Periodic Reporting for period 4 - JetDynamics (High precision multi-jet dynamics at the LHC)
Periodo di rendicontazione: 2022-04-01 al 2023-11-30
JetDynamics aims to bring together new ideas in theoretical physics, mathematics and computer technologies to make the most precise predictions for modern collider experiments at CERN's Large Hadron Collider. The aim is for a radical breakthrough in the precision that can be obtained an enable deeper probes into fundamental forces of nature.
The Standard Model of fundamental interactions continues to baffle high energy physicists. There is increasing evidence of physical phenomena that cannot be explained by this theory that describes smallest scale physics we can currently probe. Cosmological and astrophysical experiments have reliable data supporting ideas like Dark Matter and Dark Energy that are not part of the Standard Model. There is also Gravity which has a negligible effect at the small scales of collider experiments but cannot be included in the mathematical framework of the Standard Model - Quantum Field Theory. As a result, as we probe the SM at colliders at higher and higher energies and with greater precision, we are expecting to see deviations from the Standard Model's predictions. So far no significant deviations have been seen.
Quantum field theory is a complicated theoretical environment and it is remarkably difficult to make concrete predictions with it. Probing fundamental particles at high energies allows us to obtain the high resolution image of the fundamental image and our theoretical predictions must also obtain this level of resolution if we hope to learn about the nature of our models. Hadron colliders are notoriously complicated environments with a lot of different elements. In this project we focus on the highest energy interactions where we apply a valid perturbation theory and make direct connections with scattering amplitudes. The nature of quantum field theory means that higher resolution also means larger numbers of particles. Out project targets a new class of processes which our both high order in perturbation theory as well as involving a high number of particles. To go beyond the state-of-the-art we need to looks at 2->3 scattering problems.
The aim of our project is to develop new computational frameworks and build a complete chain of tools able to make NNLO predictions for 2->3 scattering problems at the LHC. This is not a simple task and our team find innovative solutions to the large number of hurdles that stand in the way of achieving this.
Aim 1: To find a way to break through the complexity barrier of the high multiplicity two-loop amplitude computations and provide the missing NNLO ingredients in a form suitable for use in experimental analyses.
Aim 2: To combine tree-level, one-loop and two-loop amplitudes to cancel the intricate structure of infrared divergences and make differential NNLO predictions that can be compared with experiments.
Aim 3: To look beyond NNLO and make steps towards 1% level perturbative precision for 2->2 scattering.
If successful, our research program will result in a deeper understanding of the strong interaction and improved measurements of the fundamental parameters of the Standard Model
The Standard Model of fundamental interactions continues to baffle high energy physicists. There is increasing evidence of physical phenomena that cannot be explained by this theory that describes smallest scale physics we can currently probe. Cosmological and astrophysical experiments have reliable data supporting ideas like Dark Matter and Dark Energy that are not part of the Standard Model. There is also Gravity which has a negligible effect at the small scales of collider experiments but cannot be included in the mathematical framework of the Standard Model - Quantum Field Theory. As a result, as we probe the SM at colliders at higher and higher energies and with greater precision, we are expecting to see deviations from the Standard Model's predictions. So far no significant deviations have been seen.
Quantum field theory is a complicated theoretical environment and it is remarkably difficult to make concrete predictions with it. Probing fundamental particles at high energies allows us to obtain the high resolution image of the fundamental image and our theoretical predictions must also obtain this level of resolution if we hope to learn about the nature of our models. Hadron colliders are notoriously complicated environments with a lot of different elements. In this project we focus on the highest energy interactions where we apply a valid perturbation theory and make direct connections with scattering amplitudes. The nature of quantum field theory means that higher resolution also means larger numbers of particles. Out project targets a new class of processes which our both high order in perturbation theory as well as involving a high number of particles. To go beyond the state-of-the-art we need to looks at 2->3 scattering problems.
The aim of our project is to develop new computational frameworks and build a complete chain of tools able to make NNLO predictions for 2->3 scattering problems at the LHC. This is not a simple task and our team find innovative solutions to the large number of hurdles that stand in the way of achieving this.
Aim 1: To find a way to break through the complexity barrier of the high multiplicity two-loop amplitude computations and provide the missing NNLO ingredients in a form suitable for use in experimental analyses.
Aim 2: To combine tree-level, one-loop and two-loop amplitudes to cancel the intricate structure of infrared divergences and make differential NNLO predictions that can be compared with experiments.
Aim 3: To look beyond NNLO and make steps towards 1% level perturbative precision for 2->2 scattering.
If successful, our research program will result in a deeper understanding of the strong interaction and improved measurements of the fundamental parameters of the Standard Model
JetDynamics set out to make new precision predictions for key jet observables with multi-particle final states (2->3 scattering problems) up to next-to-next-to-leading order in QCD. Major theoretical obstacles had to be overcome to achieve this and a team with expertise in perturbative computations and the mathematical description of scattering amplitudes was assembled to complete the task. During the course of the project the use of finite field arithmetic to bypass traditional bottlenecks became a standard tool in the field, thanks, in part, to the the techniques developed for the project. We achieved new results for two-loop amplitudes in QCD and put them together into NNLO predictions.
Analytic forms for gluon scattering:
The first steps towards refining a finite-field based amplitude tool were taken in the context of 5-gluon scattering and we were the first group to obtain leading colour result for the single minus helicity amplitude and full colour correction in the all-plus helicity case. While the first results for analytic amplitudes were obtain by another group (using the same type of approach) the groups final results for 5-parton scattering were used to validate the results and have been made available for phenomenological application via the NJet C++ library.
Non-planar 5-point amplitudes and NLO corrections to di-photon + jet production:
The extension to non-planar (full colour) corrections to generic helicity amplitudes was taken using the di-photon plus three gluon process which was also used to make differential cross-sections. NLO analysis showed this contribution should be considered along with the quark initiated channels at NNLO.
2->3 amplitudes and cross-sections with an off-shell leg:
Wbb, Hbb and W+photon+jet processes were all computed in the leading colour approximation by our group. Wbb went on to be used in used for fully differential cross-sections and compared with experimental data by some group members.
2->3 amplitudes with internal masses:
Our group took the first steps along the daunting path towards NNLO corrections to process like tt+jet and tt+photon which can be used to make precision tests of top-quark properties.
NNLO differential cross-sections for photon+jets:
The results for pp->photon+2 jets achieved near the end of the project are first (and so far only) cross-sections to be compared with experimental data with full colour NNLO QCD corrections.
Overall, the project has witnessed a transition from a period where 2->3 scattering at NNLO was considered a pipe dream to a one where it is a readily available for experimental analysis. The results for the project contributed to this community wide effort and we look forward to their continued use for precision predictions at the LHC.
Analytic forms for gluon scattering:
The first steps towards refining a finite-field based amplitude tool were taken in the context of 5-gluon scattering and we were the first group to obtain leading colour result for the single minus helicity amplitude and full colour correction in the all-plus helicity case. While the first results for analytic amplitudes were obtain by another group (using the same type of approach) the groups final results for 5-parton scattering were used to validate the results and have been made available for phenomenological application via the NJet C++ library.
Non-planar 5-point amplitudes and NLO corrections to di-photon + jet production:
The extension to non-planar (full colour) corrections to generic helicity amplitudes was taken using the di-photon plus three gluon process which was also used to make differential cross-sections. NLO analysis showed this contribution should be considered along with the quark initiated channels at NNLO.
2->3 amplitudes and cross-sections with an off-shell leg:
Wbb, Hbb and W+photon+jet processes were all computed in the leading colour approximation by our group. Wbb went on to be used in used for fully differential cross-sections and compared with experimental data by some group members.
2->3 amplitudes with internal masses:
Our group took the first steps along the daunting path towards NNLO corrections to process like tt+jet and tt+photon which can be used to make precision tests of top-quark properties.
NNLO differential cross-sections for photon+jets:
The results for pp->photon+2 jets achieved near the end of the project are first (and so far only) cross-sections to be compared with experimental data with full colour NNLO QCD corrections.
Overall, the project has witnessed a transition from a period where 2->3 scattering at NNLO was considered a pipe dream to a one where it is a readily available for experimental analysis. The results for the project contributed to this community wide effort and we look forward to their continued use for precision predictions at the LHC.
Based on the results achieved so far, we expect to have new predictions for high multiplicity NNLO scattering that can be compared with experiments and fulfil the main goal of the project. The new tool box for amplitude computations is likely to have an impact beyond the duration of the project and we will release as much of this in public implementations as possible. JetDynamics has been one of a few international groups breaking new ground using finite field arithmetic to overcome traditional bottlenecks. By the end of the project we expect to see a range of new public results as well as public implementations that can be used by the whole theory community.
For direct comparison with the experiments we aim for differential predictions at NNLO in QCD for key processes in the SM:
a) pp->3 jets
b) pp->W+2 jets
c) pp->H+2 jets
d) The first steps towards pp->tt+jet
These processes have many facets and a successful project will lead to a rich program of phenomenology.
At the end of the project quite a lot of progress towards this goals has been achieved as described above. One of the key missing processes is pp->H+2j which is also perhaps one of the more interesting processes for SM tests. This process remains just out of reach since even in the leading colour approximation there are non-planar topologies with present a major challenge to both integral reduction and numerical evaluation. Nevertheless the technology developed during the course of this project looks as if it will provide a promising path to achieve these results in the near future.
For direct comparison with the experiments we aim for differential predictions at NNLO in QCD for key processes in the SM:
a) pp->3 jets
b) pp->W+2 jets
c) pp->H+2 jets
d) The first steps towards pp->tt+jet
These processes have many facets and a successful project will lead to a rich program of phenomenology.
At the end of the project quite a lot of progress towards this goals has been achieved as described above. One of the key missing processes is pp->H+2j which is also perhaps one of the more interesting processes for SM tests. This process remains just out of reach since even in the leading colour approximation there are non-planar topologies with present a major challenge to both integral reduction and numerical evaluation. Nevertheless the technology developed during the course of this project looks as if it will provide a promising path to achieve these results in the near future.