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Maximal unitarity at two loops
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2012 (English)In: Physical Review D, ISSN 1550-7998, Vol. 85, no 4, 045017- p.Article in journal (Refereed) Published
Abstract [en]

We show how to compute the coefficients of the double-box basis integrals in a massless four-point amplitude in terms of tree amplitudes. We show how to choose suitable multidimensional contours for performing the required cuts, and derive consistency equations from the requirement that integrals of total derivatives vanish. Our formulas for the coefficients can be used either analytically or numerically.

Place, publisher, year, edition, pages
2012. Vol. 85, no 4, 045017- p.
National Category
Physical Sciences
URN: urn:nbn:se:uu:diva-170345DOI: 10.1103/PhysRevD.85.045017ISI: 000300241200004OAI: oai:DiVA.org:uu-170345DiVA: diva2:509191
Available from: 2012-03-12 Created: 2012-03-12 Last updated: 2012-08-31Bibliographically approved
In thesis
1. Maximal Unitarity at Two Loops: A New Method for Computing Two-Loop Scattering Amplitudes
Open this publication in new window or tab >>Maximal Unitarity at Two Loops: A New Method for Computing Two-Loop Scattering Amplitudes
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The study of scattering amplitudes beyond one loop is necessary for precision phenomenology for the Large Hadron Collider and may also provide deeper insights into the theoretical foundations of quantum field theory. In this thesis we develop a new method for computing two-loop amplitudes, based on unitarity rather than Feynman diagrams. In this approach, the two-loop amplitude is first expanded in a linearly independent basis of integrals. The process dependence thereby resides in the coefficients of the integrals. These expansion coefficients are then the object of calculation.

Our main results include explicit formulas for a subset of the integral coefficients, expressing them as products of tree-level amplitudes integrated over specific contours in the complex plane. We give a general selection principle for determining these contours. This principle is then applied to obtain the coefficients of integrals with the topology of a double box. We show that, for four-particle scattering, each double-box integral in the two-loop basis is associated with a uniquely defined complex contour, referred to as its master contour. We provide a classification of the solutions to setting all propagators of the general double-box integral on-shell. Depending on the number of external momenta at the vertices of the graph, these solutions are given as a chain of pointwise intersecting Riemann spheres, or a torus. This classification is needed to define master contours for amplitudes with arbitrary multiplicities.

We point out that a basis of two-loop integrals with as many infrared finite elements as possible allows substantial technical simplications, in terms of obtaining the coefficients of the integrals, as well as for the analytic evaluation of the integrals themselves. We compute two such integrals at four points, obtaining remarkably compact expressions. Finally, we provide a check on a recently developed recursion relation for the all-loop integrand of the amplitudes of N=4 supersymmetric Yang-Mills theory, examining the two-loop six-gluon MHV amplitude and finding agreement. The validity of the approach to two-loop amplitudes developed in this thesis extends to all four-dimensional gauge theories, in particular QCD. The approach is suited for obtaining compact analytical expressions as well as for numerical implementations.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2012. 135 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 952
Amplitudes, NNLO calculations, Quantum Chromodynamics, Unitarity
National Category
Subatomic Physics
Research subject
Physics with specialization in Elementary Particle Physics
urn:nbn:se:uu:diva-179203 (URN)978-91-554-8423-1 (ISBN)
Public defence
2012-09-21, Å2001, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 09:15 (English)
Available from: 2012-08-31 Created: 2012-08-09 Last updated: 2013-01-22Bibliographically approved

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