Global Bases for Nonplanar Loop Integrands, Generalized Unitarity, and the Double Copy to All Loop Orders

Fuente: arXiv
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Autores principales: Bern, Zvi, Herrmann, Enrico, Roiban, Radu, Ruf, Michael S., Zeng, Mao
Formato: Preprint
Publicado: 2024
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author Bern, Zvi
Herrmann, Enrico
Roiban, Radu
Ruf, Michael S.
Zeng, Mao
author_facet Bern, Zvi
Herrmann, Enrico
Roiban, Radu
Ruf, Michael S.
Zeng, Mao
contents We introduce a constructive method for defining a global loop-integrand basis for scattering amplitudes, encompassing both planar and nonplanar contributions. Our approach utilizes a graph-based framework to establish a well-defined, non-redundant basis of integrands. This basis, constructed from a chosen set of non-redundant graphs together with a selection of irreducible scalar products, provides clear insights into various physical properties of scattering amplitudes and proves useful in multiple contexts, such as on-shell Ward identities and manifesting gauge-choice independence. A key advantage of our integrand basis is its ability to streamline the generalized unitarity method. Specifically, we can directly read off the coefficients of basis elements without resorting to ansatze or solving linear equations. This novel approach allows us to lift generalized unitarity cuts -- expressed as products of tree amplitudes -- to loop-level integrands, facilitating the use of the tree-level double copy to generate complete gravitational integrands at any loop order. This method circumvents the difficulties in identifying complete higher-loop-order gauge-theory integrands that adhere to the color-kinematics duality. Additionally, our cut-based organization is well-suited for expansion in hard or soft limits, aiding in the exploration of ultraviolet or classical limits of scattering amplitudes.
format Preprint
id arxiv_https___arxiv_org_abs_2408_06686
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Global Bases for Nonplanar Loop Integrands, Generalized Unitarity, and the Double Copy to All Loop Orders
Bern, Zvi
Herrmann, Enrico
Roiban, Radu
Ruf, Michael S.
Zeng, Mao
High Energy Physics - Theory
High Energy Physics - Phenomenology
We introduce a constructive method for defining a global loop-integrand basis for scattering amplitudes, encompassing both planar and nonplanar contributions. Our approach utilizes a graph-based framework to establish a well-defined, non-redundant basis of integrands. This basis, constructed from a chosen set of non-redundant graphs together with a selection of irreducible scalar products, provides clear insights into various physical properties of scattering amplitudes and proves useful in multiple contexts, such as on-shell Ward identities and manifesting gauge-choice independence. A key advantage of our integrand basis is its ability to streamline the generalized unitarity method. Specifically, we can directly read off the coefficients of basis elements without resorting to ansatze or solving linear equations. This novel approach allows us to lift generalized unitarity cuts -- expressed as products of tree amplitudes -- to loop-level integrands, facilitating the use of the tree-level double copy to generate complete gravitational integrands at any loop order. This method circumvents the difficulties in identifying complete higher-loop-order gauge-theory integrands that adhere to the color-kinematics duality. Additionally, our cut-based organization is well-suited for expansion in hard or soft limits, aiding in the exploration of ultraviolet or classical limits of scattering amplitudes.
title Global Bases for Nonplanar Loop Integrands, Generalized Unitarity, and the Double Copy to All Loop Orders
topic High Energy Physics - Theory
High Energy Physics - Phenomenology
url https://arxiv.org/abs/2408.06686