Soft resummation and hard evolution : Renormalization group methods in effective theories and multi scalar models

Sammanfattning: This thesis is composed out of five papers that deal with various problems intheoretical particle physics. While paper I is a precision calculation in aneffective theory of the Standard Model, paper II to V all deal with beyond theStandard Model physics. Paper IV is a manual for the tools developed during ourwork on paper II to V.Paper I. We calculate the 2-loop soft function for the transverse momentumspectrum of a color-neutral final state in proton collisions in the framework ofSoft-Collinear-Effective Theory. Also the 2-loop beam functions are derived inthe same framework by a comparison to other works. This framework relies onrapidity renormalization group equations to resum logarithms, which gives animproved handling of theoretical uncertainties in the resummation. With ourresult, one can perform next-to-next-leading log resummation of the mentionedobservable.Paper II. In this paper, we show that there is no need to introduce scalarkinetic mixing for models containing several identical scalar fields. This isshown by an explicit 1-loop calculation of the renormalization group equationsusing a toy model. The calculation is performed in separate renormalizationschemes; with and without kinetic mixing. We also derive the renormalizationscale dependent transformations that relate each of these schemes to oneanother. Paper III. This paper analyzes how breaking an imposed Z2 symmetry spreadsduring renormalization group evolution of the CP~conserved Two-Higgs-DoubletModel. We derive the 2-loop renormalization group equations and performnumerical parameter scans of several physical scenarios.Paper IV. This is a manual for the software 2HDME that was developed toperform the numerical calculations in paper III. The code can evolve anyTwo-Higgs-Doublet Model at 2-loop order and perform many tree-level calculationssuch as masses and oblique parameters, but also tests of stability andunitarity.Paper V. In this paper, we use 2HDME in a similar way to paper III, butthis time with the CP~violating Two-Higgs-Doublet Model. We also implement acalculation of the electron's electric dipole moment that we use to constrainthe amount of CP~violation. We perform several numerical parameter scans ofscenarios with different levels of Z2 symmetry breaking.