The nonlinear Heisenberg-Euler theory is capable of describing the dynamics of vacuum polarization, a key prediction by quantum electrodynamics. Due to vast progress in the field of laser technology in recent years vacuum polarization can be triggered in the lab by colliding high-intensity laser pulses, leading to a variety of interesting novel phenomena. Since analytical methods for highly nonlinear problems are generally limited and since the experimental requirements for the detection of the signals from the nonlinear quantum vacuum are high, the need for numerical support is apparent. The paper presents a highly-accurate, efficient numerical scheme for solving the nonlinear Heisenberg-Euler equations in weak-field expansion up to six-photon interactions. Properties of the numerical scheme are discussed and an implementation accurate up to order thirteen in terms of spatial resolution is given. Simulations are presented and benchmarked with known analytical results. The versatility of the numerical solver is demonstrated by solving problems in complicated configurations.

Vacuum polarization, a key prediction of quantum theory, can cause a variety of intriguing phenomena that can be triggered by high-intensity laser pulses.The Heisenberg-Euler theory of the quantum vacuum supplements Maxwell's theory of electromagnetism with nonlinear photon-photon interactions mediated by vacuum fluctuations.This work presents a numerical solver for the leading weak-field Heisenberg-Euler corrections.The present code implementation reaches an accuracy of order thirteen in the numerical scheme and takes into account up to six-photon interactions.Since theoretical approaches are limited to approximations and the experimental requirements for signal detection are high, the need for support from the numerical side is apparent.

We match the electroweak chiral Lagrangian with two singlet scalars to the next-to-minimal composite Higgs model with $ SO(6)/SO(5) $ coset structure and extract the scalar divergences to one loop. Assuming the additional scalar to be heavy, we integrate it out and perform a matching to the well-established electroweak chiral Lagrangian with one light Higgs.

The framework of the electroweak chiral Lagrangian with a light Higgs is extended by an additional scalar and then generalized to N scalars in the Higgs sector. Divergences from scalar fluctuations are renormalized up to one loop using the background field method. The results are crosschecked against the case of one scalar. A subset of the divergences is demonstrated and crosschecked diagrammatically. Together with the complete one-loop renormalization of the electroweak chiral theory with one light Higgs conducted previously, this constitutes a renormalization framework of any pure scalar extension to the electroweak chiral theory.

The large volume of data expected to be produced by the Belle II experiment presents the opportunity for studies of rare, previously inaccessible processes. Investigating such rare processes in a high data volume environment necessitates a correspondingly high volume of Monte Carlo simulations to prepare analyses and gain a deep understanding of the contributing physics processes to each individual study. This resulting challenge, in terms of computing resource requirements, calls for more intelligent methods of simulation, in particular for processes with very high background rejection rates. This work presents a method of predicting in the early stages of the simulation process the likelihood of relevancy of an individual event to the target study using graph neural networks. The results show a robust training that is integrated natively into the existing Belle II analysis software framework.