Download or read book Renormalization scale dependence in QCD written by Thomas Hebbeker and published by . This book was released on 1993 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Renormalization Scale Setting Problem in QCD written by and published by . This book was released on 2013 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this ad hoc procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of the scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scale ambiguity and show how to obtain renormalization scheme- and scale-independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky-Lepage-Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the [beta]-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending BLM up to any perturbative order; in fact, they are equivalent to each other through the PMC-BLM correspondence principle. Thus, all the features previously observed in the BLM literature are also adaptable to the PMC. The PMC scales and the resulting finite-order PMC predictions are to high accuracy independent of the choice of the initial renormalization scale, and thus consistent with RG invariance. The PMC is also consistent with the renormalization scale-setting procedure for QED in the zero-color limit. The use of the PMC thus eliminates a serious systematic scale error in perturbative QCD predictions, greatly improving the precision of empirical tests of the Standard Model and their sensitivity to new physics.
Download or read book Renormalized Perturbation Theory And Its Optimization By The Principle Of Minimal Sensitivity written by P M Stevenson and published by World Scientific. This book was released on 2022-03-21 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The results of renormalized perturbation theory, in QCD and other quantum field theories, are ambiguous at any finite order, due to renormalization-scheme dependence. The perturbative results depend upon extraneous scheme variables, including the renormalization scale, that the exact result cannot depend on. Such 'non-invariant approximations' occur in many other areas of physics, too. The sensible strategy is to find where the approximant is stationary under small variations of the extraneous variables. This general principle is explained and illustrated with various examples. Also dimensional transmutation, RG equations, the essence of renormalization and the origin of its ambiguities are explained in simple terms, assuming little or no background in quantum field theory. The minimal-sensitivity approach leads to 'optimized perturbation theory,' which is developed in detail. Applications to Re⁺e⁻, the infrared limit, and to the optimization of factorized quantities, are also discussed thoroughly.
Download or read book Scale Setting Using the Extended Renormalization Group and the Principle of Maximal Conformality written by and published by . This book was released on 2012 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The extended renormalization group equations, which express the invariance of physical observables under both the renormalization scale- and scheme-parameter transformations, provide a convenient way for estimating the scale- and scheme-dependence of the physical process. In this paper, we present a solution for the scale-equation of the extended renormalization group equations at the four-loop level. Using the principle of maximum conformality (PMC)/Brodsky-Lepage-Mackenzie (BLM) scale-setting method, all non-conformal?{sub i} terms in the perturbative expansion series can be summed into the running coupling, and the resulting scale-fixed predictions are independent of the renormalization scheme. Different schemes lead to different effective PMC/BLM scales, but the final results are scheme independent. Conversely, from the requirement of scheme independence, one not only can obtain scheme-independent commensurate scale relations among different observables, but also determine the scale displacements among the PMC/BLM scales which are derived under different schemes. In principle, the PMC/BLM scales can be fixed order-by-order, and as a useful reference, we present a systematic and scheme-independent procedure for setting PMC/BLM scales up to NNLO. An explicit application for determining the scale setting of R{sub e{sup +}e−}(Q) up to four loops is presented. By using the world average?{sub s}{sup {ovr MS}}(MZ) = 0.1184 ± 0.0007, we obtain the asymptotic scale for the 't Hooft associated with the {ovr MS} scheme,?{sub {ovr MS}}{sup 'tH} = 24510{sup +9} MeV, and the asymptotic scale for the conventional {ovr MS} scheme,?{sub {ovr MS}} = 213−{sup +19} MeV.
Download or read book Particle Physics Reference Library written by Herwig Schopper and published by Springer Nature. This book was released on 2020 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first open access volume of the handbook series contains articles on the standard model of particle physics, both from the theoretical and experimental perspective. It also covers related topics, such as heavy-ion physics, neutrino physics and searches for new physics beyond the standard model. A joint CERN-Springer initiative, the "Particle Physics Reference Library" provides revised and updated contributions based on previously published material in the well-known Landolt-Boernstein series on particle physics, accelerators and detectors (volumes 21A, B1,B2,C), which took stock of the field approximately one decade ago. Central to this new initiative is publication under full open access
Download or read book QCD written by and published by . This book was released on 2000 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book At The Frontier Of Particle Physics Handbook Of Qcd In 3 Vols written by Misha Shifman and published by World Scientific. This book was released on 2001-04-10 with total page 2196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of reviews covering all aspects of quantum chromodynamics as we know it today. The articles have been written by recognized experts in this field, in honor of the 75th birthday of Professor Boris Ioffe. Combining features of a handbook and a textbook, this is the most comprehensive source of information on the present status of QCD. It is intended for students as well as physicists — both theorists and experimentalists.Each review is self-contained and pedagogically structured, providing the general formulation of the problem, telling where it stands with respect to other issues and why it is interesting and important, presenting the history of the subject, qualitative insights, and so on. The first part of the book is historical in nature. It includes, among other articles, Boris Ioffe's and Yuri Orlov's memoirs on high energy physics in the 1950's, a note by B V Geshkenbein on Ioffe's career in particle physics, and an essay on the discovery of asymptotic freedom written by David Gross.
Download or read book Conceptual Foundations of Quantum Field Theory written by Tian Yu Cao and published by Cambridge University Press. This book was released on 2004-03-25 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-author volume on the history and philosophy of physics.
Download or read book Foundations of Perturbative QCD written by John Collins and published by Cambridge University Press. This book was released on 2023-07-31 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scale Dependence and Renormalon inspired Resummations for Some QCD Observables written by Abolfazl Mirjalili and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Setting the Renormalization Scale in QCD written by and published by . This book was released on 2011 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale [mu] of the running coupling [alpha]{sub s}([mu]2): The purpose of the running coupling in any gauge theory is to sum all terms involving the [beta] function; in fact, when the renormalization scale is set properly, all non-conformal [beta] ≠ 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with [beta] = 0. The resulting scale-fixed predictions using the 'principle of maximum conformality' (PMC) are independent of the choice of renormalization scheme - a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale-setting in the Abelian limit. The PMC is also the theoretical principle underlying the BLM procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors nf in the QCD [beta] function is also correctly determined. We discuss several methods for determining the PMC/BLM scale for QCD processes. We show that a single global PMC scale, valid at leading order, can be derived from basic properties of the perturbative QCD cross section. The elimination of the renormalization scheme ambiguity using the PMC will not only increase the precision of QCD tests, but it will also increase the sensitivity of collider experiments to new physics beyond the Standard Model.
Download or read book XVIth International Congress on Mathematical Physics written by Pavel Exner and published by World Scientific. This book was released on 2010 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Congress on Mathematical Physics is the flagship conference in this exciting field. Convening every three years, it gives a survey on the progress achieved in all branches of mathematical physics. It also provides a superb platform to discuss challenges and new ideas. The present volume collects material from the XVIth ICMP which was held in Prague, August 2009, and features most of the plenary lectures and invited lectures in topical sessions as well as information on other parts of the congress program. This volume provides a broad coverage of the field of mathematical physics, from dominantly mathematical subjects to particle physics, condensed matter, and application of mathematical physics methods in various areas such as astrophysics and ecology, amongst others.
Download or read book Modern Perspectives in Lattice QCD Quantum Field Theory and High Performance Computing written by Laurent Lellouch and published by Oxford University Press. This book was released on 2011-08-25 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to familiarize the new generation of PhD students and postdoctoral fellows with the principles and methods of modern lattice field theory, which aims to resolve fundamental, non-perturbative questions about QCD without uncontrolled approximations.
Download or read book Eliminating the Renormalization Scale Ambiguity for Top Pair Production Using the Principle of Maximum Conformality written by and published by . This book was released on 2012 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: The uncertainty in setting the renormalization scale in finite-order perturbative QCD predictions using standard methods substantially reduces the precision of tests of the Standard Model in collider experiments. It is conventional to choose a typical momentum transfer of the process as the renormalization scale and take an arbitrary range to estimate the uncertainty in the QCD prediction. However, predictions using this procedure depend on the choice of renormalization scheme, leave a non-convergent renormalon perturbative series, and moreover, one obtains incorrect results when applied to QED processes. In contrast, if one fixes the renormalization scale using the Principle of Maximum Conformality (PMC), all non-conformal {l_brace}?{sub i}{r_brace}-terms in the perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC renormalization scale?{sub R}{sup PMC} and the resulting finite-order PMC prediction are both to high accuracy independent of choice of the initial renormalization scale?{sub R}{sup init}, consistent with renormalization group invariance. Moreover, after PMC scale-setting, the n!-growth of the pQCD expansion is eliminated. Even the residual scale-dependence at fixed order due to unknown higher-order {l_brace}?{sub i}{r_brace}-terms is substantially suppressed. As an application, we apply the PMC procedure to obtain NNLO predictions for the t{bar t}-pair hadroproduction cross-section at the Tevatron and LHC colliders. There are no renormalization scale or scheme uncertainties, thus greatly improving the precision of the QCD prediction. The PMC prediction for?{sub t{bar t}} is larger in magnitude in comparison with the conventional scale-setting method, and it agrees well with the present Tevatron and LHC data. We also verify that the initial scale-independence of the PMC prediction is satisfied to high accuracy at the NNLO level: the total cross-section remains almost unchanged even when taking very disparate initial scales?{sub R}{sup init} equal to m{sub t}, 20 m{sub t}, √s.
Download or read book The Two Loop Scale Dependence of the Static QCD Potential Including Quark Masses written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The interaction potential V(Q[sup 2]) between static test charges can be used to define an effective charge[alpha][sub V](Q[sup 2]) and a physically-based renormalization scheme for quantum chromodynamics and other gauge theories. In this paper we use recent results for the finite-mass fermionic corrections to the heavy-quark potential at two-loops to derive the next-to-leading order term for the Gell Mann-Low function of the V-scheme. The resulting effective number of flavors N[sub F](Q[sup 2]/m[sup 2]) in the[alpha][sub V] scheme is determined as a gauge-independent and analytic function of the ratio of the momentum transfer to the quark pole mass. The results give automatic decoupling of heavy quarks and are independent of the renormalization procedure. Commensurate scale relations then provide the next-to-leading order connection between all perturbatively calculable observables to the analytic and gauge-invariant[alpha][sub V] scheme without any scale ambiguity and a well defined number of active flavors. The inclusion of the finite quark mass effects in the running of the coupling is compared with the standard treatment of finite quark mass effects in the[ovr MS] scheme.
Download or read book Basics of Perturbative QCD written by Yuri Dokshitzer and published by Atlantica Séguier Frontières. This book was released on 1991 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book QCD 99 written by S. Narison and published by . This book was released on 2000 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt:
