HOPSRES · Higher Order Parton Showers and Resummation to meet the High Luminosity LHC's accuracy goal

With the upcoming high-luminosity phase of the Large Hadron Collider (LHC), the high energy physics community is gearing up to explore the fundamental building blocks of our universe with unprecedented precision. Consequently, the demand for precise and widely available theoretical predictions is at its highest level. Resummation of logarithmically enhanced terms plays a crucial role in achieving accurate phenomenological predictions, in addition to higher-order fixed-order predictions.During my fellowship, I will to work on the design, implementation, and application of tools dedicated to Next-to-Next-to-Leading Logarithmic (NNLL) resummation, including novel applications, as well as the first complete dipole parton shower with validated NNLL accuracy. Both represent critical tasks to meet the accuracy needs of the next phase of the LHC and of future collider experiments.As a first step, I intend to extend the established CAESAR formalism for NLL resummation to NNLL, inside a comprehensive framework within the Sherpa event generator, one of the major simulation tools used by the LHC experiments. The Sherpa-CAESAR framework will then be extended to accommodate hadron collider environments like the LHC. The integration of this baseline for NNLL resummation serves as a foundation for the following efforts. Subsequently, I plan to enhance the recently introduced Alaric parton shower with inclusion of established Next-To-Next-To-Leading Order (NLO) splitting functions. Ultimately, I will utilise the tools and methods developed in the initial phase to validate the NNLL accuracy of the enhanced Alaric parton shower.By the projects conclusion, not only will a significant enhancement in NNLL resummation have been realised, but novel novel strategies for NLO subtraction and parton shower matching will emerge. This project stands to make a substantial contribution to the advancement of particle physics and the successful execution of experiments at the LHC and beyond.