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 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 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 The Principle of Maximum Conformality written by and published by . This book was released on 2011 with total page 2 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 of the running coupling [alpha]{sub s}([mu]2). It is common practice to guess a physical scale [mu] = Q which is of order of a typical momentum transfer Q in the process, and then vary the scale over a range Q/2 and 2Q. This procedure is clearly problematic since the resulting fixed-order pQCD prediction will depend on the renormalization scheme, and it can even predict negative QCD cross sections at next-to-leading-order. Other heuristic methods to set the renormalization scale, such as the 'principle of minimal sensitivity', give unphysical results for jet physics, sum physics into the running coupling not associated with renormalization, and violate the transitivity property of the renormalization group. Such scale-setting methods also give incorrect results when applied to Abelian QED. Note that the factorization scale in QCD is introduced to match nonperturbative and perturbative aspects of the parton distributions in hadrons; it is present even in conformal theory and thus is a completely separate issue from renormalization scale setting. The PMC provides a consistent method for determining the renormalization scale in pQCD. The PMC scale-fixed prediction is 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 global scale can be derived efficiently at NLO from basic properties of the PQCD cross section. The elimination of the renormalization scheme ambiguity using the PMC will not only increases the precision of QCD tests, but it will also increase the sensitivity of colliders to new physics beyond the Standard Model.
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 Setting the Renormalization Scale in PQCD written by and published by . This book was released on 2015 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: A key problem in making precise perturbative QCD (pQCD) predictions is how to set the renormalization scale of the running coupling unambiguously at each finite order. The elimination of the uncertainty in setting the renormalization scale in pQCD will greatly increase the precision of collider tests of the Standard Model and the sensitivity to new phenomena. Renormalization group invariance requires that predictions for observables must also be independent on the choice of the renormalization scheme. The well-known Brodsky-Lepage-Mackenzie (BLM) approach cannot be easily extended beyond next-to-next-to-leading order of pQCD. Several suggestions have been proposed to extend the BLM approach to all orders. In this paper we discuss two distinct methods. One is based on the "Principle of Maximum Conformality" (PMC), which provides a systematic all-orders method to eliminate the scale and scheme ambiguities of pQCD. The PMC extends the BLM procedure to all orders using renormalization group methods; as an outcome, it significantly improves the pQCD convergence by eliminating renormalon divergences. An alternative method is the "sequential extended BLM" (seBLM) approach, which has been primarily designed to improve the convergence of pQCD series. The seBLM, as originally proposed, introduces auxiliary fields and follows the pattern of the [beta]0-expansion to fix the renormalization scale. However, the seBLM requires a recomputation of pQCD amplitudes including the auxiliary fields; due to the limited availability of calculations using these auxiliary fields, the seBLM has only been applied to a few processes at low orders. In order to avoid the complications of adding extra fields, we propose a modified version of seBLM which allows us to apply this method to higher orders. As a result, we then perform detailed numerical comparisons of the two alternative scale-setting approaches by investigating their predictions for the annihilation cross section ratio Re+e- at four-loop order in pQCD.
Download or read book Renormalization Group Invariance and Optimal QCD Renormalization Scale Setting written by and published by . This book was released on 2014 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 A Novel All Orders Single Scale Approach to QCD Renormalization Scale Setting written by and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Collider Physics within the Standard Model written by Guido Altarelli and published by Springer. This book was released on 2017-04-19 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is open access under a CC BY 4.0 license. With this graduate-level primer, the principles of the standard model of particle physics receive a particular skillful, personal and enduring exposition by one of the great contributors to the field. In 2013 the late Prof. Altarelli wrote: The discovery of the Higgs boson and the non-observation of new particles or exotic phenomena have made a big step towards completing the experimental confirmation of the standard model of fundamental particle interactions. It is thus a good moment for me to collect, update and improve my graduate lecture notes on quantum chromodynamics and the theory of electroweak interactions, with main focus on collider physics. I hope that these lectures can provide an introduction to the subject for the interested reader, assumed to be already familiar with quantum field theory and some basic facts in elementary particle physics as taught in undergraduate courses. “These lecture notes are a beautiful example of Guido’s unique pedagogical abilities and scientific vision”. From the Foreword by Gian Giudice
Download or read book Physics Help written by Nicolae Sfetcu and published by MultiMedia Publishing. This book was released on 2014-05-10 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an overview of the major subfields and concepts in physics, including a brief outline of the history of physics and its subfields. Physics (from Greek from φυσικός (phusikos): natural, from φύσις (fysis): Nature) is the science of Nature in the broadest sense. Physicists study the behaviour and interactions of matter and radiation. Theories of physics are generally expressed as mathematical relations. Well-established theories are often referred to as physical laws or laws of physics; however, like all scientific theories, they are ultimately provisional. Physics is very closely related to the other natural sciences, particularly chemistry. The book is an overview of the major subfields and concepts in physics, including a brief outline of the history of physics and its subfields.
Download or read book Photon Physics at the LHC written by Michael Hance and published by Springer Science & Business Media. This book was released on 2012-11-08 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis reports on the first studies of Standard Model photon production at the Large Hadron Collider (LHC) using the ATLAS detector. Standard Model photon production is a large background in the search for Higgs bosons decaying into photon pairs, and is thus critical to understand. The thesis explains the techniques used to reconstruct and identify photon candidates using the ATLAS detector, and describes a measurement of the production cross section for isolated prompt photons. The thesis also describes a search for the Higgs boson in which the analysis techniques used in the measurement are exploited to reduce and estimate non-prompt backgrounds in diphoton events.
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 and Collider Physics written by R. K. Ellis and published by Cambridge University Press. This book was released on 2003-12-04 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed overview of the physics of high-energy colliders emphasising the role of QCD.
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 The Anomalous Magnetic Moment of the Muon written by Fred Jegerlehner and published by Springer Science & Business Media. This book was released on 2008 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews the present state of knowledge of the anomalous magnetic moment a=(g-2)/2 of the muon. The muon anomalous magnetic moment is one of the most precisely measured quantities in elementary particle physics and provides one of the most stringent tests of relativistic quantum field theory as a fundamental theoretical framework. It allows for an extremely precise check of the standard model of elementary particles and of its limitations.
Download or read book Heavy Flavours II written by A. J. Buras and published by World Scientific. This book was released on 1998 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of review articles on the most outstanding topics in heavy flavour physics. All the authors have made significant contributions to this field. The book reviews in detail the theoretical structure of heavy flavour physics and confronts the Standard Model and some of its extensions with existing experimental data.This new edition covers new trends and ideas and includes the latest experimental information. Compared to the previous edition interesting new activities are included and some of the key contributions are updated. Particular attention is paid to the discovery of the top quark and the determination of its mass.
