Diphoton production

The fixed-order NNLO calculation has been implemented in ref. ¹. Transverse momentum resummation at the level of $\text{N}^3\text{LL}+\text{NNLO}$ has been implemented in ref. ². By including the three-loop hard ³ and beam functions ⁴,⁵,⁶ it has been upgraded to $\text{N}^3\text{LL}'$ in ref. ⁷.

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. ⁷.

This process also includes the one-loop gluon-gluon contribution as given in ref. ⁸. 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.

Transverse momentum resummation

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

---

1. John M. Campbell, R. Keith Ellis, Ye Li, and Ciaran Williams. Predictions for diphoton production at the LHC through NNLO in QCD. JHEP, 07:148, 2016. arXiv:1603.02663, doi:10.1007/JHEP07$2016$148. ↩

2. Thomas Becher and Tobias Neumann. Fiducial qT resummation of color-singlet processes at N³LL+NNLO. JHEP, 03:199, 2021. arXiv:2009.11437, doi:10.1007/JHEP03$2021$199. ↩

3. Fabrizio Caola, Andreas Von Manteuffel, and Lorenzo Tancredi. Diphoton Amplitudes in Three-Loop Quantum Chromodynamics. Phys. Rev. Lett., 126$11$:112004, 2021. arXiv:2011.13946, doi:10.1103/PhysRevLett.126.112004. ↩

4. Ming-xing Luo, Tong-Zhi Yang, Hua Xing Zhu, and Yu Jiao Zhu. Unpolarized quark and gluon TMD PDFs and FFs at N$^3$LO. JHEP, 06:115, 2021. arXiv:2012.03256, doi:10.1007/JHEP06$2021$115. ↩

5. Markus A. Ebert, Bernhard Mistlberger, and Gherardo Vita. Transverse momentum dependent PDFs at N³LO. JHEP, 09:146, 2020. arXiv:2006.05329, doi:10.1007/JHEP09$2020$146. ↩

6. Ming-xing Luo, Tong-Zhi Yang, Hua Xing Zhu, and Yu Jiao Zhu. Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order. Phys. Rev. Lett., 124$9$:092001, 2020. arXiv:1912.05778, doi:10.1103/PhysRevLett.124.092001. ↩

7. Tobias Neumann. The Diphoton $q\_T$ spectrum at N³LL$^\prime $+NNLO. EPJC, 7 2021. arXiv:2107.12478. ↩↩

8. Zvi Bern, Lance J. Dixon, and Carl Schmidt. Isolating a light Higgs boson from the diphoton background at the CERN LHC. Phys. Rev. D, 66:074018, 2002. arXiv:hep-ph/0206194, doi:10.1103/PhysRevD.66.074018. ↩