Built on

R. Baumeister, D. Mediger, J. Pečovnik, and S. Weinzierl, “Vanishing of Certain Cuts or Residues of Loop Integrals with Higher Powers of the Propagators,” Phys. Rev. D
Original
1903
Earlier work this paper cites.
S. Caron-Huot, L. J. Dixon, F. Dulat, M. von Hippel, A. J. McLeod, and G. Papathanasiou, “Six-Gluon Amplitudes in planar 𝒩 = 4 \mathcal{N}\!=\!4 super-Yang-Mills theory at Six and Seven Loops,” JHEP
Original
1903
Earlier work this paper cites.
E. Herrmann and J. Parra-Martinez, “Logarithmic Forms and Differential Equations for Feynman Integrals,” JHEP
Original
1909
Earlier work this paper cites.
J. L. Bourjaily, E. Herrmann, C. Langer, A. J. McLeod, and J. Trnka, “Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops,” JHEP
Original
1909
Earlier work this paper cites.
J. L. Bourjaily, E. Herrmann, C. Langer, A. J. McLeod, and J. Trnka, “All-Multiplicity Nonplanar Amplitude Integrands in Maximally Supersymmetric Yang-Mills Theory at Two Loops,” Phys. Rev. Lett
Original
1911
Earlier work this paper cites.
J. L. Bourjaily, E. Gardi, A. J. McLeod, and C. Vergu, “All-Mass n n -gon Integrals in n n Dimensions,” JHEP
Original
1912
Earlier work this paper cites.
T. Kinoshita, “Mass Singularities of Feynman Amplitudes,” J. Math. Phys
1962
Earlier work this paper cites.
T. D. Lee and M. Nauenberg, “Degenerate Systems and Mass Singularities,” Phys. Rev
1964
Earlier work this paper cites.
C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, “Energy Correlations in electron-Positron Annihilation: Testing QCD,” Phys. Rev. Lett
1978
Earlier work this paper cites.
G. Passarino and M. Veltman, “One Loop Corrections for e + e − e^{+}\,e^{-} Annihilation Into μ + μ − \mu^{+}\,\mu^{-} in the Weinberg Model,” Nucl. Phys
1979
Earlier work this paper cites.
F. Cachazo, “Sharpening The Leading Singularity,” arXiv:0803.1988 [hep-th]
Original
1988
Earlier work this paper cites.
Cambridge University Press, 8, 1993
G. F. Sterman, An Introduction to Quantum Field Theory · 1993
Earlier work this paper cites.
W. T. Giele, E. W. N. Glover, and D. A. Kosower, “Higher Order Corrections to Jet Cross-Sections in Hadron Colliders,” Nucl. Phys. B
1993
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, “One-Loop n n -Point Gauge Theory Amplitudes, Unitarity and Collinear Limits,” Nucl. Phys
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, “Fusing Gauge Theory Tree Amplitudes into Loop Amplitudes,” Nucl. Phys
1995
Earlier work this paper cites.
Z. Bern and A. G. Morgan, “Massive Loop Amplitudes from Unitarity,” Nucl. Phys
1996
Earlier work this paper cites.
S. Frixione, Z. Kunszt, and A. Signer, “Three-Jet Cross-Sections to Next-to-Leading Order,” Nucl. Phys. B
1996
Earlier work this paper cites.
S. Catani and M. H. Seymour, “A General Algorithm for Calculating Jet Cross-Sections in NLO QCD,” Nucl. Phys. B
1998
Earlier work this paper cites.
S. Catani, “The Singular Behavior of QCD Amplitudes at Two Loop Order,” Phys. Lett
1998
Earlier work this paper cites.
N. Kidonakis, G. Oderda, and G. F. Sterman, “Evolution of Color Exchange in QCD Hard Scattering,” Nucl. Phys. B
1998
Earlier work this paper cites.
Z. Bern, L. J. Dixon, and D. A. Kosower, “Two-Loop g → g g g\to gg Splitting Amplitudes in QCD,” JHEP
2004
Earlier work this paper cites.

Similar

R. Britto, F. Cachazo, and B. Feng, “New Recursion Relations for Tree Amplitudes of Gluons,” Nucl. Phys
2005
Cited alongside, same era.
R. Britto, F. Cachazo, B. Feng, and E. Witten, “Direct Proof of Tree-Level Recursion Relation in Yang- Mills Theory,” Phys. Rev. Lett
2005
Cited alongside, same era.
R. Britto, F. Cachazo, and B. Feng, “Generalized Unitarity and One-Loop Amplitudes in 𝒩 = 4 \mathcal{N}\!=\!4 Super-Yang-Mills,” Nucl. Phys
2005
Cited alongside, same era.
Z. Bern, N. E. J. Bjerrum-Bohr, and D. C. Dunbar, “Inherited Swistor-Space Structure of Gravity Loop Amplitudes,” JHEP
2005
Cited alongside, same era.
A. Gehrmann-De Ridder, T. Gehrmann, and E. W. N. Glover, “Antenna Subtraction at NNLO,” JHEP
2005
Cited alongside, same era.

Then

J. Drummond, J. Henn, G. Korchemsky, and E. Sokatchev, “Dual Superconformal Symmetry of Scattering Amplitudes in 𝒩 = 4 \mathcal{N}\!=\!4 super Yang-Mills Theory,” Nucl. Phys
Original
2010
Later among the works it cites.
P. Mastrolia, G. Ossola, T. Reiter, and F. Tramontano, “Scattering Amplitudes from Unitarity-Based Reduction Algorithm at the Integrand-Level,” JHEP
Original
2010
Later among the works it cites.
N. Arkani-Hamed, F. Cachazo, and J. Kaplan, “What is the Simplest Quantum Field Theory?,” JHEP
Original
2010
Later among the works it cites.
H. Elvang, Y.-t. Huang, and C. Peng, “On-Shell Superamplitudes in 𝒩 < 4 \mathcal{N}\!<\!4 SYM,” JHEP
Original
2011
Later among the works it cites.
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, S. Caron-Huot, and J. Trnka, “The All-Loop Integrand For Scattering Amplitudes in Planar 𝒩 = 4 \mathcal{N}\!=\!4 SYM,” JHEP

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2021

Integrands of Less-Supersymmetric Yang-Mills at One Loop

Bourjaily, Jacob L., Herrmann, Enrico, Langer, Cameron et al.

Understand

We construct a prescriptive, bubble power-counting basis of one-loop integrands suitable for representing amplitude integrands in less-supersymmetric Yang-Mills theory.

With the exception of massless bubbles, all integrands have unambiguous, leading singularities as coefficients defined in field theory; for the massless bubbles on external legs, we find two natural choices which lead to different integrands that highlight distinct aspects of field theory.
For concreteness, we give the all-multiplicity integrands for MHV amplitudes, and the split-helicity amplitude integrand for six-particle NMHV.
The basis we construct is mostly pure and is divided into to separately UV- and IR-finite sectors of fixed transcendental weight, resulting in UV- and IR-finite ratio functions of n-particle helicity amplitudes.

Built on

R. Baumeister, D. Mediger, J. Pečovnik, and S. Weinzierl, “Vanishing of Certain Cuts or Residues of Loop Integrals with Higher Powers of the Propagators,” Phys. Rev. D
Original
1903
Earlier work this paper cites.
S. Caron-Huot, L. J. Dixon, F. Dulat, M. von Hippel, A. J. McLeod, and G. Papathanasiou, “Six-Gluon Amplitudes in planar 𝒩 = 4 \mathcal{N}\!=\!4 super-Yang-Mills theory at Six and Seven Loops,” JHEP
Original
1903
Earlier work this paper cites.
E. Herrmann and J. Parra-Martinez, “Logarithmic Forms and Differential Equations for Feynman Integrals,” JHEP
Original
1909
Earlier work this paper cites.
J. L. Bourjaily, E. Herrmann, C. Langer, A. J. McLeod, and J. Trnka, “Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops,” JHEP
Original
1909
Earlier work this paper cites.
J. L. Bourjaily, E. Herrmann, C. Langer, A. J. McLeod, and J. Trnka, “All-Multiplicity Nonplanar Amplitude Integrands in Maximally Supersymmetric Yang-Mills Theory at Two Loops,” Phys. Rev. Lett
Original
1911
Earlier work this paper cites.
J. L. Bourjaily, E. Gardi, A. J. McLeod, and C. Vergu, “All-Mass n n -gon Integrals in n n Dimensions,” JHEP
Original
1912
Earlier work this paper cites.
T. Kinoshita, “Mass Singularities of Feynman Amplitudes,” J. Math. Phys
1962
Earlier work this paper cites.
T. D. Lee and M. Nauenberg, “Degenerate Systems and Mass Singularities,” Phys. Rev
1964
Earlier work this paper cites.
C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, “Energy Correlations in electron-Positron Annihilation: Testing QCD,” Phys. Rev. Lett
1978
Earlier work this paper cites.
G. Passarino and M. Veltman, “One Loop Corrections for e + e − e^{+}\,e^{-} Annihilation Into μ + μ − \mu^{+}\,\mu^{-} in the Weinberg Model,” Nucl. Phys
1979
Earlier work this paper cites.
F. Cachazo, “Sharpening The Leading Singularity,” arXiv:0803.1988 [hep-th]
Original
1988
Earlier work this paper cites.
Cambridge University Press, 8, 1993
G. F. Sterman, An Introduction to Quantum Field Theory · 1993
Earlier work this paper cites.
W. T. Giele, E. W. N. Glover, and D. A. Kosower, “Higher Order Corrections to Jet Cross-Sections in Hadron Colliders,” Nucl. Phys. B
1993
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, “One-Loop n n -Point Gauge Theory Amplitudes, Unitarity and Collinear Limits,” Nucl. Phys
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, “Fusing Gauge Theory Tree Amplitudes into Loop Amplitudes,” Nucl. Phys
1995
Earlier work this paper cites.
Z. Bern and A. G. Morgan, “Massive Loop Amplitudes from Unitarity,” Nucl. Phys
1996
Earlier work this paper cites.
S. Frixione, Z. Kunszt, and A. Signer, “Three-Jet Cross-Sections to Next-to-Leading Order,” Nucl. Phys. B
1996
Earlier work this paper cites.
S. Catani and M. H. Seymour, “A General Algorithm for Calculating Jet Cross-Sections in NLO QCD,” Nucl. Phys. B
1998
Earlier work this paper cites.
S. Catani, “The Singular Behavior of QCD Amplitudes at Two Loop Order,” Phys. Lett
1998
Earlier work this paper cites.
N. Kidonakis, G. Oderda, and G. F. Sterman, “Evolution of Color Exchange in QCD Hard Scattering,” Nucl. Phys. B
1998
Earlier work this paper cites.
Z. Bern, L. J. Dixon, and D. A. Kosower, “Two-Loop g → g g g\to gg Splitting Amplitudes in QCD,” JHEP
2004
Earlier work this paper cites.

Similar

R. Britto, F. Cachazo, and B. Feng, “New Recursion Relations for Tree Amplitudes of Gluons,” Nucl. Phys
2005
Cited alongside, same era.
R. Britto, F. Cachazo, B. Feng, and E. Witten, “Direct Proof of Tree-Level Recursion Relation in Yang- Mills Theory,” Phys. Rev. Lett
2005
Cited alongside, same era.
R. Britto, F. Cachazo, and B. Feng, “Generalized Unitarity and One-Loop Amplitudes in 𝒩 = 4 \mathcal{N}\!=\!4 Super-Yang-Mills,” Nucl. Phys
2005
Cited alongside, same era.
Z. Bern, N. E. J. Bjerrum-Bohr, and D. C. Dunbar, “Inherited Swistor-Space Structure of Gravity Loop Amplitudes,” JHEP
2005
Cited alongside, same era.
A. Gehrmann-De Ridder, T. Gehrmann, and E. W. N. Glover, “Antenna Subtraction at NNLO,” JHEP
2005
Cited alongside, same era.

Then

J. Drummond, J. Henn, G. Korchemsky, and E. Sokatchev, “Dual Superconformal Symmetry of Scattering Amplitudes in 𝒩 = 4 \mathcal{N}\!=\!4 super Yang-Mills Theory,” Nucl. Phys
Original
2010
Later among the works it cites.
P. Mastrolia, G. Ossola, T. Reiter, and F. Tramontano, “Scattering Amplitudes from Unitarity-Based Reduction Algorithm at the Integrand-Level,” JHEP
Original
2010
Later among the works it cites.
N. Arkani-Hamed, F. Cachazo, and J. Kaplan, “What is the Simplest Quantum Field Theory?,” JHEP
Original
2010
Later among the works it cites.
H. Elvang, Y.-t. Huang, and C. Peng, “On-Shell Superamplitudes in 𝒩 < 4 \mathcal{N}\!<\!4 SYM,” JHEP
Original
2011
Later among the works it cites.
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, S. Caron-Huot, and J. Trnka, “The All-Loop Integrand For Scattering Amplitudes in Planar 𝒩 = 4 \mathcal{N}\!=\!4 SYM,” JHEP

Beyond the bibliography

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

Open on alphaXiv

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N. E. J. Bjerrum-Bohr, D. C. Dunbar, H. Ita, W. B. Perkins, and K. Risager, “The No-Triangle Hypothesis for 𝒩 = 8 \mathcal{N}\!=\!8 Supergravity,” JHEP

2006

Cited alongside, same era.

S. M. Aybat, L. J. Dixon, and G. F. Sterman, “The Two-Loop Soft Anomalous Dimension Matrix and Resummation at Next-to-Next-to Leading Pole,” Phys. Rev. D

2006

Cited alongside, same era.

J. Drummond, J. Henn, V. Smirnov, and E. Sokatchev, “Magic Identities for Conformal Four-Point Integrals,” JHEP

2007

Cited alongside, same era.

L. F. Alday and J. M. Maldacena, “Gluon Scattering Amplitudes at Strong Coupling,” JHEP