title: New Representations of the Perturbative S Matrix.
abstract: We propose a new framework to represent the perturbative S matrix which is well defined for all quantum field theories of massless particles, constructed from tree-level amplitudes and integrable term by term. This representation is derived from the Feynman expansion through a series of partial fraction identities, discarding terms that vanish upon integration. Loop integrands are expressed in terms of "Q-cuts" that involve both off-shell and on-shell loop momenta, defined with a precise contour prescription that can be evaluated by ordinary methods. This framework implies recent results found in the scattering equation formalism at one loop, and it has a natural extension to all orders--even nonplanar theories without well-defined forward limits or good ultraviolet behavior.
authors.affiliation: Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.|Niels Bohr International Academy & Discovery Center, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark.
authors.forename: Christian
authors.initials: C
authors.lastname: Baadsgaard
authors.affiliation: Niels Bohr International Academy & Discovery Center, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark.
authors.forename: N E J
authors.initials: NE
authors.lastname: Bjerrum-Bohr
authors.affiliation: Niels Bohr International Academy & Discovery Center, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark.
authors.forename: Jacob L
authors.initials: JL
authors.lastname: Bourjaily
authors.affiliation: Niels Bohr International Academy & Discovery Center, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark.
authors.forename: Simon
authors.initials: S
authors.lastname: Caron-Huot
authors.affiliation: Niels Bohr International Academy & Discovery Center, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark.
authors.forename: Poul H
authors.initials: PH
authors.lastname: Damgaard
authors.affiliation: Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310000, People's Republic of China.
authors.forename: Bo
authors.initials: B
authors.lastname: Feng