SciPost Submission Page
Two-Loop QCD Corrections for Three-Photon Production at Hadron Colliders
by Samuel Abreu, Giuseppe De Laurentis, Harald Ita, Maximillian Klinkert, Ben Page, Vasily Sotnikov
This Submission thread is now published as
|Authors (as registered SciPost users):||Samuel Abreu · Vasily Sotnikov|
|Preprint Link:||scipost_202308_00043v1 (pdf)|
|Date submitted:||2023-08-29 18:49|
|Submitted by:||Sotnikov, Vasily|
|Submitted to:||SciPost Physics|
We complete the computation of the two-loop helicity amplitudes for the production of three photons at hadron colliders, including all contributions beyond the leading-color approximation. We reconstruct the analytic form of the amplitudes from numerical finite-field samples obtained with the numerical unitarity method. This method requires as input surface terms for all relevant five-point non-planar integral topologies, which we obtain by solving the associated syzygy problem in embedding space. The numerical samples are used to constrain compact spinor-helicity ans\"atze, which are optimized by taking advantage of the known one-loop analytic structure. We make our analytic results available in a public C++ library, which is suitable for immediate phenomenological applications. We estimate that the inclusion of the subleading-color contributions will decrease the size of the two-loop corrections by about 30% to 50% compared to the results in the leading-color approximation.
Published as SciPost Phys. 15, 157 (2023)
Author comments upon resubmission
We would like to address the comment from the report 2:
"The relatively large sub-leading colour double virtual corrections are highlighted throughout the article as being larger than expected, ~30-50%. It is also stated that the differential cross sections are dominated be real radiation contributions. It would be useful if the authors could also provide a quantitative estimate of the correction for the NNLO predictions based on the new results presented here. The conclusions highlight that the currently available leading colour predictions are likely sufficient, which is not clear from the phrasing in the abstract."
We fully agree that a quantitative study of the effects of the new results on the NNLO cross sections would be very interesting. Due to the fact that the exact size of these effects is observable and scheme dependent, we believe that a dedicated study is appropriate, which we leave for future research. Nevertheless, we have performed an estimate (see the list of changes) based on the observed size of subleading contributions calculated in our work, and on the overall size of leading-color double virtual corrections reported in earlier studies. This estimate is quoted already in the abstract to address the second concern. We hope that this will further help the reader to understand the expected impact of the new corrections.
List of changes
1. In the abstract we replace the sentence
" We estimate that the inclusion of the subleading-color contributions will decrease the size of the two-loop corrections by about $30\%$ to $50\%$, compared to the results in the leading-color approximation."
"We estimate that the inclusion of the subleading-color contributions will decrease the size of the two-loop corrections by about $30\%$ to $50\%$, and the NNLO cross sections by a few percent, compared to the results in the leading-color approximation.
2. In conclusions we replace the next-to-last sentence
"Due to an overall small contribution from double-virtual corrections to the NNLO cross sections [12, 13], we conclude that the approximation employed in ref. [12–14] is likely sufficient, though in practice it is important to verify this conclusion for each observable."
"Due to an overall small contribution from double-virtual corrections to the NNLO cross sections [12, 13], we conclude that the approximation employed in ref. [12–14] should be valid within a few percent, although in practice it is important to verify this conclusion for each observable."
Submission & Refereeing History
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