Grants and Contributions:

Grant or Award spanning more than one fiscal year. (2017-2018 to 2020-2021)

I propose to investigate new analytic structures in quantum field theory. I will develop new methods to simplify precision calculations of scattering amplitudes, which will allow us to better understand and describe more accurately the interactions between elementary particles at the most microscopic level. I will rely on and extend our best tool and guiding principle: the use of on-shell particles, which havs already begun to produce revolutionary advances in the past years.

Experiments in particle physics are described quantitatively by quantum field theory. In many important situations, the key degrees of freedom are weakly coupled to each other. This includes the strong and electroweak interactions at the weak scale, where experiments at the Large Hadron Collider (LHC), near Geneva in Switzerland, are actively searching for minute deviations from the Standard Model. The small coupling justifies a perturbative approximation: it enables the precise comparison of theory and experiment. I will work toward significantly improving perturbative techniques.

Quantum effects in this regime are traditionally understood in the language of virtual particles. Recent advances have shown that much simplifications occur when one focuses instead on the viewpoint of particles coming in from infinity. Such particles, called on-shell, see a much simpler world and yet appear to contain all the essential information. This has enabled incredible new calculations in the past years but much of this progress has focused on special cases, special theories or to the lowest orders in perturbation theory. Addressing these shortcomings is essential not only to meet the practical needs of collider experiments, but also to our fundamental understanding of quantum field theory.

I propose to attack directly two major bottlenecks: dealing with the combinatorial growth of the algebraic expressions which provide so-called loop integrands, and converting Feynman integrals to useful analytic expressions. I also propose to investigate in detail the special limit of forward scattering. This limit offers an exciting new area for direct contact with experiment through forward-backward correlations, in addition to rich opportunities for a fruitful interplay with other subfields, including: chaos theory, black hole dynamics through holography and the nonperturbative bootstrap. On the long term, this line of research will not only enable new theoretical calculations at the precision frontier for the LHC and future colliders, but also simplify the way we practise and teach quantum field theory and understand microscopic interactions.