| 1. |
- Johansson, Henrik, et al.
(författare)
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Cross-order integral relations from maximal cuts
- 2015
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Ingår i: Physical Review D. - : American Physical Society (APS). - 1550-7998 .- 1550-2368. ; 92:2
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Tidskriftsartikel (refereegranskat)abstract
- We study the Anastasiou-Bern-Dixon-Kosower relation using maximal cuts of one-and two-loop integrals with up to five external legs. We show how to find a special combination of integrals that allows the relation to exist, and how to reconstruct the terms with one-loop integrals squared. The reconstruction relies on the observation that integrals across different loop orders can have support on the same generalized unitarity cuts and can share global poles. We discuss the appearance of nonhomologous integration contours in multivariate residues. Their origin can be understood in simple terms, and their existence enables us to distinguish contributions from different integrals. Our analysis suggests that maximal and near-maximal cuts can be used to infer the existence of integral identities more generally.
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| 2. |
- Johansson, Henrik, et al.
(författare)
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Two-Loop Maximal Unitarity with External Masses
- 2013
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Ingår i: Physical Review D. - 1550-7998 .- 1550-2368. ; 87:2, s. 025030-
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Tidskriftsartikel (refereegranskat)abstract
- We extend the maximal unitarity method at two loops to double-box basis integrals with up to three external massive legs. We use consistency equations based on the requirement that integrals of total derivatives vanish. We obtain unique formulae for the coefficients of the master double-box integrals. These formulae can be used either analytically or numerically.
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| 3. |
- Kosower, David A., et al.
(författare)
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Maximal unitarity at two loops
- 2012
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Ingår i: Physical Review D. - 1550-7998 .- 1550-2368. ; 85:4, s. 045017-
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 4. |
- Larsen, Kasper J.
(författare)
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Maximal Unitarity at Two Loops : A New Method for Computing Two-Loop Scattering Amplitudes
- 2012
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 5. |
- Travaglini, Gabriele, et al.
(författare)
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The SAGEX review on scattering amplitudes
- 2022
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Ingår i: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 55:44
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Forskningsöversikt (refereegranskat)abstract
- This is an introduction to, and invitation to read, a series of review articles on scattering amplitudes in gauge theory, gravity, and superstring theory. Our aim is to provide an overview of the field, from basic aspects to a selection of current (2022) research and developments.
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