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How much color do we really need? Two-loop subleading-color effects in photon and jet physics

Michał Czakon, Rene Poncelet

TL;DR

The paper addresses whether subleading-color contributions significantly affect NNLO QCD predictions for LHC processes ending in photons or jets. It uses full-color two-loop amplitudes to compare against leading-color finite remainders in both MS-bar and Catani schemes, focusing on pp→3 jets and pp→γγγ (with additional checks for γγ+jet and γ+2 jets). The main findings are that subleading-color effects are typically below 2% for most observables, with up to ~5% impact on the R3/2 ratio at low HT2, and that these differences are usually smaller than the remaining perturbative uncertainties; Catani's remainder can be slightly more favorable for jets. The work provides a prior-based framework to estimate color uncertainties and supports the continued use of leading-color approximations with quantified error bands, informing high-precision extractions of αs and guiding future color-complete NNLO calculations.

Abstract

In recent years, the complete set of cross sections for Large Hadron Collider (LHC) processes ending with three resolved final states consisting of either photons or jets has been evaluated at next-to-next-to-leading order in QCD and leading order in QED. Results for three photons or three jets have only been obtained using the leading-color approximation of the virtual two-loop amplitudes. In the meantime, the required amplitudes have become available without recourse to the color expansion. In the present publication, we quantify the effects of the subleading-color contributions, and show that they do not exceed 2\% for most of the previously published results. The one exception is the ratio of three- to two-jet cross sections, where subleading-color effects can reach up to 5\%. Furthermore, we show that these conclusions hold for both popular infrared renormalization schemes, minimal subtraction and Catani's. The size of the effects is usually overshadowed by the size of the remaining uncertainty due to the truncation of the perturbation series. This is particularly important in the case of three-jet distributions that have already been used for the extraction of the strong-coupling constant at the very high energies available at the LHC.

How much color do we really need? Two-loop subleading-color effects in photon and jet physics

TL;DR

The paper addresses whether subleading-color contributions significantly affect NNLO QCD predictions for LHC processes ending in photons or jets. It uses full-color two-loop amplitudes to compare against leading-color finite remainders in both MS-bar and Catani schemes, focusing on pp→3 jets and pp→γγγ (with additional checks for γγ+jet and γ+2 jets). The main findings are that subleading-color effects are typically below 2% for most observables, with up to ~5% impact on the R3/2 ratio at low HT2, and that these differences are usually smaller than the remaining perturbative uncertainties; Catani's remainder can be slightly more favorable for jets. The work provides a prior-based framework to estimate color uncertainties and supports the continued use of leading-color approximations with quantified error bands, informing high-precision extractions of αs and guiding future color-complete NNLO calculations.

Abstract

In recent years, the complete set of cross sections for Large Hadron Collider (LHC) processes ending with three resolved final states consisting of either photons or jets has been evaluated at next-to-next-to-leading order in QCD and leading order in QED. Results for three photons or three jets have only been obtained using the leading-color approximation of the virtual two-loop amplitudes. In the meantime, the required amplitudes have become available without recourse to the color expansion. In the present publication, we quantify the effects of the subleading-color contributions, and show that they do not exceed 2\% for most of the previously published results. The one exception is the ratio of three- to two-jet cross sections, where subleading-color effects can reach up to 5\%. Furthermore, we show that these conclusions hold for both popular infrared renormalization schemes, minimal subtraction and Catani's. The size of the effects is usually overshadowed by the size of the remaining uncertainty due to the truncation of the perturbation series. This is particularly important in the case of three-jet distributions that have already been used for the extraction of the strong-coupling constant at the very high energies available at the LHC.

Paper Structure

This paper contains 6 sections, 28 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The ambiguous finite remainder
  3. Subleading color in past results
  4. Prior-based estimates of subleading-color effects
  5. Conclusions
  6. Setups for multi-photon cross sections

Figures (4)

  • Figure 1: Differential distributions for the $pp \to \gamma\gamma\gamma$ process. The lowest panel presents the ratio of the leading-color approximated results to the full-color prediction. Scale-uncertainty bands correspond to seven-point scale variation. Histograms "l.c. VVF Cat." have been obtained with Catani's finite remainder at leading color, while "l.c. VVF" with minimal subtraction. The dashed grey lines in the lowest panel demark the uncertainty estimated according to Section \ref{['sec:TNP']}.
  • Figure 2: Differential distributions for the $pp \to \gamma\gamma+$jet process. The format is the same as in Fig. \ref{['fig:aaa']}.
  • Figure 3: Transverse energy-energy correlator. The format is the same as in Fig. \ref{['fig:aaa']}.
  • Figure 4: Ratio of three- to two-jet cross sections, $R_{3/2}$. The format is the same as in Fig. \ref{['fig:aaa']}. The data points are from Ref. ATLAS:2024png.