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F. Driencourt-Mangin, G. Rodrigo, G. F. R. Sborlini and W. J. Torres Bobadilla, Universal four-dimensional representation of H → γ γ H\to\gamma\gamma at two loops through the Loop-Tree Duality , JHEP 02
Original
1901
Earlier work this paper cites.
R. Runkel, Z. Szőr, J. P. Vesga and S. Weinzierl, Causality and loop-tree duality at higher loops , Phys. Rev. Lett. 122
Original
1902
Earlier work this paper cites.
J. J. Aguilera-Verdugo, F. Driencourt-Mangin, J. Plenter, S. Ramírez-Uribe, G. Rodrigo, G. F. Sborlini et al., Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders , JHEP 12
Original
1904
Earlier work this paper cites.
Z. Capatti, V. Hirschi, D. Kermanschah and B. Ruijl, Loop-Tree Duality for Multiloop Numerical Integration , Phys. Rev. Lett. 123
Original
1906
Earlier work this paper cites.
PhD thesis, U. Valencia (main), 2019
Original
F. Driencourt-Mangin, Four-dimensional representation of scattering amplitudes and physical observables through the application of the Loop-Tree Duality theorem · 1907
Earlier work this paper cites.
F. Driencourt-Mangin, G. Rodrigo, G. F. Sborlini and W. J. Torres Bobadilla, On the interplay between the loop-tree duality and helicity amplitudes , 1911.11125
Original
1911
Earlier work this paper cites.
Z. Capatti, V. Hirschi, D. Kermanschah, A. Pelloni and B. Ruijl, Numerical Loop-Tree Duality: contour deformation and subtraction , JHEP 04
Original
1912
Earlier work this paper cites.
C. G. Bollini and J. J. Giambiagi, Dimensional Renormalization: The Number of Dimensions as a Regularizing Parameter , Nuovo Cim. B12
1972
Earlier work this paper cites.
G. ’t Hooft and M. J. G. Veltman, Regularization and Renormalization of Gauge Fields , Nucl. Phys. B44
1972
Earlier work this paper cites.
J. Plenter, Asymptotic Expansions Through the Loop-Tree Duality , Acta Phys. Polon. B 50
1992
Earlier work this paper cites.
L. K. Grover, Quantum mechanics helps in searching for a needle in a haystack , Phys. Rev. Lett. 79
1997
Earlier work this paper cites.
M. Beneke and V. A. Smirnov, Asymptotic expansion of Feynman integrals near threshold , Nucl. Phys. B522
1998
Earlier work this paper cites.

Similar

M. Boyer, G. Brassard, P. Hoyer and A. Tapp, Tight bounds on quantum searching , Fortsch. Phys. 46
1998
Cited alongside, same era.
J. J. Aguilera-Verdugo, F. Driencourt-Mangin, R. J. Hernandez Pinto, J. Plenter, S. Ramirez-Uribe, A. E. Renteria Olivo et al., Open loop amplitudes and causality to all orders and powers from the loop-tree duality , Phys. Rev. Lett. 124
Original
2001
Cited alongside, same era.
J. Plenter and G. Rodrigo, Asymptotic expansions through the loop-tree duality , Eur.Phys.J.C 81
Original
2005
Cited alongside, same era.
J. J. Aguilera-Verdugo, R. J. Hernandez-Pinto, G. Rodrigo, G. F. R. Sborlini and W. J. Torres Bobadilla, Causal representation of multi-loop Feynman integrands within the loop-tree duality . JHEP 01
Original
2006
Cited alongside, same era.
S. Ramírez-Uribe, R. J. Hernández-Pinto, G. Rodrigo, G. F. R. Sborlini and W. J. Torres Bobadilla, Universal opening of four-loop scattering amplitudes to trees . JHEP 04

Then

R. J. Hernandez-Pinto, G. F. R. Sborlini and G. Rodrigo, Towards gauge theories in four dimensions , JHEP 02
Original
2016
Later among the works it cites.
G. F. R. Sborlini, F. Driencourt-Mangin, R. Hernandez-Pinto and G. Rodrigo, Four-dimensional unsubtraction from the loop-tree duality , JHEP 08
Original
2016
Later among the works it cites.
G. F. R. Sborlini, F. Driencourt-Mangin and G. Rodrigo, Four-dimensional unsubtraction with massive particles , JHEP 10
Original
2016
Later among the works it cites.
E. Tomboulis, Causality and Unitarity via the Tree-Loop Duality Relation , JHEP 05
Original
2017
Later among the works it cites.
S. Buchta, G. Chachamis, P. Draggiotis and G. Rodrigo, Numerical implementation of the loop–tree duality method , Eur. Phys. J. C77

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2021

Four-loop scattering amplitudes journey into the forest

Ramírez-Uribe, Selomit, Hernández-Pinto, Roger J., Rentería-Olivo, Andrés E. et al.

Understand

We present an overview of the analysis of the multiloop topologies that appear for the first time at four loops and the assembly of them in a general expression, the N$^4$MLT universal topology.

Based on the fact that the Loop-Tree Duality enables to open any scattering amplitude in terms of convolutions of known subtopologies, we go through the dual representation of the universal N$^4$MLT topology and the manifestly causal representation.
Additionally, we expose the application of a quantum algorithm as an alternative methodology to identify the causal singular configurations of multiloop Feynman diagrams.

Built on

F. Driencourt-Mangin, G. Rodrigo, G. F. R. Sborlini and W. J. Torres Bobadilla, Universal four-dimensional representation of H → γ γ H\to\gamma\gamma at two loops through the Loop-Tree Duality , JHEP 02
Original
1901
Earlier work this paper cites.
R. Runkel, Z. Szőr, J. P. Vesga and S. Weinzierl, Causality and loop-tree duality at higher loops , Phys. Rev. Lett. 122
Original
1902
Earlier work this paper cites.
J. J. Aguilera-Verdugo, F. Driencourt-Mangin, J. Plenter, S. Ramírez-Uribe, G. Rodrigo, G. F. Sborlini et al., Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders , JHEP 12
Original
1904
Earlier work this paper cites.
Z. Capatti, V. Hirschi, D. Kermanschah and B. Ruijl, Loop-Tree Duality for Multiloop Numerical Integration , Phys. Rev. Lett. 123
Original
1906
Earlier work this paper cites.
PhD thesis, U. Valencia (main), 2019
Original
F. Driencourt-Mangin, Four-dimensional representation of scattering amplitudes and physical observables through the application of the Loop-Tree Duality theorem · 1907
Earlier work this paper cites.
F. Driencourt-Mangin, G. Rodrigo, G. F. Sborlini and W. J. Torres Bobadilla, On the interplay between the loop-tree duality and helicity amplitudes , 1911.11125
Original
1911
Earlier work this paper cites.
Z. Capatti, V. Hirschi, D. Kermanschah, A. Pelloni and B. Ruijl, Numerical Loop-Tree Duality: contour deformation and subtraction , JHEP 04
Original
1912
Earlier work this paper cites.
C. G. Bollini and J. J. Giambiagi, Dimensional Renormalization: The Number of Dimensions as a Regularizing Parameter , Nuovo Cim. B12
1972
Earlier work this paper cites.
G. ’t Hooft and M. J. G. Veltman, Regularization and Renormalization of Gauge Fields , Nucl. Phys. B44
1972
Earlier work this paper cites.
J. Plenter, Asymptotic Expansions Through the Loop-Tree Duality , Acta Phys. Polon. B 50
1992
Earlier work this paper cites.
L. K. Grover, Quantum mechanics helps in searching for a needle in a haystack , Phys. Rev. Lett. 79
1997
Earlier work this paper cites.
M. Beneke and V. A. Smirnov, Asymptotic expansion of Feynman integrals near threshold , Nucl. Phys. B522
1998
Earlier work this paper cites.

Similar

M. Boyer, G. Brassard, P. Hoyer and A. Tapp, Tight bounds on quantum searching , Fortsch. Phys. 46
1998
Cited alongside, same era.
J. J. Aguilera-Verdugo, F. Driencourt-Mangin, R. J. Hernandez Pinto, J. Plenter, S. Ramirez-Uribe, A. E. Renteria Olivo et al., Open loop amplitudes and causality to all orders and powers from the loop-tree duality , Phys. Rev. Lett. 124
Original
2001
Cited alongside, same era.
J. Plenter and G. Rodrigo, Asymptotic expansions through the loop-tree duality , Eur.Phys.J.C 81
Original
2005
Cited alongside, same era.
J. J. Aguilera-Verdugo, R. J. Hernandez-Pinto, G. Rodrigo, G. F. R. Sborlini and W. J. Torres Bobadilla, Causal representation of multi-loop Feynman integrands within the loop-tree duality . JHEP 01
Original
2006
Cited alongside, same era.
S. Ramírez-Uribe, R. J. Hernández-Pinto, G. Rodrigo, G. F. R. Sborlini and W. J. Torres Bobadilla, Universal opening of four-loop scattering amplitudes to trees . JHEP 04

Then

R. J. Hernandez-Pinto, G. F. R. Sborlini and G. Rodrigo, Towards gauge theories in four dimensions , JHEP 02
Original
2016
Later among the works it cites.
G. F. R. Sborlini, F. Driencourt-Mangin, R. Hernandez-Pinto and G. Rodrigo, Four-dimensional unsubtraction from the loop-tree duality , JHEP 08
Original
2016
Later among the works it cites.
G. F. R. Sborlini, F. Driencourt-Mangin and G. Rodrigo, Four-dimensional unsubtraction with massive particles , JHEP 10
Original
2016
Later among the works it cites.
E. Tomboulis, Causality and Unitarity via the Tree-Loop Duality Relation , JHEP 05
Original
2017
Later among the works it cites.
S. Buchta, G. Chachamis, P. Draggiotis and G. Rodrigo, Numerical implementation of the loop–tree duality method , Eur. Phys. J. C77

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2006

Cited alongside, same era.

S. Catani, T. Gleisberg, F. Krauss, G. Rodrigo and J.-C. Winter, From loops to trees by-passing Feynman’s theorem , JHEP 09

Original

2008

Cited alongside, same era.

I. Bierenbaum, S. Catani, P. Draggiotis and G. Rodrigo, A Tree-Loop Duality Relation at Two Loops and Beyond , JHEP 10

Original

2010

Cited alongside, same era.

J. Jesús Aguilera-Verdugo, R. J. Hernández-Pinto, G. Rodrigo, G. F. R. Sborlini and W. J. Torres Bobadilla, Mathematical properties of nested residues and their application to multi-loop scattering amplitudes , JHEP 02

Original

2010

Cited alongside, same era.

R. M. Prisco and F. Tramontano, Dual subtractions , JHEP 06

Original

2012

Cited alongside, same era.

I. Bierenbaum, S. Buchta, P. Draggiotis, I. Malamos and G. Rodrigo, Tree-Loop Duality Relation beyond simple poles , JHEP 03

Original

2013

Cited alongside, same era.

S. Buchta, G. Chachamis, P. Draggiotis, I. Malamos and G. Rodrigo, On the singular behaviour of scattering amplitudes in quantum field theory , JHEP 11

Original

2014

Cited alongside, same era.

PhD thesis, Valencia U., 2015

Original

S. Buchta, Theoretical foundations and applications of the Loop-Tree Duality in Quantum Field Theories · 2015

Cited alongside, same era.

Original

2017

Later among the works it cites.

J. L. Jurado, G. Rodrigo and W. J. Torres Bobadilla, From Jacobi off-shell currents to integral relations , JHEP 12

Original

2017

Later among the works it cites.

F. Driencourt-Mangin, G. Rodrigo and G. F. Sborlini, Universal dual amplitudes and asymptotic expansions for g g → H gg\rightarrow H and H → γ γ H\rightarrow\gamma\gamma in four dimensions , Eur. Phys. J. C 78

Original

2018

Later among the works it cites.

J. Aguilera-Verdugo, R. J. Hernández-Pinto, S. Ramírez-Uribe, G. Rodrigo, G. F. R. Sborlini and W. J. Torres Bobadilla, Manifestly Causal Scattering Amplitudes in Snowmass 2021 - Letter of Intention , August 2020

2020

Later among the works it cites.

G. F. R. Sborlini, Geometrical approach to causality in multiloop amplitudes . PhysRevD 104

Original

2021

Closest in time.

W. J. T. Bobadilla, Lotty – The loop-tree duality automation , Eur. Phys. J. C 81

Original

2021

Closest in time.

W. J. Torres Bobadilla, Loop-tree duality from vertices and edges . JHEP 04

Original

2021

Closest in time.