Process 285 represents the production of a pair of real photons. Since this process
includes two real photons, the cross section diverges when one of the photons is very
soft or in the direction of the beam. Thus in order to produce sensible results, the
input file must supply values for both ptmin_{photon} and etamax_{photon}. This will ensure
that the cross section is well-defined.

The calculation of process 285 may be performed using either the Frixione algorithm or standard cone isolation. Since version 10.1 also a fixed cone size can be specificed as well as a simple hybrid cone isolation, see ref. [1].

This process also includes the one-loop gluon-gluon contribution as given in ref. [2]. The production of a photon via parton fragmentation is included at NLO and can be run separately by using the frag option in part. This option includes the contributions from the integrated photon dipole subtraction terms and the LO QCD matrix element multiplied by the fragmentation function.

The phase space cuts for the final state photons are defined in input.ini,
for multiple photon processes such as 285 - 287 the pT’s of the individual
photons (hardest, second hardest and third hardest or softer) can be controlled
independently. The remaining cuts on R_{γj}, η_{γ} etc. are applied universally to all
photons. Process 286, corresponding to γγ+jet production, can be computed at
NLO.

This process can be calculated at LO, NLO, and NNLO. NLO calculations can be performed by subtraction, zero-jettiness slicing and qT-slicing. NNLO calculations can be performed by zero-jettiness slicing and qT-slicing. Input files for these 6 possibilities are given in the link below.

The fixed-order NNLO calculation has been implemented in ref. [3]. Transverse
momentum resummation at the level of N^{3}LL + NNLO has been implemented in ref.
[4]. By including the three-loop hard [5] and beam functions [6],[7],[8] it has been
upgraded to N^{3}LL′ in ref. [1].

Transverse momentum resummation can be enabled for process 285 at highest order
N^{3}LL′ + NNLO with ‘part=resNNLOp‘. The setting ‘part=resNNLO‘ resums to
order N^{3}LL + NNLO (α_{s}^{2} accuracy in improved perturbation theory power
counting) and ‘part=resNLO‘ to order N^{3}LL + NLO. Note that process 285 with
resummation only includes the q channel. The gg channel enters at an
increased relative level of α_{s}, so has to be added with process number 2851 at
order ‘part=resNLO‘ for overall N^{3}LL′ + NNLO precision. For an overall
consistent precision of N^{3}LL + NNLO the gg channel can be added with
‘part=resLO‘.

Note that at fixed-order the gg channel is included at NNLO automatically at the
level of α_{s}^{2}.

The fixed-order NNLO calculation has been implemented in ref. [3]. Transverse
momentum resummation at the level of N^{3}LL+NNLO has been implemented in ref.
[4]. By including the three-loop hard [5] and beam functions [6],[7],[8] it has been
upgraded to N^{3}LL’ in ref. [1].

Process 285 represents the production of a pair of real photons. Since this process
includes two real photons, the cross section diverges when one of the photons is very
soft or in the direction of the beam. Thus in order to produce sensible results, the
input file must supply values for both ptmin_{photon} and etamax_{photon}. This will ensure
that the cross section is well-defined.

The calculation of process 285 may be performed using either the Frixione algorithm or standard cone isolation. Since version 10.1 also a fixed cone size can be specificed as well as a simple hybrid cone isolation, see ref. [1].

This process also includes the one-loop gluon-gluon contribution as given in ref. [2]. The production of a photon via parton fragmentation is included at NLO and can be run separately by using the frag option in part. This option includes the contributions from the integrated photon dipole subtraction terms and the LO QCD matrix element multiplied by the fragmentation function.

The phase space cuts for the final state photons are defined in input.ini, for
multiple photon processes such as 285 - 287 the p_{T}’s of the individual
photons (hardest, second hardest and third hardest or softer) can be controlled
independently.The remaining cuts on R_{γj}, η_{γ} etc. are applied universally to all
photons. Users wishing to alter this feature should edit the file photon_cuts.f in the
directory src/User.

This process can be calculated at LO, NLO, and NNLO. NLO calculations can be
performed by subtraction, zero-jettiness slicing and q_{T}-slicing. NNLO calculations
can be performed by zero-jettiness slicing and q_{T}-slicing. Input files for these 6
possibilities are given in the link below.

The fixed-order NNLO calculation has been implemented in ref. [3]. Transverse
momentum resummation at the level of N^{3}LL + NNLO has been implemented in ref.
[4]. By including the three-loop hard [5] and beam functions [6],[7],[8] it has been
upgraded to N^{3}LL′ in ref. [1].

Transverse momentum resummation can be enabled for process 285 at highest order
N^{3}LL′ + NNLO with ‘part=resNNLOp‘. The setting ‘part=resNNLO‘ resums to
order N^{3}LL + NNLO (α_{s}^{2} accuracy in improved perturbation theory power
counting) and ‘part=resNLO‘ to order N^{3}LL + NLO. Note that process 285 with
resummation only includes the q channel. The gg channel enters at an
increased relative level of α_{s}, so has to be added with process number 2851 at
order ‘part=resNLO‘ for overall N^{3}LL′ + NNLO precision. For an overall
consistent precision of N^{3}LL + NNLO the gg channel can be added with
‘part=resLO‘.

Note that at fixed-order the gg channel is included at NNLO automatically at the
level of α_{s}^{2}.

The fixed-order NNLO calculation has been implemented in ref. [3]. Transverse
momentum resummation at the level of N^{3}LL+NNLO has been implemented in ref.
[4]. By including the three-loop hard [5] and beam functions [6],[7],[8] it has been
upgraded to N^{3}LL’ in ref. [1].

nplotter_gamgam.f is the default plotting routine.

[1]
T. Neumann,
The
diphoton
q_{T}
spectrum
at
N^{3}LL^{′} + NNLO,
Eur.
Phys.
J.
C
81
(2021)
905
[2107.12478].

[2] Z. Bern, L.J. Dixon and C. Schmidt, Isolating a light Higgs boson from the diphoton background at the CERN LHC, Phys. Rev. D66 (2002) 074018 [hep-ph/0206194].

[3] J.M. Campbell, R.K. Ellis, Y. Li and C. Williams, Predictions for diphoton production at the LHC through NNLO in QCD, JHEP 07 (2016) 148 [1603.02663].

[4]
T. Becher
and
T. Neumann,
Fiducial
q_{T}
resummation
of
color-singlet
processes
at
N^{3}LL+NNLO,
JHEP
03
(2021)
199
[2009.11437].

[5] F. Caola, A. Von Manteuffel and L. Tancredi, Diphoton Amplitudes in Three-Loop Quantum Chromodynamics, Phys. Rev. Lett. 126 (2021) 112004 [2011.13946].

[6]
M.-x. Luo,
T.-Z. Yang,
H.X. Zhu
and
Y.J. Zhu,
Unpolarized
quark
and
gluon
TMD
PDFs
and
FFs
at
N^{3}LO,
JHEP
06
(2021)
115
[2012.03256].

[7]
M.A. Ebert,
B. Mistlberger
and
G. Vita,
Transverse
momentum
dependent
PDFs
at
N^{3}LO,
JHEP
09
(2020)
146
[2006.05329].

[8] M.-x. Luo, T.-Z. Yang, H.X. Zhu and Y.J. Zhu, Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order, Phys. Rev. Lett. 124 (2020) 092001 [1912.05778].

[9] J.M. Campbell, R.K. Ellis and S. Seth, Non-local slicing approaches for NNLO QCD in MCFM, 2202.07738.