Download or read book Self Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale written by and published by . This book was released on 2012 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: In conventional treatments, predictions from fixed-order perturbative QCD calculations cannot be fixed with certainty due to ambiguities in the choice of the renormalization scale as well as the renormalization scheme. In this paper we present a general discussion of the constraints of the renormalization group (RG) invariance on the choice of the renormalization scale. We adopt the RG based equations, which incorporate the scheme parameters, for a general exposition of RG invariance, since they simultaneously express the invariance of physical observables under both the variation of the renormalization scale and the renormalization scheme parameters. We then discuss the self-consistency requirements of the RG, such as reflexivity, symmetry, and transitivity, which must be satisfied by the scale-setting method. The Principle of Minimal Sensitivity (PMS) requires the slope of the approximant of an observable to vanish at the renormalization point. This criterion provides a scheme-independent estimation, but it violates the symmetry and transitivity properties of the RG and does not reproduce the Gell-Mann-Low scale for QED observables. The Principle of Maximum Conformality (PMC) satisfies all of the deductions of the RG invariance - reflectivity, symmetry, and transitivity. Using the PMC, all non-conformal {{u03B2}Ri}-terms (R stands for an arbitrary renormalization scheme) 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 scales and the resulting finite-order PMC predictions are both to high accuracy independent of the choice of initial renormalization scale, consistent with RG invariance.
Download or read book Strong Interactions in Spacelike and Timelike Domains written by Alexander V. Nesterenko and published by Elsevier. This book was released on 2016-11-26 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Strong Interactions in Spacelike and Timelike Domains: Dispersive Approach provides the theoretical basis for the description of the strong interactions in the spacelike and timelike domains. The book primarily focuses on the hadronic vacuum polarization function, R-ratio of electron-positron annihilation into hadrons, and the Adler function, which govern a variety of the strong interaction processes at various energy scales. Specifically, the book presents the essentials of the dispersion relations for these functions, recaps their perturbative calculation, and delineates the dispersively improved perturbation theory. The book also elucidates the peculiarities of the continuation of the spacelike perturbative results into the timelike domain, which is indispensable for the studies of electron-positron annihilation into hadrons and the related processes. Covers the topics that play an essential role in contemporary particle physics and future collider projects Applicable for self-education alongside standard textbooks Makes the subject easily accessible without the need of an extensive theoretical background
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 50 Years Of The Renormalization Group Dedicated To The Memory Of Michael E Fisher written by Amnon Aharony and published by World Scientific. This book was released on 2024-07-26 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in the book are devoted to the memory of Michael E Fisher, and hence include many personal memories from people whose work was influenced by him. Also, the book is a collection of articles from leaders in the field of phase transitions and critical phenomena, to celebrate 50 years of the renormalization group and the 1972 paper by Wilson and Fisher. Many of the articles review, in tutorial form, the progress in the fields of phase transitions and the renormalization group.
Download or read book Importance of Proper Renormalization Scale setting for QCD Testing at Colliders written by and published by . This book was released on 2015 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived from the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant ?s to eliminate all non-conformal {βi} terms in the pQCD series. The {βi} terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the NC → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the ?increasing-decreasing? behavior observed by the D0 collaboration for increasing tt¯ invariant mass. At lower energies, the angular distributions of heavy quarks can be used to obtain a direct determination of the heavy quark potential. A discussion of the angular distributions of massive quarks and leptons is also presented, including the fermionic component of the two-loop corrections to the electromagnetic form factors. Furthermore, these results demonstrate that the application of the PMC systematically eliminates a major theoretical uncertainty for pQCD predictions, thus increasing collider sensitivity to possible new physics beyond the Standard Model.
Download or read book Instantons in Gauge Theories written by M. Shifman and published by World Scientific. This book was released on 1994 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a compilation of works which, taken together, give a complete and consistent presentation of instanton calculus in non-Abelian gauge theories, as it exists now. Some of the papers reproduced are instanton classics. Among other things, they show from a historical perspective how the instanton solution has been found, the motivation behind it and how the physical meaning of instantons has been revealed. Other papers are devoted to different aspects of instanton formalism including instantons in supersymmetric gauge theories. A few unsolved problems associated with instantons are described in great detail. The papers are organized into several sections that are linked both logically and historically, accompanied by extensive comments.
Download or read book Lectures On Phase Transitions And The Renormalization Group written by Nigel Goldenfeld and published by CRC Press. This book was released on 2018-03-08 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.
Download or read book Quantum Gravity and the Functional Renormalization Group written by Martin Reuter and published by Cambridge University Press. This book was released on 2019-01-03 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained pedagogical introduction to asymptotic safety and the functional renormalization group in quantum gravity, for graduate students and researchers.
Download or read book Research Directions For The Decade Snowmass 1990 Proceedings Of The 1990 Summer Study On High Energy Physics written by Berger Edmond L and published by World Scientific. This book was released on 1992-09-16 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the advent of the Superconducting Super Collider and other new technologies, coupled with the development of particle astrophysics and other non-accelerator based physics, research in high energy particle physics in the nineties promises to break into new and exciting frontiers. To chart the directions and opportunities for this new decade, the 1990 Summer Study on High Energy Physics was organized in Snowmass, Colorado. Like previous Snowmass Summer Studies, it plays a key role in shaping research directions and in drawing the particle physics community together.This book of the proceedings examines the full spectrum of important scientific issues and opportunities in high energy particle physics in the decade of the 1990's, including research at existing and anitcipated hadron-hadron, e+e-, and ep colliders; research at fixed-target facilities; the scientific potential of possible new facilities such as B factories; particle astrophysics and non-accelerator based physics; and accelerator and detector initiatives. It also discusses the physics and technical aspects of the initial Superconducting Super Collider experimental program.This volume, therefore, offers a captivating glimpse into the future of high energy physics, and makes essential reading for all physicists interested in assessing the exciting new research opportunities the future technologies would bring.
Download or read book Fusion Energy Update written by and published by . This book was released on 1979 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book From the Fermi Scale to Cosmology written by Alberto Salvio and published by Frontiers Media SA. This book was released on 2019-12-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Eleventh Marcel Grossmann Meeting The On Recent Developments In Theoretical And Experimental General Relativity Gravitation And Relativistic Field Theories In 3 Volumes Proceedings Of The Mg11 Meeting On General Relativity written by Hagen Kleinert and published by World Scientific. This book was released on 2008-09-04 with total page 3129 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Marcel Grossmann Meetings are three-yearly forums that meet to discuss recent advances in gravitation, general relativity and relativistic field theories, emphasizing their mathematical foundations, physical predictions and experimental tests. These meetings aim to facilitate the exchange of ideas among scientists, to deepen our understanding of space-time structures, and to review the status of ongoing experiments and observations testing Einstein's theory of gravitation either from ground or space-based experiments. Since the first meeting in 1975 in Trieste, Italy, which was established by Remo Ruffini and Abdus Salam, the range of topics presented at these meetings has gradually widened to accommodate issues of major scientific interest, and attendance has grown to attract more than 900 participants from over 80 countries.This proceedings volume of the eleventh meeting in the series, held in Berlin in 2006, highlights and records the developments and applications of Einstein's theory in diverse areas ranging from fundamental field theories to particle physics, astrophysics and cosmology, made possible by unprecedented technological developments in experimental and observational techniques from space, ground and underground observatories. It provides a broad sampling of the current work in the field, especially relativistic astrophysics, including many reviews by leading figures in the research community.
Download or read book The QCD Vacuum Hadrons and Superdense Matter written by E. V. Shuryak and published by World Scientific. This book was released on 2004 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book is an extensive set of lecture notes on various aspects of non-perturbative quantum chromodynamics ? the fundamental theory of strong interaction on which nuclear and hadronic physics is based.The original edition of the book, written in the mid-1980's, had more of a review style. In the second edition the outline remains the same, but the text has been completely rewritten, and extended. Apart from the new developments over the years, this edition has benefited from several graduate courses which the author has taught at Stony Brook during the last decade. The text is now complemented by exercises and has a total of about 1000 references to major works, arranged by subject.Three major issues ? the structure of the QCD vacuum, the structure of hadrons, and the physics of hot/dense matter ? are addressed as physics problems. Therefore, when discussing any specific subject, the book attempts to incorporate (1) all the solid theoretical results, (2) experimental information, and (3) results of numerical (lattice) simulations, which are playing an increasing role in quantum field theory in general, and the development of QCD in particular.The QCD Vacuum, Hadrons and Superdense Matter takes the reader from the first encounter with the subject to the front line of research, as quickly as possible.
Download or read book Qcd Vacuum Hadrons And Superdense Matter The 2nd Edition written by Edward V Shuryak and published by World Scientific. This book was released on 2004-10-07 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book is an extensive set of lecture notes on various aspects of non-perturbative quantum chromodynamics — the fundamental theory of strong interaction on which nuclear and hadronic physics is based.The original edition of the book, written in the mid-1980's, had more of a review style. In the second edition the outline remains the same, but the text has been completely rewritten, and extended. Apart from the new developments over the years, this edition has benefited from several graduate courses which the author has taught at Stony Brook during the last decade. The text is now complemented by exercises and has a total of about 1000 references to major works, arranged by subject.Three major issues — the structure of the QCD vacuum, the structure of hadrons, and the physics of hot/dense matter — are addressed as physics problems. Therefore, when discussing any specific subject, the book attempts to incorporate (1) all the solid theoretical results, (2) experimental information, and (3) results of numerical (lattice) simulations, which are playing an increasing role in quantum field theory in general, and the development of QCD in particular.The QCD Vacuum, Hadrons and Superdense Matter takes the reader from the first encounter with the subject to the front line of research, as quickly as possible.
Download or read book Energy Research Abstracts written by and published by . This book was released on 1994 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semiannual, with semiannual and annual indexes. References to all scientific and technical literature coming from DOE, its laboratories, energy centers, and contractors. Includes all works deriving from DOE, other related government-sponsored information, and foreign nonnuclear information. Arranged under 39 categories, e.g., Biomedical sciences, basic studies; Biomedical sciences, applied studies; Health and safety; and Fusion energy. Entry gives bibliographical information and abstract. Corporate, author, subject, report number indexes.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Annual Review written by 岡崎国立共同研究機構分子科学研究所 and published by . This book was released on 2011 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
