Feynman Graph Expansions for high Precision

To an astonishing degree the laws of physics are described by the Standard Model of particle physics.

Having discovered its final miTo an astonishing degree the laws of physics are described by the Standard Model of particle physics.

Having discovered its final missing piece, the Higgs boson, CERNs Large Hadron Collider has now entered its high-precision phase challenging not only the SM but also our abilities to draw sufficiently precise predictions from it.

A formidable challenge will be to bring the accuracy of theoretical calculations to the percent level and, if possible, beyond. There are various bottlenecks associated to the different ingredients entering these predictions.

An enormous challenge will be to improve the accuracy of partonic cross sections, which describe the scattering of the proton's constituent quarks and gluons, in perturbative quantum chromo dynamics.

To reach the required precision we already now desire next-to-next-to-leading order (NNLO) predictions for 2-to-3 processes, next-to-NNLO (N3LO) predictions for 2-to-2 processes and even N4LO predictions for 2-to-1 processes.

At the same time further improvements to N4LO will be required for the splitting functions which are needed for a systematic treatment of parton density functions.

With the high luminosity phase of the LHC commencing in 2029 we can expect, however, that predictions of even more complicated final states will be required. It is clear that our current methods are not be up to the task.

This project aspires to fill this gap through a new methodology based on very recent advances I made in Feynman graph Theory and its applications to asymptotic expansions and infrared subtraction schemes.

This methodology will allow for the efficient automation of expansions around kinematic limits, leading to new pathways to obtain reliable and systematically improvable approximations for scattering amplitudes and the cross sections to which they contribute, which are currently out of reach.