise measurements for both the thrust differential distributions and the thrust mean values. Moreover, we provide a new remarkable way to determine the running of the coupling constant αs(Q2) from the measurement of the jet distributions in electron-positron annihilation at a single given value of the center-of-mass energy s
Infinite-order scale-setting using the principle of maximum conformality: A remarkably efficient method for eliminating renormalization scale ambiguities for perturbative QCD
No full textWe identify a property of renormalizable SU(N)/U(1) gauge theories, intrinsic conformality (iCF), which underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional renormalization scale ambiguity at every order in perturbative QCD (pQCD): the PMC∞. This new method reflects the underlying conformal properties displayed by pQCD at next-to-next-to-leading order, eliminates the scheme dependence of pQCD predictions, and is consistent with the general properties of the principle of maximum conformality (PMC). We introduce a new method to identify conformal and β-terms which can be applied from either a numerical or an analytical calculations. We illustrate the PMC∞ for the thrust and C-parameter distributions in e+e- annihilation and then show how to apply this new method to general observables in QCD. We point out how the implementation of the PMC∞ can significantly improve the precision of pQCD predictions; its implementation in a multiloop analysis also simplifies the calculation of higher order corrections in a general renormalizable gauge theory
Scheme-independent determination of the QCD running coupling at all scales from jet observables using the principle of maximum conformality and infinite-order scale setting
No full textWe present a new approach to determining the strong coupling αs(Q), over the entire range of validity of perturbative QCD, for scales above ΛQCD and up to the Planck scale ∼1.22·1019 GeV, with the highest precision and using the data of a single experiment. In particular, we use the results obtained for the thrust (T) and C-parameter (C) distributions in e+e− annihilation at a single annihilation energy s=MZ (i.e. at the Z0 peak). This new method is based on the intrinsic conformality (iCF) and on the Infinite-Order Scale Setting, using the Principle of Maximum Conformality (i.e. the PMC∞), which allows a rigorous determination of the renormalization scales for the event-shape variable distributions satisfying all of the requirements of Renormalization Group Invariance, including renormalization-scheme independence and consistency with Abelian theory in the NC→0 limit. This new method is based on the scale-invariance of the iCF, which allows determination of αs(μ0) at any scale μ0, and on the Maximum Likelihood statistical approach. We propose a novel approach to determining the best-fitting range by considering all possible intervals over the entire range of bins available in the perturbative region and selecting that which returns the most-likely-lowest χmin2. This new method is designed to eliminate the errors that arise due to selection of the bin-interval and that have been neglected in previous analyses. In particular, using data for thrust and C-parameter at the Z0 peak from ALEPH, OPAL, DELPHI and L3 experiments, we obtain the average value: αs(MZ)=0.1182−0.0007+0.0007, for the strong coupling. This determination of αs(MZ) is consistent with the world average and has an improved precision with respect to the values obtained from the analysis of event shape observables currently used in the world average
The Principle of Maximum Conformality Correctly Resolves the Renormalization-Scheme-Dependence Problem
No full textIn this paper, we clarify a serious misinterpretation and consequent misuse of the Principle of Maximum Conformality (PMC), which also can serve as a mini-review of PMC. In a recently published article, P. M. Stevenson has claimed that “the PMC is ineffective and does nothing to resolve the renormalization-scheme-dependence problem”, concluding incorrectly that the success of PMC predictions is due to the PMC being a “laborious, ad hoc, and back-door” version of the Principle of Minimal Sensitivity (PMS). We show that such conclusions are incorrect, deriving from a misinterpretation of the PMC and an overestimation of the applicability of the PMS. The purpose of the PMC is to achieve precise fixed-order pQCD predictions, free from conventional renormalization schemes and scale ambiguities. We demonstrate that the PMC predictions satisfy all the self-consistency conditions of the renormalization group and standard renormalization-group invariance; the PMC predictions are thus independent of any initial choice of renormalization scheme and scale. The scheme independence of the PMC is also ensured by commensurate scale relations, which relate different observables to each other. Moreover, in the Abelian limit, the PMC dovetails into the well-known Gell-Mann–Low framework, a method universally revered for its precision in QED calculations. Due to the elimination of factorially divergent renormalon terms, the PMC series not only attains a convergence behavior far superior to that of its conventional counterparts but also deftly curtails any residual scale dependence caused by the unknown higher-order terms. This refined convergence, coupled with its robust suppression of residual uncertainties, furnishes a sound and reliable foundation for estimating the contributions from unknown higher-order terms. Anchored in the bedrock of standard renormalization-group invariance, the PMC simultaneously eradicates the factorial divergences and eliminates superfluous systematic errors, which inversely provides a good foundation for achieving high-precision pQCD predictions. Consequently, owing to its rigorous theoretical underpinnings, the PMC is eminently applicable to virtually all high-energy hadronic processes
Ab initio study of the Fe∕NiO interface: Structural and magnetic properties
No full textThe structural and magnetic properties of the Fe/NiO(100) interface have been theoretically studied by density-functional theory within generalized gradient approximation (GGA) and, in selected cases, GGA+U methods. By total energy calculation, we find that Fe atoms adsorb preferentially on O sites and that a chemical reduction of NiO occurs, giving rise, for adsorption of more than one monolayer, to an interface of complex chemical and structural compositions, characterized by oxygen migration toward the surface. The magnetic moments at the interface and their alignment in a ferromagnetic and/or antiferromagnetic ordering are deeply influenced by the geometrical configuration of the atoms, pointing out to an important interplay between structure and magnetic configuration. This mechanism, at small oxidation level, leads quite naturally to the appearance of uncompensated spins at the interface
Renormalization scale setting for heavy quark pair production in e+e- annihilation near the threshold region
No full textHeavy fermion pair production in e+e- annihilation is a fundamental process in hadron physics and is of considerable interest for various phenomena. In this paper, we will apply the principle of maximum conformality (PMC) to provide a comprehensive analysis of these processes. The PMC provides a systematic, unambiguous method for determining the renormalization scales of the QCD coupling constant for single-scale and multiple-scale applications. The resulting predictions eliminate any renormalization scheme-and-scale ambiguities, eliminate the factorial renormalon divergences, and are consistent with the requirements of the renormalization group. It is remarkable that two distinctly different scales are determined by using the PMC for heavy fermion pair production near the threshold region. One scale is the order of the fermion mass mf, which enters the hard virtual corrections, and the other scale is of order vmf, where v is the quark velocity, which enters the Coulomb rescattering amplitude. The PMC scales yield the correct physical behavior and reflect the virtuality of the propagating gluons (photons) for the QCD (QED) processes. Moreover, we demonstrate the consistency of PMC scale setting from QCD to QED. Perfect agreement between the Abelian unambiguous Gell-Mann-Low and the PMC scale-setting methods in the limit of zero number of colors is demonstrated
Novel method for the precise determination of the QCD running coupling from event shape distributions in electron-positron annihilation
No full textWe present a novel method for precisely determining the running QCD coupling constant αs(Q2) over a wide range of Q2 from event shapes for electron-positron annihilation measured at a single annihilation energy s. The renormalization scale Q2 of the running coupling depends dynamically on the virtuality of the underlying quark and gluon subprocess and thus the specific kinematics of each event. The determination of the renormalization scale for event shape distributions is obtained by using the principle of maximum conformality (PMC), a rigorous scale-setting method for gauge theories which satisfies all the requirements of renormalization group invariance, including renormalization-scheme independence and consistency with Abelian theory in the NC→0 limit. In this paper, we apply the PMC to two classic event shapes measured in e+e-annihilation: The thrust (T) and C-parameter (C). The PMC renormalization scale depends differentially on the values of T and C. The application of PMC scale-setting determines the running coupling αs(Q2) to high precision over a wide range of Q2 from 10 to 250 GeV2 from measurements of the event shape distributions at the Z0 peak. The extrapolation of the running coupling using pQCD evolution gives the value αs(MZ2)=0.1185±0.0012 from the thrust and αs(MZ2)=0.1193-0.0019+0.0021 from the C-parameter in the MS scheme. These determinations of αs(MZ2) are consistent with the world average and are more precise than the values obtained from analyses of event shapes currently used in the world average. The highly consistent results for the T and C event-shape distributions provide an additional verification of the applicability of the PMC to pQCD
High precision tests of QCD without scale or scheme ambiguities: The 40th anniversary of the Brodsky–Lepage–Mackenzie method
No full textA key issue in making precise predictions in QCD is the uncertainty in setting the renormalization scale μr and thus determining the correct values of the QCD running coupling αs(μr) at each order in the perturbative expansion of a QCD observable. It has often been conventional to simply set the renormalization scale to the typical scale of the process Q and vary it in the range μr∈[Q/2,2Q] in order to estimate the theoretical error. This is the practice of Conventional Scale Setting (CSS). The resulting CSS prediction will however depend on the theorist's choice of renormalization scheme and the resulting pQCD series will diverge factorially. It will also disagree with renormalization scale setting used in QED and electroweak theory thus precluding grand unification. A solution to the renormalization scale-setting problem is offered by the Principle of Maximum Conformality (PMC), which provides a systematic way to eliminate the renormalization scale-and-scheme dependence in perturbative calculations. The PMC method has rigorous theoretical foundations, it satisfies Renormalization Group Invariance (RGI) and preserves all self-consistency conditions derived from the renormalization group. The PMC cancels the renormalon growth, reduces to the Gell-Mann–Low scheme in the Nc→0 Abelian limit and leads to scale- and scheme-invariant results. The PMC has now been successfully applied to many high-energy processes. In this article we summarize recent developments and results in solving the renormalization scale and scheme ambiguities in perturbative QCD. In particular, we present a recently developed method the PMC∞ and its applications, comparing the results with CSS. The method preserves the property of renormalizable SU(N)/U(1) gauge theories defined as Intrinsic Conformality (iCF). This property underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional renormalization scale ambiguity at every order in pQCD. This new method reflects the underlying conformal properties displayed by pQCD at NNLO, eliminates the scheme dependence of pQCD predictions and is consistent with the general properties of the PMC. A new method to identify conformal and β-terms, which can be applied either to numerical or to theoretical calculations is also shown. We present results for the thrust and C-parameter distributions in e+e− annihilation showing errors and comparison with the CSS. We also show results for a recent innovative comparison between the CSS and the PMC∞ applied to the thrust distribution investigating both the QCD conformal window and the QED Nc→0 limit. In order to determine the thrust distribution along the entire renormalization group flow from the highest energies to zero energy, we consider the number of flavors near the upper boundary of the conformal window. In this flavor-number regime the theory develops a perturbative infrared interacting fixed point. These results show that PMC∞ leads to higher precision and introduces new interesting features in the PMC. In fact, this method preserves with continuity the position of the peak, showing perfect agreement with the experimental data already at NNLO. We also show a detailed comparison of the PMC∞ with the other PMC approaches: the multi-scale-setting approach (PMCm) and the single-scale-setting approach (PMCs) by comparing their predictions for three important fully integrated quantities Re, Rτ and Γ(H→bb̄) up to the four-loop accuracy
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