Built on

M. Fael and M. Passera, Muon-Electron Scattering at Next-To-Next-To-Leading Order: The Hadronic Corrections , Phys. Rev. Lett. 122
Original
1901
Earlier work this paper cites.
F. Buccioni, J.-N. Lang, J. M. Lindert, P. Maierhöfer, S. Pozzorini, H. Zhang et al., OpenLoops 2 , Eur. Phys. J. C 79
Original
1907
Earlier work this paper cites.
M. Davier, A. Hoecker, B. Malaescu and Z. Zhang, A new evaluation of the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment and to 𝛂 ⁡ ( 𝐦 𝐙 𝟐 ) \mathbf{\boldsymbol{\alpha}(m_{Z}^{2})} , Eur. Phys. J. C 80
Original
1908
Earlier work this paper cites.
T. Engel, A. Signer and Y. Ulrich, A subtraction scheme for massive QED , JHEP 01
Original
1909
Earlier work this paper cites.
A. Keshavarzi, D. Nomura and T. Teubner, g − 2 g-2 of charged leptons, α ⁡ ( M Z 2 ) \alpha(M^{2}_{Z}) , and the hyperfine splitting of muonium , Phys. Rev. D 101
Original
1911
Earlier work this paper cites.
V. Bertone, M. Cacciari, S. Frixione and G. Stagnitto, The partonic structure of the electron at the next-to-leading logarithmic accuracy in QED , JHEP 03
Original
1911
Earlier work this paper cites.
J. Ronca, NNLO QED Contribution to the μ e → μ e \mu e\to\mu e Elastic Scattering , EPJ Web Conf. 234
Original
1912
Earlier work this paper cites.
D. R. Yennie, S. C. Frautschi and H. Suura, The infrared divergence phenomena and high-energy processes , Annals Phys. 13
1961
Earlier work this paper cites.
L. W. Mo and Y.-S. Tsai, Radiative Corrections to Elastic and Inelastic e p and mu p Scattering , Rev. Mod. Phys. 41
1969
Earlier work this paper cites.
P. Nogueira, Automatic Feynman graph generation , J.Comput.Phys. 105
1993
Earlier work this paper cites.
S. Laporta, Hyperspherical integration and the triple cross vertex graphs , Nuovo Cim. A 107
1994
Earlier work this paper cites.
A. Djouadi and P. Gambino, Electroweak gauge bosons selfenergies: Complete QCD corrections , Phys. Rev. D 49
1994
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.
L. C. Maximon and J. A. Tjon, Radiative corrections to electron-proton scattering , Physical Review C 62
2000
Earlier work this paper cites.
S. Dittmaier, A General approach to photon radiation off fermions , Nucl. Phys. B565
2000
Earlier work this paper cites.
S. Pozzorini, H. Zhang and M. F. Zoller, Rational Terms of UV Origin at Two Loops , JHEP 05
Original
2001
Earlier work this paper cites.
S. Borsanyi et al., Leading-order hadronic vacuum polarization contribution to the muon magnetic moment from lattice QCD , 2002.12347
Original
2002
Earlier work this paper cites.
A. Masiero, P. Paradisi and M. Passera, New physics at the MUonE experiment at CERN , 2002.05418
Original
2002
Earlier work this paper cites.
A. Denner and S. Dittmaier, Reduction of one loop tensor five point integrals , Nucl. Phys. B 658
2003
Earlier work this paper cites.
A. B. Yoo, M. A. Jette and M. Grondona, Slurm: Simple linux utility for resource management , in Job Scheduling Strategies for Parallel Processing , (Berlin, Heidelberg), pp. 44–60, Springer Berlin Heidelberg, 2003
2003
Earlier work this paper cites.
A. B. Arbuzov, D. Haidt, C. Matteuzzi, M. Paganoni and L. Trentadue, The Running of the electromagnetic coupling alpha in small angle Bhabha scattering , Eur. Phys. J. C34
2004
Earlier work this paper cites.
P. Banerjee et al., Theory for muon-electron scattering @ 10ppm: A report of the MUonE theory initiative , Eur. Phys. J. C 80
Original
2004
Earlier work this paper cites.
A. A. Penin, Two-loop corrections to Bhabha scattering , Phys. Rev. Lett. 95
2005
Earlier work this paper cites.
W. Bernreuther, R. Bonciani, T. Gehrmann, R. Heinesch, T. Leineweber, P. Mastrolia et al., Two-loop QCD corrections to the heavy quark form-factors: The Vector contributions , Nucl. Phys. B706
2005
Earlier work this paper cites.
A. Keshavarzi, W. J. Marciano, M. Passera and A. Sirlin, The muon g g -2 and Δ α \Delta\alpha connection , Phys. Rev. D 102
Original
2006
Earlier work this paper cites.
A. A. Penin, Two-loop photonic corrections to massive Bhabha scattering , Nucl. Phys. B734
2006
Earlier work this paper cites.
A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals , Nucl. Phys. B 734
2006
Earlier work this paper cites.

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Then

G. Lee, J. R. Arrington and R. J. Hill, Extraction of the proton radius from electron-proton scattering data , Phys. Rev. D 92
Original
2015
Later among the works it cites.
O. Tomalak and M. Vanderhaeghen, Two-photon exchange correction to muon–proton elastic scattering at low momentum transfer , Eur. Phys. J. C 76
Original
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Later among the works it cites.
O. Tomalak and M. Vanderhaeghen, Two-photon exchange correction in elastic unpolarized electron-proton scattering at small momentum transfer , Phys. Rev. D 93
Original
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Later among the works it cites.
G. M. Pruna, A. Signer and Y. Ulrich, Fully differential NLO predictions for the radiative decay of muons and taus , Phys. Lett. B772
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2020

QED at NNLO with McMule

Banerjee, P., Engel, T., Signer, A. et al.

Understand

McMule is a framework for fully differential higher-order QED calculations of scattering and decay processes involving leptons.

It keeps finite lepton masses, which regularises collinear singularities.
Soft singularities are treated with dimensional regularisation and using FKS$^\ell$ subtraction.
We describe the implementation of the framework in Fortran 95, list the processes that are currently implemented, and give instructions on how to run the code.

Built on

M. Fael and M. Passera, Muon-Electron Scattering at Next-To-Next-To-Leading Order: The Hadronic Corrections , Phys. Rev. Lett. 122
Original
1901
Earlier work this paper cites.
F. Buccioni, J.-N. Lang, J. M. Lindert, P. Maierhöfer, S. Pozzorini, H. Zhang et al., OpenLoops 2 , Eur. Phys. J. C 79
Original
1907
Earlier work this paper cites.
M. Davier, A. Hoecker, B. Malaescu and Z. Zhang, A new evaluation of the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment and to 𝛂 ⁡ ( 𝐦 𝐙 𝟐 ) \mathbf{\boldsymbol{\alpha}(m_{Z}^{2})} , Eur. Phys. J. C 80
Original
1908
Earlier work this paper cites.
T. Engel, A. Signer and Y. Ulrich, A subtraction scheme for massive QED , JHEP 01
Original
1909
Earlier work this paper cites.
A. Keshavarzi, D. Nomura and T. Teubner, g − 2 g-2 of charged leptons, α ⁡ ( M Z 2 ) \alpha(M^{2}_{Z}) , and the hyperfine splitting of muonium , Phys. Rev. D 101
Original
1911
Earlier work this paper cites.
V. Bertone, M. Cacciari, S. Frixione and G. Stagnitto, The partonic structure of the electron at the next-to-leading logarithmic accuracy in QED , JHEP 03
Original
1911
Earlier work this paper cites.
J. Ronca, NNLO QED Contribution to the μ e → μ e \mu e\to\mu e Elastic Scattering , EPJ Web Conf. 234
Original
1912
Earlier work this paper cites.
D. R. Yennie, S. C. Frautschi and H. Suura, The infrared divergence phenomena and high-energy processes , Annals Phys. 13
1961
Earlier work this paper cites.
L. W. Mo and Y.-S. Tsai, Radiative Corrections to Elastic and Inelastic e p and mu p Scattering , Rev. Mod. Phys. 41
1969
Earlier work this paper cites.
P. Nogueira, Automatic Feynman graph generation , J.Comput.Phys. 105
1993
Earlier work this paper cites.
S. Laporta, Hyperspherical integration and the triple cross vertex graphs , Nuovo Cim. A 107
1994
Earlier work this paper cites.
A. Djouadi and P. Gambino, Electroweak gauge bosons selfenergies: Complete QCD corrections , Phys. Rev. D 49
1994
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.
L. C. Maximon and J. A. Tjon, Radiative corrections to electron-proton scattering , Physical Review C 62
2000
Earlier work this paper cites.
S. Dittmaier, A General approach to photon radiation off fermions , Nucl. Phys. B565
2000
Earlier work this paper cites.
S. Pozzorini, H. Zhang and M. F. Zoller, Rational Terms of UV Origin at Two Loops , JHEP 05
Original
2001
Earlier work this paper cites.
S. Borsanyi et al., Leading-order hadronic vacuum polarization contribution to the muon magnetic moment from lattice QCD , 2002.12347
Original
2002
Earlier work this paper cites.
A. Masiero, P. Paradisi and M. Passera, New physics at the MUonE experiment at CERN , 2002.05418
Original
2002
Earlier work this paper cites.
A. Denner and S. Dittmaier, Reduction of one loop tensor five point integrals , Nucl. Phys. B 658
2003
Earlier work this paper cites.
A. B. Yoo, M. A. Jette and M. Grondona, Slurm: Simple linux utility for resource management , in Job Scheduling Strategies for Parallel Processing , (Berlin, Heidelberg), pp. 44–60, Springer Berlin Heidelberg, 2003
2003
Earlier work this paper cites.
A. B. Arbuzov, D. Haidt, C. Matteuzzi, M. Paganoni and L. Trentadue, The Running of the electromagnetic coupling alpha in small angle Bhabha scattering , Eur. Phys. J. C34
2004
Earlier work this paper cites.
P. Banerjee et al., Theory for muon-electron scattering @ 10ppm: A report of the MUonE theory initiative , Eur. Phys. J. C 80
Original
2004
Earlier work this paper cites.
A. A. Penin, Two-loop corrections to Bhabha scattering , Phys. Rev. Lett. 95
2005
Earlier work this paper cites.
W. Bernreuther, R. Bonciani, T. Gehrmann, R. Heinesch, T. Leineweber, P. Mastrolia et al., Two-loop QCD corrections to the heavy quark form-factors: The Vector contributions , Nucl. Phys. B706
2005
Earlier work this paper cites.
A. Keshavarzi, W. J. Marciano, M. Passera and A. Sirlin, The muon g g -2 and Δ α \Delta\alpha connection , Phys. Rev. D 102
Original
2006
Earlier work this paper cites.
A. A. Penin, Two-loop photonic corrections to massive Bhabha scattering , Nucl. Phys. B734
2006
Earlier work this paper cites.
A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals , Nucl. Phys. B 734
2006
Earlier work this paper cites.

Similar

Muon g-2
2006
Cited alongside, same era.
A. Mitov and S. Moch, The Singular behavior of massive QCD amplitudes , JHEP 05
2007
Cited alongside, same era.
T. Becher and K. Melnikov, Two-loop QED corrections to Bhabha scattering , JHEP 06
Original
2007
Cited alongside, same era.
C. Anastasiou, K. Melnikov and F. Petriello, The Electron energy spectrum in muon decay through O ⁡ ( α 2 ) O(\alpha^{2}) , JHEP 0709
2007
Cited alongside, same era.
J. D. Hunter, Matplotlib: A 2d graphics environment , Computing in Science & Engineering 9
2007
Cited alongside, same era.
F. Pérez and B. E. Granger, Ipython: A system for interactive scientific computing , Computing in Science & Engineering 9