Download or read book Two loop Helicity Amplitudes in QCD written by Lee W. Garland and published by . This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Two Loop Helicity Amplitudes for Gluon Gluon Scattering in QCD and Supersymmetric Yang Mills Theory written by and published by . This book was released on 2002 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present the two-loop helicity amplitudes for the scattering of two gluons into two gluons in QCD, which are relevant for next-to-next-to-leading order corrections to jet production at hadron colliders. We give the results in the 't Hooft-Veltman and four-dimensional helicity variants of dimensional regularization. Summing our expressions over helicities and colors, and converting to conventional dimensional regularization, gives results in complete agreement with those of Glover, Oleari and Tejeda-Yeomans. We also present the amplitudes for 2 --> 2 scattering in pure N = 1 supersymmetric Yang-Mills theory.

Download or read book Two Loop Helicity Amplitudes for Quark Gluon Scattering in QCD and Supersymmetric Yang Mills Theory written by and published by . This book was released on 2003 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present the two-loop QCD helicity amplitudes for quark-gluon scattering, and for quark-antiquark annihilation into two gluons. These amplitudes are relevant for next-to-next-to-leading order corrections to (polarized) jet production at hadron colliders. We give the results in the 't Hooft-Veltman and four-dimensional helicity (FDH) variants of dimensional regularization. The transition rules for converting the amplitudes between the different variants are much more intricate than for the previously discussed case of gluon-gluon scattering. Summing our two-loop expressions over helicities and colors, and converting to conventional dimensional regularization, gives results in complete agreement with those of Anastasiou, Glover, Oleari and Tejeda-Yeomans. We describe the amplitudes for 2 --> 2 scattering in pure N = 1 supersymmetric Yang-Mills theory, obtained from the QCD amplitudes by modifying the color representation and multiplicities, and verify supersymmetry Ward identities in the FDH scheme.

Download or read book Two loop Helicity Amplitudes for Quark gluon Scattering in QCD and Gluino gluon Scattering in Supersymmetric Yang Mills Theory written by Zvi Bern and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Two loop Leading colour QCD Helicity Amplitudes for Two photon Plus Jet Production at the LHC written by Herschel A. Chawdhry and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Two Loop Helicity Amplitudes for Quark Quark Scattering in QCD and Gluino Gluino Scattering in Supersymmetric Yang Mills Theory written by Abilio De Freitas and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Two loop Four gluon Helicity Amplitude in QCD written by and published by . This book was released on 2000 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present the two-loop pure gauge contribution to the gluon-gluon scattering amplitude with maximal helicity violation. The construction of the amplitude does not rely directly on Feynman diagrams, but instead uses its analytic properties 4--2[epsilon] dimensions. The authors evaluate the loop integrals appearing in the amplitude through order([epsilon]°)in terms of polylogarithms.

Download or read book Supersymmetric Regularization Two Loop QCD Amplitudes and Coupling Shifts written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a definition of the four-dimensional helicity (FDH) regularization scheme valid for two or more loops. This scheme was previously defined and utilized at one loop. It amounts to a variation on the standard 't Hooft-Veltman scheme and is designed to be compatible with the use of helicity states for ''observed'' particles. It is similar to dimensional reduction in that it maintains an equal number of bosonic and fermionic states, as required for preserving supersymmetry. Supersymmetry Ward identities relate different helicity amplitudes in supersymmetric theories. As a check that the FDH scheme preserves supersymmetry, at least through two loops, we explicitly verify a number of these identities for gluon-gluon scattering (gg[yields] gg) in supersymmetric QCD. These results also cross-check recent non-trivial two-loop calculations in ordinary QCD. Finally, we compute the two-loop shift between the FDH coupling and the standard[bar M][bar S] coupling, [alpha][sub s]. The FDH shift is identical to the one for dimensional reduction. The two-loop coupling shifts are then used to obtain the three-loop QCD[beta] function in the FDH and dimensional reduction schemes.

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.

Download or read book Renormalization and Galois Theories written by Frédéric Fauvet and published by European Mathematical Society. This book was released on 2009 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory. The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions. The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes, orchestrated by diverse Galois theories. It contains three lecture courses together with five research articles and will be useful to both researchers and graduate students in mathematics and physics.

Download or read book All One loop Maximally Helicity Violating Gluonic Amplitudes in QCD written by Lance J. Dixon and published by . This book was released on 2006 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: We use on-shell recursion relations to compute analytically the one-loop corrections to maximally-helicity-violating n-gluon amplitudes in QCD. The cut-containing parts have been computed previously; our work supplies the remaining rational parts for these amplitudes, which contain two gluons of negative helicity and the rest positive, in an arbitrary color ordering. We also present formulae specific to the six-gluon cases, with helicities ( -+-+++) and ( -++-++), as well as numerical results for six, seven, and eight gluons. Our construction of the n-gluon amplitudes illustrates the relatively modest growth in complexity of the on-shell-recursive calculation as the number of external legs increases. These amplitudes add to the growing body of one-loop amplitudes known for all n, which are useful for studies of general properties of amplitudes, including their twistor-space structure.

Download or read book Anti Differentiation and the Calculation of Feynman Amplitudes written by Johannes Blümlein and published by Springer Nature. This book was released on 2021-11-26 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises review papers presented at the Conference on Antidifferentiation and the Calculation of Feynman Amplitudes, held in Zeuthen, Germany, in October 2020, and a few additional invited reviews. The book aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function spaces, the theory of differential equations and summation theory. Almost all of these algorithms have a strong basis in computer algebra. The solution of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics.

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.

Download or read book Introduction to Soft Collinear Effective Theory written by Thomas Becher and published by Springer. This book was released on 2015-03-04 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among resummation techniques for perturbative QCD in the context of collider and flavor physics, soft-collinear effective theory (SCET) has emerged as both a powerful and versatile tool, having been applied to a large variety of processes, from B-meson decays to jet production at the LHC. This book provides a concise, pedagogical introduction to this technique. It discusses the expansion of Feynman diagrams around the high-energy limit, followed by the explicit construction of the effective Lagrangian - first for a scalar theory, then for QCD. The underlying concepts are illustrated with the quark vector form factor at large momentum transfer, and the formalism is applied to compute soft-gluon resummation and to perform transverse-momentum resummation for the Drell-Yan process utilizing renormalization group evolution in SCET. Finally, the infrared structure of n-point gauge-theory amplitudes is analyzed by relating them to effective-theory operators. This text is suitable for graduate students and non-specialist researchers alike as it requires only basic knowledge of perturbative QCD.

Download or read book Bootstrapping Multi Parton Loop Amplitudes in QCD written by and published by . This book was released on 2005 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present a new method for computing complete one-loop amplitudes, including their rational parts, in non-supersymmetric gauge theory. This method merges the unitarity method with on-shell recursion relations. It systematizes a unitarity-factorization bootstrap approach previously applied by the authors to the one-loop amplitudes required for next-to-leading order QCD corrections to the processes ee− 2!Z, [gamma]* 2!4 jets and pp 2!W + 2 jets. We illustrate the method by reproducing the one-loop color-ordered five-gluon helicity amplitudes in QCD that interfere with the tree amplitude, namely A{sub 5;1}(1−, 2−, 3, 4+, 5+) and A{sub 5;1}(1−, 2+, 3−, 4+, 5+). Then we describe the construction of the six- and seven-gluon amplitudes with two adjacent negative-helicity gluons, A{sub 6;1}(1−, 2−, 3+, 4+, 5+, 6+) and A{sub 7;1}(1−, 2−, 3+, 4+, 5+, 6+, 7+), which uses the previously-computed logarithmic parts of the amplitudes as input. They present a compact expression for the six-gluon amplitude. No loop integrals are required to obtain the rational parts.

Download or read book Universality and Renormalization written by Ilia Binder and published by American Mathematical Soc.. This book was released on with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers a wide range of phenomena in the natural sciences dominated by notions of universality and renormalization. The contributions in this volume are equally broad in their approach to these phenomena, offering the mathematical as well as the perspective of the applied sciences. They explore renormalization theory in quantum field theory and statistical physics, and its connections to modern mathematics as well as physics on scales from the microscopic to the macroscopic. Information for our distributors: Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

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.