Michał Czakon

The production of two isolated photons at the Large Hadron Collider has applications in Higgs-boson phenomenology and in new-physics searches. In fact, measurements would provide more insight if a percent-level theoretical prediction were available. We account for next-to-next-to-next-to-leading-order strong-interaction effects in the cross section for the first time. This is not only necessary to demonstrate the convergence of perturbation theory, but also results in a reduction of the theoretical uncertainty by a factor of 3 down to 3%. With this, we pave the way to improved analyses.

A correction to this paper has been published: https://doi.org/10.1007/JHEP12(2023)126

The production of a top-quark pair, the heaviest known elementary particle, in association with a light jet is a key process for studying the properties of the standard model of particle physics. Due to its significance as a signal process with considerable sensitivity to the top-quark mass and as a background process for new physics searches, it is crucial to predict differential cross sections with high precision. In this Letter, we present, for the first time, predictions for various kinematical observables at next-to-next-to-leading order in quantum chromodynamics. The perturbative behavior is analyzed, and uncertainties arising from missing higher-order contributions are substantially reduced. The necessary two-loop amplitudes have been evaluated in the leading-color approximation, and we provide estimates for the impact of the missing contributions.

A bstract: 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, i.e. minimal subtraction and a scheme based on Catani’s magic formula for infrared divergences of two-loop amplitudes. 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.

A bstract: We present a leading colour computation of the double virtual contributions to top-quark pair production in association with a jet at a hadron collider at next-to-next-to-leading order in QCD. The finite remainders of the two-loop amplitudes, after subtraction of infrared and ultraviolet divergences, are extracted analytically from evaluations over finite fields by using a (potentially) overcomplete basis of special functions defined through their differential equations. We construct the colour- and spin-summed interference with the tree-level amplitudes and present a C++ library suitable for immediate use in phenomenological studies. We present new techniques for the evaluation of the special functions through direct numerical integration of differential equations which perform well across the full physical phase space.

A bstract: We provide the last missing ingredient necessary to approximate one-loop amplitudes in QCD with massive quarks in the limit of vanishing energy of a single gluon up to terms suppressed by this energy. Our main result is a soft operator acting in color and spin space that manipulates the momenta of the hard partons while keeping them on-shell and respecting momentum conservation. Additionally, we provide a complete expression for the subleading term of the expansion of an arbitrary tree-level amplitude in the limit where the momenta of a massless quark and a massless anti-quark of the same flavor become collinear. This limit is necessary to obtain the one-loop soft approximation whenever the process involves such a quark-anti-quark pair. Interestingly, the result involves a high-energy limit.

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.

The production of a top-quark pair, the heaviest known elementary particle, in association with a light jet is a key process for studying the properties of the Standard Model of Particle Physics. Due to its significance as a signal process with considerable sensitivity to the top-quark mass and as a background process for new physics searches, it is crucial to predict differential cross sections with high precision. In this article, we present, for the first time, predictions for various kinematical observables at next-to-next-to-leading order in Quantum Chromodynamics. The perturbative behavior is analyzed, and uncertainties arising from missing higher-order contributions are substantially reduced. The necessary two-loop amplitudes have been evaluated in the leading-color approximation, and we provide estimates for the impact of the missing contributions.

We present a leading colour computation of the double virtual contributions to top-quark pair production in association with a jet at a hadron collider at next-to-next-to-leading order in QCD. The finite remainders of the two-loop amplitudes, after subtraction of infrared and ultraviolet divergences, are extracted analytically from evaluations over finite fields by using a (potentially) overcomplete basis of special functions defined through their differential equations. We construct the colour- and spin-summed interference with the tree-level amplitudes and present a \texttt{C++} library suitable for immediate use in phenomenological studies. We present new techniques for the evaluation of the special functions through direct numerical integration of differential equations which perform well across the full physical phase space.