Periodic Reporting for period 4 - AMPLITUDES (Novel structures in scattering amplitudes)
Reporting period: 2022-02-01 to 2023-09-30
The overall goal of research in fundamental physics is to improve our understanding of Nature. Particle collider experiments provide a valuable source of experimental data. To fully exploit this data, it is vital to understand well the theory predicting outcomes of such scattering experiments, which is the focus of this ERC-funded project.
This project focuses on developing quantum field theory methods and applying them to the phenomenology of elementary particles. At the Large Hadron Collider (LHC) our current best theoretical understanding of particle physics is being tested against experiment by measuring e.g. properties of the recently discovered Higgs boson. With run two of the LHC, currently underway, the experimental accuracy will further increase. Theoretical predictions matching the latter are urgently needed. Obtaining these requires extremely difficult calculations of scattering amplitudes and cross sections in quantum field theory, including calculations to correctly describe large contributions due to long-distance physics in the latter. Major obstacles in such computations are the large number of Feynman diagrams that are difficult to handle, even with the help of modern computers, and the computation of Feynman loop integrals. To address these issues, we will develop innovative methods that are inspired by new structures found in supersymmetric field theories. We will extend the scope of the differential equations method for computing Feynman integrals, and apply it to scattering processes that are needed for phenomenology, but too complicated to analyze using current methods. Our results will help measure fundamental parameters of Nature, such as, for example, couplings of the Higgs boson, with unprecedented precision. Moreover, by accurately
predicting backgrounds from known physics, our results will also be invaluable for searches of new particles.
The research done within this ERC-funded project provided the research community with novel methods and algorithms for making precise predictions for scattering amplitudes needed for phenomenological studies of collider physics experiments. This removed an important bottleneck for making precise predictions, as required to match the data from upcoming LHC runs. Employing novel methods from supersymmetric toy models, the most accurate formulas to date for predicting the physics of soft exchanges in those amplitudes were derived. In addition, new structural properties of scattering amplitudes were found that have the potential to lead to completely different ways of thinking about quantum field theory.
This project focuses on developing quantum field theory methods and applying them to the phenomenology of elementary particles. At the Large Hadron Collider (LHC) our current best theoretical understanding of particle physics is being tested against experiment by measuring e.g. properties of the recently discovered Higgs boson. With run two of the LHC, currently underway, the experimental accuracy will further increase. Theoretical predictions matching the latter are urgently needed. Obtaining these requires extremely difficult calculations of scattering amplitudes and cross sections in quantum field theory, including calculations to correctly describe large contributions due to long-distance physics in the latter. Major obstacles in such computations are the large number of Feynman diagrams that are difficult to handle, even with the help of modern computers, and the computation of Feynman loop integrals. To address these issues, we will develop innovative methods that are inspired by new structures found in supersymmetric field theories. We will extend the scope of the differential equations method for computing Feynman integrals, and apply it to scattering processes that are needed for phenomenology, but too complicated to analyze using current methods. Our results will help measure fundamental parameters of Nature, such as, for example, couplings of the Higgs boson, with unprecedented precision. Moreover, by accurately
predicting backgrounds from known physics, our results will also be invaluable for searches of new particles.
The research done within this ERC-funded project provided the research community with novel methods and algorithms for making precise predictions for scattering amplitudes needed for phenomenological studies of collider physics experiments. This removed an important bottleneck for making precise predictions, as required to match the data from upcoming LHC runs. Employing novel methods from supersymmetric toy models, the most accurate formulas to date for predicting the physics of soft exchanges in those amplitudes were derived. In addition, new structural properties of scattering amplitudes were found that have the potential to lead to completely different ways of thinking about quantum field theory.
The work was organized according to four interconnected themes, (1) Novel structures in loop integrands, (2) Novel methods for computing Feynman integrals, (3) Applications to scattering amplitudes and collider physics, and (4) Long-distance singularities. The focus of themes (1) and (2) was to develop new methodology and algorithms, while themes (3) and (4) focuses on specific applications to state-of-the-art problems in scattering amplitudes, including the calculation of amplitudes for processes of phenomenological relevance.
The research results led to more than 70 scientific articles published in peer-reviewed journal articles, including eleven in the prestigious journal Physical Review Letters. Team members presented the research results at various international conferences. Examples of research results are:
- Obtained predictions from conformal symmetry — an extension of space-time translation and rotation symmetry — for scattering amplitudes.
- Calculated the four-loop cusp anomalous dimension in QCD, which settles a longstanding open question.
- Pioneered a new approach to computing energy-energy correlations, which are an important observable at particle colliders.
- Developed novel algorithmic ways of evaluating Feynman integrals, thereby removing a bottleneck in quantum field theory calculations.
- Explored geometric representations of scattering amplitudes and found a duality that relates observables in a supersymmetric theory to all-plus helicity amplitudes in QCD.
- Used integrability methods to obtain non-perturbative predictions for form factors in maximally supersymmetric Yang-Mills theory.
An overall highlight of this project are the results for two-loop five-particle scattering processes, pioneered by our group. The relevant function space was identified, and the two-loop non-planar Feynman integrals required to describe five-particle scattering were computed. This allowed us, for the first time, to compute full five-particle two-loop amplitudes, both in supersymmetric toy models, and in quantum chromodynamics, for a certain helicity configuration; moreover, the analytic function representation made it possible to study the Regge behavior of the answer. Our streamlined approach to computing scattering amplitudes, including finite fields methods, has become state of the art, and has since been used for a number of phenomenological applications. These crucially build upon the Feynman integrals computed within this ERC project.
A public lecture and moderated discussion involving Nima Arkani-Hamed (IAS Princeton), one of the leading high-energy-physicists, and renowned sociologist Armin Nassehi (LMU Munich) on the question “What holds the world together?” reached a
large audience. Results of this research were also presented at a dedicated workshop.
The research results led to more than 70 scientific articles published in peer-reviewed journal articles, including eleven in the prestigious journal Physical Review Letters. Team members presented the research results at various international conferences. Examples of research results are:
- Obtained predictions from conformal symmetry — an extension of space-time translation and rotation symmetry — for scattering amplitudes.
- Calculated the four-loop cusp anomalous dimension in QCD, which settles a longstanding open question.
- Pioneered a new approach to computing energy-energy correlations, which are an important observable at particle colliders.
- Developed novel algorithmic ways of evaluating Feynman integrals, thereby removing a bottleneck in quantum field theory calculations.
- Explored geometric representations of scattering amplitudes and found a duality that relates observables in a supersymmetric theory to all-plus helicity amplitudes in QCD.
- Used integrability methods to obtain non-perturbative predictions for form factors in maximally supersymmetric Yang-Mills theory.
An overall highlight of this project are the results for two-loop five-particle scattering processes, pioneered by our group. The relevant function space was identified, and the two-loop non-planar Feynman integrals required to describe five-particle scattering were computed. This allowed us, for the first time, to compute full five-particle two-loop amplitudes, both in supersymmetric toy models, and in quantum chromodynamics, for a certain helicity configuration; moreover, the analytic function representation made it possible to study the Regge behavior of the answer. Our streamlined approach to computing scattering amplitudes, including finite fields methods, has become state of the art, and has since been used for a number of phenomenological applications. These crucially build upon the Feynman integrals computed within this ERC project.
A public lecture and moderated discussion involving Nima Arkani-Hamed (IAS Princeton), one of the leading high-energy-physicists, and renowned sociologist Armin Nassehi (LMU Munich) on the question “What holds the world together?” reached a
large audience. Results of this research were also presented at a dedicated workshop.
Our results will help measure fundamental parameters of Nature, such as, for example, couplings of the Higgs boson, with unprecedented precision. Moreover, by accurately predicting backgrounds from known physics, our results will also be invaluable for searches of new particles.