## Periodic Reporting for period 3 - QCDforfuture (QCD for the Future of Particle Physics)

Reporting period: 2020-01-01 to 2021-06-30

The momentous discovery of the Higgs boson in 2012 marked the start of a new era in particle physics. The energy of collisions at the Large Hadron Collider (LHC) has since increased allowing us to probe fundamental physics at an energy scale which has been out of reach until now. This presents a challenge to particle theory to keep pace with these developments, and respond to the fact that Standard Model interactions will have different features in this new energy range. We must understand these differences in order to extract as much information as possible from LHC data, and in particular to identify any signs of new physics. My framework, High Energy Jets, is the only tool of its kind to include the dominant high-energy corrections to all orders in the strong coupling and these have already been shown to be necessary to describe data at the lower collisions energies of 7 and 8~TeV. However, these corrections alone are not enough.

My research programme develops a novel and powerful framework for theoretical predictions based on the lessons learned from the first LHC run and the ongoing analysis of data from Run II. In particular it will combine the necessary high-energy corrections with state-of-the-art next-to-leading-order (NLO) fixed-order descriptions. A separate objective is to combine the high-energy corrections with the resummation contained in parton shower programs. This is necessary to describe data in regions where there is both evolution in rapidity and transverse momentum. The ultimate goal is to combine all three: high-energy corrections, NLO calculation and parton shower. Separate theoretical objectives will significantly improve our understanding of the underlying theory, which should ultimately enhance our description of data far beyond any current prediction. This will be the most complete description of quantum chromodynamics at colliders to date, and will be essential for the exploitation of future data from the LHC and beyond.

My research programme develops a novel and powerful framework for theoretical predictions based on the lessons learned from the first LHC run and the ongoing analysis of data from Run II. In particular it will combine the necessary high-energy corrections with state-of-the-art next-to-leading-order (NLO) fixed-order descriptions. A separate objective is to combine the high-energy corrections with the resummation contained in parton shower programs. This is necessary to describe data in regions where there is both evolution in rapidity and transverse momentum. The ultimate goal is to combine all three: high-energy corrections, NLO calculation and parton shower. Separate theoretical objectives will significantly improve our understanding of the underlying theory, which should ultimately enhance our description of data far beyond any current prediction. This will be the most complete description of quantum chromodynamics at colliders to date, and will be essential for the exploitation of future data from the LHC and beyond.

There have been 4 journal publications from the work so far on this project. The first three of these relate to new theoretical predictions for the production of a Higgs boson plus at least two sprays of coloured particles (jets) at the Large Hadron Collider (LHC). The first publication (Publication 1) is the first time a theory prediction was correct at all orders in alpha_s to leading log in s/pt, where s is the centre-of-mass energy of the partonic collision and pt is the transverse momentum of the coloured particles produced. The particle collisions at the LHC occur at higher energies than ever before in such an experiment which makes the corrections which grow with s all the more important so it was important to apply them to this process. In the second publication, a completely new implementation of the original theoretical ideas allowed matching to higher fixed-orders which represented another increase in accuracy. The third paper marked a real milestone. Fixed order predictions for Higgs-boson-plus-jets have struggled to cope with finite quark masses and additional coloured particles at the same time, they are stuck at leading-order for Higgs-plus-three-jets with finite quark masses and loop propagator effects. This problem is not present in predictions with the High Energy Jets (HEJ) framework because the amplitudes factorise in the high-energy limit. We therefore presented the first predictions simultaneously combining finite quark mass effects and extra QCD radiation, and found that the resulting predictions have a serious impact on predictions within typical experimental cuts, cutting the predicted cross section by a factor of two. Finally, the fourth publication accompanied the public release of the flexible Monte Carlo event generator code HEJ2, which is the new implementation mentioned above. The publication is a complete user manual.

My High Energy Jets framework is the only theoretical framework able to describe these high-energy corrections in a flexible Monte Carlo event generator (the type of tool necessary to compare predictions with analyses of LHC data). We have already published early results on corrections which allow us to apply the all-order corrections to many different types of process, and are preparing a publication on a much wider set of calculations which allows us to go much further still. The resulting predictions are the only way to model these processes at the LHC to this level of theoretical accuracy.

One of the central analyses at the LHC is that of Higgs boson plus dijet production which allows us to measure the coupling of the Higgs boson to other bosons and test the generation of particles masses in the Standard Model. Traditional fixed-order approaches are not able to include the impact of the mass of the top quark (the heaviest particle in the Standard Model) and have to make an approximation where its mass is infinite to make predictions for more than two coloured particles. This problem is far simpler in my framework making it the only method to include finite quark mass effects for 3 jets and above.

One of the central analyses at the LHC is that of Higgs boson plus dijet production which allows us to measure the coupling of the Higgs boson to other bosons and test the generation of particles masses in the Standard Model. Traditional fixed-order approaches are not able to include the impact of the mass of the top quark (the heaviest particle in the Standard Model) and have to make an approximation where its mass is infinite to make predictions for more than two coloured particles. This problem is far simpler in my framework making it the only method to include finite quark mass effects for 3 jets and above.