285 f(-p1) + f(-p2) γ(p3) + γ(p4)

285.1 Diphoton production

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 ptminphoton and etamaxphoton. 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 Rγj, ηγ 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 N3LL + 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 N3LLin ref. [1].

285.2 Transverse momentum resummation

Transverse momentum resummation can be enabled for process 285 at highest order N3LL+ NNLO with ‘part=resNNLOp‘. The setting ‘part=resNNLO‘ resums to order N3LL + NNLO (αs2 accuracy in improved perturbation theory power counting) and ‘part=resNLO‘ to order N3LL + NLO. Note that process 285 with resummation only includes the qq channel. The gg channel enters at an increased relative level of αs, so has to be added with process number 2851 at order ‘part=resNLO‘ for overall N3LL+ NNLO precision. For an overall consistent precision of N3LL + 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 αs2.

The fixed-order NNLO calculation has been implemented in ref. [3]. Transverse momentum resummation at the level of N3LL+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 N3LL’ in ref. [1].

285.3 Input files for ref. [9]

285.4 Diphoton production

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 ptminphoton and etamaxphoton. 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 Rγj, ηγ 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 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 N3LL + 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 N3LLin ref. [1].

285.5 Transverse momentum resummation

Transverse momentum resummation can be enabled for process 285 at highest order N3LL+ NNLO with ‘part=resNNLOp‘. The setting ‘part=resNNLO‘ resums to order N3LL + NNLO (αs2 accuracy in improved perturbation theory power counting) and ‘part=resNLO‘ to order N3LL + NLO. Note that process 285 with resummation only includes the qq channel. The gg channel enters at an increased relative level of αs, so has to be added with process number 2851 at order ‘part=resNLO‘ for overall N3LL+ NNLO precision. For an overall consistent precision of N3LL + 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 αs2.

The fixed-order NNLO calculation has been implemented in ref. [3]. Transverse momentum resummation at the level of N3LL+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 N3LL’ in ref. [1].

285.6 Plotter

nplotter_gamgam.f is the default plotting routine.

285.7 Example input and output file(s)

input285.ini process285.out

References

[1]    T. Neumann, The diphoton qT spectrum at N3LL + 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 qT resummation of color-singlet processes at N3LL+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 N3LO, JHEP 06 (2021) 115 [2012.03256].

[7]    M.A. Ebert, B. Mistlberger and G. Vita, Transverse momentum dependent PDFs at N3LO, 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.