High precision applications of lattice gauge theories in the quest for new physics

Abstract

We present some aspects of high precision calculations in the context of Lattice Quantum Field Theory. This work is a collection of three studies done during my Ph.D. period. First we present how to use the reweighting technique to compensate for the breaking of unitarity due to the use of different boundary conditions in the valence and sea sector. In particular when twisted boundary conditions are employed, with $θ$ twisting angle. In large volume we found that the breaking is negligible, while in rather small volumes an effect is present. The quark mass appears to change with $θ$ as a cutoff effect. In the second part of the dissertation we present an optimization method for Hybrid Monte Carlo performances. The work is based on the existence of a shadow Hamiltonian, an exactly conserved quantity along the Molecular Dynamics trajectory. The optimization method is economic since it only requires the forces to be measured, which are already used for the evolution from one configuration to the new one. We found predictions for the cost of the simulations with an accuracy of 10% and we could estimate the optimal parameters for the Omelyan integrator with mass-preconditioning and multi time-scale. In the last part of the work we address the calculation of electromagnetic corrections to the hadronic contribution to the $(g-2)$ anomaly of the muon. A long standing discrepancy between theoretical calculations and experimental results is present. But before invoking New Physics we need to clear the sight from possible effects within the Standard Model. In this exploratory study we carefully matched the masses of the charged pions in the theory with and without QED. We found a visible effect at the percent level although consistent with zero within two sigmas.