Built on

H. Frellesvig, F. Gasparotto, S. Laporta, M. K. Mandal, P. Mastrolia, L. Mattiazzi et al., Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers , JHEP 05
Original
1901
Earlier work this paper cites.
F. Driencourt-Mangin, G. Rodrigo, G. F. R. Sborlini and W. J. Torres Bobadilla, Universal four-dimensional representation of H → γ γ H\rightarrow\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.
P. Bambade et al., The International Linear Collider: A Global Project , 1903.01629
Original
1903
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.
S. Badger, D. Chicherin, T. Gehrmann, G. Heinrich, J. Henn, T. Peraro et al., Analytic form of the full two-loop five-gluon all-plus helicity amplitude , Phys. Rev. Lett. 123
Original
1905
Earlier work this paper cites.
T. Peraro, FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs , JHEP 07
Original
1905
Earlier work this paper cites.
R. Runkel, Z. Szőr, J. P. Vesga and S. Weinzierl, Integrands of loop amplitudes within loop-tree duality , Phys. Rev. D 101
Original
1906
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.
F. Moriello, Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops , JHEP 01
Original
1907
Earlier work this paper cites.
R. Bonciani, V. Del Duca, H. Frellesvig, J. Henn, M. Hidding, L. Maestri et al., Evaluating a family of two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence , JHEP 01
Original
1907
Earlier work this paper cites.
H. Frellesvig, F. Gasparotto, M. K. Mandal, P. Mastrolia, L. Mattiazzi and S. Mizera, Vector Space of Feynman Integrals and Multivariate Intersection Numbers , Phys. Rev. Lett. 123
Original
1907
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.
D. Bendle, J. Böhm, W. Decker, A. Georgoudis, F.-J. Pfreundt, M. Rahn et al., Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space , JHEP 02
Original
1908
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.
L. Magnea, E. Maina, G. Pelliccioli, C. Signorile-Signorile, P. Torrielli and S. Uccirati, Local analytic sector subtraction for final state radiation at NNLO , PoS RADCOR2019
Original
1912
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.
V. Del Duca, C. Duhr, R. Haindl, A. Lazopoulos and M. Michel, Tree-level splitting amplitudes for a quark into four collinear partons , JHEP 02
Original
1912
Earlier work this paper cites.
R. E. Cutkosky, Singularities and discontinuities of Feynman amplitudes , J. Math. Phys. 1
1960
Earlier work this paper cites.
T. Kinoshita, Mass singularities of Feynman amplitudes , J. Math. Phys. 3
1962
Earlier work this paper cites.
T. D. Lee and M. Nauenberg, Degenerate Systems and Mass Singularities , Phys. Rev. 133
1964
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.
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. M. Cicuta and E. Montaldi, Analytic renormalization via continuous space dimension , Lett. Nuovo Cim. 4
1972
Earlier work this paper cites.
J. F. Ashmore, A Method of Gauge Invariant Regularization , Lett. Nuovo Cim. 4
1972
Earlier work this paper cites.
K. G. Chetyrkin and F. V. Tkachov, Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops , Nucl. Phys. B192
1981
Earlier work this paper cites.
Z. Kunszt and D. E. Soper, Calculation of jet cross-sections in hadron collisions at order alpha-s**3 , Phys. Rev. D46
1992
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.
P. Nogueira, Automatic Feynman graph generation , J.Comput.Phys. 105
1993
Earlier work this paper cites.
P. Baikov, Explicit solutions of the three loop vacuum integral recurrence relations , Phys. Lett. B 385
1996
Earlier work this paper cites.
S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order , Nucl. Phys. B467
1996
Earlier work this paper cites.
S. Catani and M. Seymour, The Dipole formalism for the calculation of QCD jet cross-sections at next-to-leading order , Phys.Lett. B378
1996
Earlier work this paper cites.
S. Catani and M. Seymour, A General algorithm for calculating jet cross-sections in NLO QCD , Nucl.Phys. B485
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.
D. A. Kosower and P. Uwer, One loop splitting amplitudes in gauge theory , Nucl. Phys. B 563
1999
Earlier work this paper cites.
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations , Int. J. Mod. Phys. A15
2000
Earlier work this paper cites.
T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multiloop integrals , Nucl. Phys. B 585
2000
Earlier work this paper cites.
S. Catani and M. Grazzini, Infrared factorization of tree level QCD amplitudes at the next-to-next-to-leading order and beyond , Nucl. Phys. B 570
2000
Earlier work this paper cites.

Similar

S. Catani, D. de Florian and M. Grazzini, Universality of nonleading logarithmic contributions in transverse momentum distributions , Nucl. Phys. B 596
2001
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.
S. Weinzierl, On the computation of intersection numbers for twisted cocycles , 2002.01930
Original
2002
Cited alongside, same era.
S. Catani, D. de Florian and G. Rodrigo, The Triple collinear limit of one loop QCD amplitudes , Phys. Lett. B 586
2004
Cited alongside, same era.
A. Gehrmann-De Ridder, T. Gehrmann and E. W. N. Glover, Antenna subtraction at NNLO , JHEP 09

Then

A. von Manteuffel and R. M. Schabinger, A novel approach to integration by parts reduction , Phys. Lett. B 744
Original
2015
Later among the works it cites.
G. F. R. Sborlini, R. Hernández-Pinto and G. Rodrigo, From dimensional regularization to NLO computations in four dimensions , PoS EPS-HEP2015
Original
2015
Later among the works it cites.
G. F. R. Sborlini, D. de Florian and G. Rodrigo, Polarized triple-collinear splitting functions at NLO for processes with photons , JHEP 03
Original
2015
Later among the works it cites.
P. Mastrolia, A. Primo, U. Schubert and W. J. Torres Bobadilla, Off-shell currents and color–kinematics duality , Phys. Lett. B753
Original
2016
Later among the works it cites.
A. Primo and W. J. Torres Bobadilla, BCJ Identities and d d -Dimensional Generalized Unitarity , JHEP 04

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2021

A stroll through the loop-tree duality

Aguilera-Verdugo, Jesús, Driencourt-Mangin, Félix, Hernández-Pinto, Roger J. et al.

Understand

The Loop-Tree Duality (LTD) theorem is an innovative technique to deal with multi-loop scattering amplitudes, leading to integrand-level representations over an Euclidean space.

In this article, we review the last developments concerning this framework, focusing on the manifestly causal representation of multi-loop Feynman integrals and scattering amplitudes, and the definition of dual local counter-terms to cancel infrared singularities.

Built on

H. Frellesvig, F. Gasparotto, S. Laporta, M. K. Mandal, P. Mastrolia, L. Mattiazzi et al., Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers , JHEP 05
Original
1901
Earlier work this paper cites.
F. Driencourt-Mangin, G. Rodrigo, G. F. R. Sborlini and W. J. Torres Bobadilla, Universal four-dimensional representation of H → γ γ H\rightarrow\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.
P. Bambade et al., The International Linear Collider: A Global Project , 1903.01629
Original
1903
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.
S. Badger, D. Chicherin, T. Gehrmann, G. Heinrich, J. Henn, T. Peraro et al., Analytic form of the full two-loop five-gluon all-plus helicity amplitude , Phys. Rev. Lett. 123
Original
1905
Earlier work this paper cites.
T. Peraro, FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs , JHEP 07
Original
1905
Earlier work this paper cites.
R. Runkel, Z. Szőr, J. P. Vesga and S. Weinzierl, Integrands of loop amplitudes within loop-tree duality , Phys. Rev. D 101
Original
1906
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.
F. Moriello, Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops , JHEP 01
Original
1907
Earlier work this paper cites.
R. Bonciani, V. Del Duca, H. Frellesvig, J. Henn, M. Hidding, L. Maestri et al., Evaluating a family of two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence , JHEP 01
Original
1907
Earlier work this paper cites.
H. Frellesvig, F. Gasparotto, M. K. Mandal, P. Mastrolia, L. Mattiazzi and S. Mizera, Vector Space of Feynman Integrals and Multivariate Intersection Numbers , Phys. Rev. Lett. 123
Original
1907
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.
D. Bendle, J. Böhm, W. Decker, A. Georgoudis, F.-J. Pfreundt, M. Rahn et al., Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space , JHEP 02
Original
1908
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.
L. Magnea, E. Maina, G. Pelliccioli, C. Signorile-Signorile, P. Torrielli and S. Uccirati, Local analytic sector subtraction for final state radiation at NNLO , PoS RADCOR2019
Original
1912
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.
V. Del Duca, C. Duhr, R. Haindl, A. Lazopoulos and M. Michel, Tree-level splitting amplitudes for a quark into four collinear partons , JHEP 02
Original
1912
Earlier work this paper cites.
R. E. Cutkosky, Singularities and discontinuities of Feynman amplitudes , J. Math. Phys. 1
1960
Earlier work this paper cites.
T. Kinoshita, Mass singularities of Feynman amplitudes , J. Math. Phys. 3
1962
Earlier work this paper cites.
T. D. Lee and M. Nauenberg, Degenerate Systems and Mass Singularities , Phys. Rev. 133
1964
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.
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. M. Cicuta and E. Montaldi, Analytic renormalization via continuous space dimension , Lett. Nuovo Cim. 4
1972
Earlier work this paper cites.
J. F. Ashmore, A Method of Gauge Invariant Regularization , Lett. Nuovo Cim. 4
1972
Earlier work this paper cites.
K. G. Chetyrkin and F. V. Tkachov, Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops , Nucl. Phys. B192
1981
Earlier work this paper cites.
Z. Kunszt and D. E. Soper, Calculation of jet cross-sections in hadron collisions at order alpha-s**3 , Phys. Rev. D46
1992
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.
P. Nogueira, Automatic Feynman graph generation , J.Comput.Phys. 105
1993
Earlier work this paper cites.
P. Baikov, Explicit solutions of the three loop vacuum integral recurrence relations , Phys. Lett. B 385
1996
Earlier work this paper cites.
S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order , Nucl. Phys. B467
1996
Earlier work this paper cites.
S. Catani and M. Seymour, The Dipole formalism for the calculation of QCD jet cross-sections at next-to-leading order , Phys.Lett. B378
1996
Earlier work this paper cites.
S. Catani and M. Seymour, A General algorithm for calculating jet cross-sections in NLO QCD , Nucl.Phys. B485
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.
D. A. Kosower and P. Uwer, One loop splitting amplitudes in gauge theory , Nucl. Phys. B 563
1999
Earlier work this paper cites.
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations , Int. J. Mod. Phys. A15
2000
Earlier work this paper cites.
T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multiloop integrals , Nucl. Phys. B 585
2000
Earlier work this paper cites.
S. Catani and M. Grazzini, Infrared factorization of tree level QCD amplitudes at the next-to-next-to-leading order and beyond , Nucl. Phys. B 570
2000
Earlier work this paper cites.

Similar

S. Catani, D. de Florian and M. Grazzini, Universality of nonleading logarithmic contributions in transverse momentum distributions , Nucl. Phys. B 596
2001
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.
S. Weinzierl, On the computation of intersection numbers for twisted cocycles , 2002.01930
Original
2002
Cited alongside, same era.
S. Catani, D. de Florian and G. Rodrigo, The Triple collinear limit of one loop QCD amplitudes , Phys. Lett. B 586
2004
Cited alongside, same era.
A. Gehrmann-De Ridder, T. Gehrmann and E. W. N. Glover, Antenna subtraction at NNLO , JHEP 09

Then

A. von Manteuffel and R. M. Schabinger, A novel approach to integration by parts reduction , Phys. Lett. B 744
Original
2015
Later among the works it cites.
G. F. R. Sborlini, R. Hernández-Pinto and G. Rodrigo, From dimensional regularization to NLO computations in four dimensions , PoS EPS-HEP2015
Original
2015
Later among the works it cites.
G. F. R. Sborlini, D. de Florian and G. Rodrigo, Polarized triple-collinear splitting functions at NLO for processes with photons , JHEP 03
Original
2015
Later among the works it cites.
P. Mastrolia, A. Primo, U. Schubert and W. J. Torres Bobadilla, Off-shell currents and color–kinematics duality , Phys. Lett. B753
Original
2016
Later among the works it cites.
A. Primo and W. J. Torres Bobadilla, BCJ Identities and d d -Dimensional Generalized Unitarity , JHEP 04

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2005

Cited alongside, same era.

J. Plenter and G. Rodrigo, Asymptotic expansions through the loop-tree duality , 2005.02119

Original

2005

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

Original

2006

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.

G. Ossola, C. G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level , Nucl. Phys. B763

2007

Cited alongside, same era.

V. Del Duca, C. Duhr, R. Haindl, A. Lazopoulos and M. Michel, Tree-level splitting amplitudes for a gluon into four collinear partons , JHEP 10

Original

2007

Cited alongside, same era.

M. Czakon, Tops from Light Quarks: Full Mass Dependence at Two-Loops in QCD , Phys. Lett. B 664

Original

2008

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.

Original

2016