Calculational Techniques in Particle Theory

Abstract

In this contribution, I review some of the latest advances in calculational techniques in theoretical particle physics. I focus, in particular, on their application to the calculation of highly non-trivial scattering processes, which are relevant for precision phenomenology studies at the Large Hadron Collider at CERN.

Planar three-loop master integrals for 2 → 2 processes with one external massive particle

“…The mapping between our results and that of [5] yields that the variable y = s 23 s 12 that we introduced earlier is equal to the dimensionless parameter x used therein. 4 In the case of the F2 family the respective relation is y = 1…”

“…It has been estimated that the scheduled High Luminosity upgrade of the LHC will require the calculation of many scattering processes at the Next-to-Next-to-Next-to-Leading-Order (N3LO) to reach per-cent level of precision [2]. At that order of perturbative expansion the computation of three-loop FI becomes a necessity, a highly non-trivial task despite the major breakthroughs that have occurred in our understanding of their mathematical structure and the development of many methods for their analytical and numerical calculation [3,4]. Currently, at N3LO all FI for 2 → 2 scattering involving massless propa-…”

Two-loop non-planar hexa-box integrals with one massive leg

“…A typical NNLO calculation involves, among other things, the computation of twoloop Feynman diagrams [6]. The established method for performing such calculations is by solving first-order differential equations (DE) satisfied by the relevant Feynman integrals (FI) [7][8][9][10].…”