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Modern Analytic Methods For Scattering Amplitudes With An Application To Two Loop Five Particle Processes
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Book Synopsis Modern Analytic Methods for Computing Scattering Amplitudes by : Simone Zoia
Download or read book Modern Analytic Methods for Computing Scattering Amplitudes written by Simone Zoia and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents some essential techniques that constitute the modern strategy for computing scattering amplitudes. It begins with an introductory chapter to fill the gap between a standard QFT course and the latest developments in the field. The author then tackles the main bottleneck: the computation of the loop Feynman integrals. The most efficient technique for their computation is the method of the differential equations. This is discussed in detail, with a particular focus on the mathematical aspects involved in the derivation of the differential equations and their solution. Ample space is devoted to the special functions arising from the differential equations, to their analytic properties, and to the mathematical techniques which allow us to handle them systematically. The thesis also addresses the application of these techniques to a cutting-edge problem of importance for the physics programme of the Large Hadron Collider: five-particle amplitudes at two-loop order. It presents the first analytic results for complete two-loop five-particle amplitudes, in supersymmetric theories and QCD. The techniques discussed here open the door to precision phenomenology for processes of phenomenological interest, such as three-photon, three-jet, and di-photon + jet production.sses of phenomenological interest, such as three-photon, three-jet, and di-photon + jet production.
Book Synopsis Modern Analytic Methods for Scattering Amplitudes, with an Application to Two-loop Five-particle Processes by : Simone Zoia
Download or read book Modern Analytic Methods for Scattering Amplitudes, with an Application to Two-loop Five-particle Processes written by Simone Zoia and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modern Analytic Methods for Computing Scattering Amplitudes by : Simone Zoia
Download or read book Modern Analytic Methods for Computing Scattering Amplitudes written by Simone Zoia and published by Springer Nature. This book was released on 2022-05-18 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents some essential techniques that constitute the modern strategy for computing scattering amplitudes. It begins with an introductory chapter to fill the gap between a standard QFT course and the latest developments in the field. The author then tackles the main bottleneck: the computation of the loop Feynman integrals. The most efficient technique for their computation is the method of the differential equations. This is discussed in detail, with a particular focus on the mathematical aspects involved in the derivation of the differential equations and their solution. Ample space is devoted to the special functions arising from the differential equations, to their analytic properties, and to the mathematical techniques which allow us to handle them systematically. The thesis also addresses the application of these techniques to a cutting-edge problem of importance for the physics programme of the Large Hadron Collider: five-particle amplitudes at two-loop order. It presents the first analytic results for complete two-loop five-particle amplitudes, in supersymmetric theories and QCD. The techniques discussed here open the door to precision phenomenology for processes of phenomenological interest, such as three-photon, three-jet, and di-photon + jet production.
Book Synopsis Analyticity Properties and Bounds of the Scattering Amplitudes by : André Martin (Professeur.)
Download or read book Analyticity Properties and Bounds of the Scattering Amplitudes written by André Martin (Professeur.) and published by M.E. Sharpe. This book was released on 1970 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures in Scattering Theory by : A. G. Sitenko
Download or read book Lectures in Scattering Theory written by A. G. Sitenko and published by Elsevier. This book was released on 2013-10-22 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures in Scattering Theory discusses problems in quantum mechanics and the principles of the non-relativistic theory of potential scattering. This book describes in detail the properties of the scattering matrix and its connection with physically observable quantities. This text presents a stationary formulation of the scattering problem and the wave functions of a particle found in an external field. This book also examines the analytic properties of the scattering matrix, dispersion relations, complex angular moments, as well as the separable representation of the scattering amplitude. The text also explains the method of factorizing the potential and the two-particle scattering amplitude, based on the Hilbert-Schmidt theorem for symmetric integral equations. In investigating the problem of scattering in a three-particle system, this book notes that the inapplicability of the Lippman-Schwinger equations can be fixed by appropriately re-arranging the equations. Faddeev equations are the new equations formed after such re-arrangements. This book also cites, as an example, the scattering of a spin-1/2 particle by a spinless particle (such as the scattering of a nucleon by a spinless nucleus). This text is suitable for students and professors dealing with quantum mechanics, theoretical nuclear physics, or other fields of advanced physics.
Book Synopsis Scattering Amplitudes with the Multi-loop Numerical Unitarity Method by : Vasily Sotnikov
Download or read book Scattering Amplitudes with the Multi-loop Numerical Unitarity Method written by Vasily Sotnikov and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: In this thesis, we develop and apply the D-dimensional numerical unitarity method for the computation of multi-loop scattering amplitudes, which are the key building blocks for precise theoretical predictions for the ongoing physics program of the Large Hadron Collider experiment at CERN. We formulate a framework for consistently implementing dimensional regularization in numerical approaches, which in particular can be applied for efficient numerical evaluations of dimensionally-regularized helicity amplitudes with external fermions. We present the next-to-leading order QCD predictions for the production of W boson in association with a pair of bottom quarks and light jets at the Large Hadron Collider, which is an irreducible background to the the studies of decays of the Higgs boson to a pair of bottom quarks. We include all the effects of the non-vanishing bottom-quark mass. To obtain the one-loop matrix elements required for the process, we implement an extension of the numerical unitarity method to massive particles in the loop. We present the first benchmark values and analytic form of all two-loop five-parton helicity amplitudes in QCD in the leading-color approximation. The analytic expressions are reconstructed from exact numerical evaluations with the numerical unitarity method. Our results provide all two-loop amplitudes required for the calculation of next-to-next-to-leading order QCD corrections to the production of three jets at hadron colliders in the leading-color approximation.
Book Synopsis Toward Two Loops Five Massless Partons Scattering Amplitudes from Kinematic Limits by : Mathieu Giroux
Download or read book Toward Two Loops Five Massless Partons Scattering Amplitudes from Kinematic Limits written by Mathieu Giroux and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "The computation of massless 5-point 2-loop scattering amplitudes requires the analytical expressions for about 32400 master integrals. In this thesis, we present a method to evaluate all these integrals from a much smaller set corresponding to a fix ordering of the external particles. The integration constants for different leg orderings are determined by using multiple scaling limits of the associated (canonical) differential equations' alphabet letters. The choice of scaling limits is constrained by the requirement the paths they describe in the kinematic space are generated only by harmonic polylogarithms (HPLs). Such constraint ensures using scaling limits makes the analytic evaluation of the solutions fast and simple. Our method is suitable to show the existence of a web of computational highways in the kinematic space relating all evaluated master integrals"--
Book Synopsis Journeys Through The Precision Frontier: Amplitudes For Colliders (Tasi 2014) - Proceedings Of The 2014 Theoretical Advanced Study Institute In Elementary Particle Physics by : Lance Dixon
Download or read book Journeys Through The Precision Frontier: Amplitudes For Colliders (Tasi 2014) - Proceedings Of The 2014 Theoretical Advanced Study Institute In Elementary Particle Physics written by Lance Dixon and published by World Scientific. This book was released on 2015-09-17 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a compilation of the lectures at TASI 2014. The coverage focuses on modern calculational techniques for scattering amplitudes, and on the phenomenology of QCD in hadronic collisions. Introductions to flavor physics, dark matter, and physics beyond the Standard Model are also provided. The lectures are accessible to graduate students at the initial stages of their research careers.
Book Synopsis Scattering Amplitudes in Gauge Theory and Gravity by : Henriette Elvang
Download or read book Scattering Amplitudes in Gauge Theory and Gravity written by Henriette Elvang and published by Cambridge University Press. This book was released on 2015-02-05 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive, pedagogical introduction to scattering amplitudes in gauge theory and gravity for graduate students.
Book Synopsis Digestible Quantum Field Theory by : Andrei Smilga
Download or read book Digestible Quantum Field Theory written by Andrei Smilga and published by Springer. This book was released on 2017-12-30 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an intermediate level treatment of quantum field theory, appropriate to a reader with a first degree in physics and a working knowledge of special relativity and quantum mechanics. It aims to give the reader some understanding of what QFT is all about, without delving deep into actual calculations of Feynman diagrams or similar. The author serves up a seven‐course menu, which begins with a brief introductory Aperitif. This is followed by the Hors d'oeuvres, which set the scene with a broad survey of the Universe, its theoretical description, and how the ideas of QFT developed during the last century. In the next course, the Art of Cooking, the author recaps on some basic facts of analytical mechanics, relativity, quantum mechanics and also presents some nutritious “extras” in mathematics (group theory at the elementary level) and in physics (theory of scattering). After these preparations, the reader should have a good appetite for the Entrées ‐ the central par t of the book where the Standard Model is described and explained. After Trou Normand, the restive pause including human stories about physicists and no formulas, the author serves the Dessert, devoted to supersymmetry (a very beautiful theory that is still awaiting a direct experimental confirmation), to general relativity and to the mystery of quantum gravity.
Book Synopsis Modern Applications of Scattering Amplitudes and Topological Phases by : Julio Parra Martinez
Download or read book Modern Applications of Scattering Amplitudes and Topological Phases written by Julio Parra Martinez and published by . This book was released on 2020 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation we discuss some novel applications of the methods of scattering amplitudes and topological phases. First, we describe on-shell tools to calculate anomalous dimensions in effective field theories with higer-dimension operators. Using such tools we prove and apply a new perturbative non-renormalization theorem, and we explore the structure of the two-loop anomalous dimension matrix of dimension-six operators in the Standard Model Effective Theory (SMEFT). Second, we introduce new methods to calculate the classical limit of gravitational scattering amplitudes. Using these methods, in conjunction with eikonal techniques, we calculate the classical gravitational deflection angle of massive and massles particles in a variety of theories, which reveal graviton dominance beyond 't Hooft's. Finally, we point out that different choices of Gliozzi-Scherk-Olive (GSO) projections in superstring theory can be conveniently understood by the inclusion of fermionic invertible topological phases, or equivalently topological superconductors, on the worldsheet. We explain how the classification of fermionic topological phases, recently achieved by the condensed matter community, provides a complete and systematic classification of ten-dimensional superstrings and gives a new perspective on the K-theoretic classification of D-branes.
Book Synopsis Scattering Theory by : Asim Orhan Barut
Download or read book Scattering Theory written by Asim Orhan Barut and published by . This book was released on 1969 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Analytic S-Matrix by : R. J. Eden
Download or read book The Analytic S-Matrix written by R. J. Eden and published by Cambridge University Press. This book was released on 2002-04-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theory of the S-Matrix, starting from physically plausible assumptions and looking at the mathematical consequences.
Book Synopsis Scattering Amplitudes in Flat Space and Anti-de Sitter Space by : Savan Kharel
Download or read book Scattering Amplitudes in Flat Space and Anti-de Sitter Space written by Savan Kharel and published by . This book was released on 2014 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: We calculate gauge theory one-loop amplitudes with the aid of the complex shift used in the Britto- Cachazo-Feng-Witten (BCFW) recursion relations of tree amplitudes. We apply the shift to the integrand and show that the contribution from the limit of infinite shift vanishes after integrating over the loop momentum, with a judicious choice of basis for polarization vectors. This enables us to write the one-loop amplitude in terms of on-shell tree and lower-point one-loop amplitudes. Some of the tree amplitudes are forward amplitudes. We show that their potential singularities do not contribute and the BCFW recursion relations can be applied in such a way as to avoid these singularities altogether. We calculate in detail n-point one-loop amplitudes for n = 2, 3, 4, and outline the generalization of our method to n > 4. In addition to scattering amplitudes in flat space, we studied amplitudes in Anti-de Sitter (AdS) space, which is equivalent to conformal correlators in the boundary of the Anti-de Sitter space. We discuss the use of the embedding formalism and Mellin transform in the calculation of tree-level correlators of scalar and vector fields in AdS/CFT. We present an iterative procedure that builds amplitudes by sewing together lower-point off-shell diagrams. Both scalar and vector correlators are shown to be given in terms of Mellin amplitudes. We apply the procedure to the explicit calculation of three-, four- and five-point correlators.
Book Synopsis Applications of Modern Methods for Scattering Amplitudes by : Francesco Buciuni
Download or read book Applications of Modern Methods for Scattering Amplitudes written by Francesco Buciuni and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Particle Kinematics by : Eero Byckling
Download or read book Particle Kinematics written by Eero Byckling and published by . This book was released on 1973 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ideals, Varieties, and Algorithms by : David Cox
Download or read book Ideals, Varieties, and Algorithms written by David Cox and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. Contains a new section on Axiom and an update about MAPLE, Mathematica and REDUCE.
