Periodic Reporting for period 1 - TopJAm (Two-loop scattering amplitudes for top-pair production in association with a jet at hadron colliders)
Période du rapport: 2023-10-01 au 2025-09-30
Particle collider experiments give us a window into the fundamental laws of nature. The interpretation of the outcomes of these experiments rely on the comparison against theoretical predictions based on the Standard Model of particle physics. With the support of the Marie Skłodowska-Curie Actions programme, the TopJAm project paved the way to the compution of the two-loop scattering amplitudes for the production of a top-quark pair in association with a jet at the Large Hadron Collider (LHC). The targeted amplitudes are the main barrier to improving the accuracy of the predictions for this process. This will allow us to make the most of the measurements at the LHC, and thus improve our understanding of the heaviest known elementary particle: the top quark.
Although the early termination of the grant prevented us from reaching the final objective - the calculation of two-loop amplitudes for top-pair production in association with a jet at the LHC - the project nonetheless accomplished several significant objectives.
1) My collaborators and I proposed a novel method for the numerical evaluation of Feynman integrals. The key idea is to apply the recently-introduced framework of physics-informed deep learning to train neural networks that approximate the solutions to the differential equations governing the Feynman integrals. We developed and publicly released a proof-of-concept implementation, which we successfully tested on a range of advanced examples. With further development, this method could prove invaluable in cases where an analytic solution to these differential equations is beyond reach.
2) We also constructed the necessary bases of Feynman integrals required for calculating the targeted amplitudes in the leading-color approximation, and computed the differential equations they satisfy. This progress put us in the position to numerically evaluate these crucial building blocks, and to initiate the computation of the actual amplitudes and the development of a novel method for their expansion in a basis of special functions, along with their efficient numerical evaluation.
3) In addition to the Feynman integrals mentioned in point 2, we derived bases and differential equations for another set of Feynman integrals. This result paves the way for calculating the two-loop QCD amplitudes for another crucial LHC process: the production of two heavy vector bosons in association with a jet.
4) We completed the computation of the two-loop QCD amplitudes for yet another interesting scattering process within the LHC's physics program: the production of a W-boson in association with two photons. These amplitudes, which exhibit algebraic complexity similar to that of top-pair production in association with a photon, allowed us to stress-test our methodology and develop new techniques that we are now applying to the project's main objective.
In addition to these achievements, I also established the foundation for several further objectives, which will be completed in the months following the conclusion of the grant.
1) My collaborators and I proposed a novel method for the numerical evaluation of Feynman integrals. The key idea is to apply the recently-introduced framework of physics-informed deep learning to train neural networks that approximate the solutions to the differential equations governing the Feynman integrals. We developed and publicly released a proof-of-concept implementation, which we successfully tested on a range of advanced examples. With further development, this method could prove invaluable in cases where an analytic solution to these differential equations is beyond reach.
2) We also constructed the necessary bases of Feynman integrals required for calculating the targeted amplitudes in the leading-color approximation, and computed the differential equations they satisfy. This progress put us in the position to numerically evaluate these crucial building blocks, and to initiate the computation of the actual amplitudes and the development of a novel method for their expansion in a basis of special functions, along with their efficient numerical evaluation.
3) In addition to the Feynman integrals mentioned in point 2, we derived bases and differential equations for another set of Feynman integrals. This result paves the way for calculating the two-loop QCD amplitudes for another crucial LHC process: the production of two heavy vector bosons in association with a jet.
4) We completed the computation of the two-loop QCD amplitudes for yet another interesting scattering process within the LHC's physics program: the production of a W-boson in association with two photons. These amplitudes, which exhibit algebraic complexity similar to that of top-pair production in association with a photon, allowed us to stress-test our methodology and develop new techniques that we are now applying to the project's main objective.
In addition to these achievements, I also established the foundation for several further objectives, which will be completed in the months following the conclusion of the grant.
The work carried out during this year laid the ground for the achievement of all the final objectives of the action: the computation of the two-loop amplitudes for top-pair production in association with a jet at the LHC, as well as a method for the efficient numerical evaluation of the appearing special functions. In addition, it opened further research directions beyond the original plan: the study of the production of two heavy vector bosons in association with a jet at the LHC, in particular. The completion and exploitation of these results will require further research, and will be guaranteed by the secured funding (more info at https://data.snf.ch/grants/grant/215960(s’ouvre dans une nouvelle fenêtre)).