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

This thesis is composed out of five papers that deal with various problems in
theoretical particle physics. While paper I is a precision calculation in an
effective theory of the Standard Model, paper II to V all deal with beyond the
Standard Model physics. Paper IV is a manual for the tools developed during our
work on paper II to V.

Paper I. We calculate the 2-loop soft function for the transverse momentum
spectrum of a color-neutral final state in proton collisions in the framework of
Soft-Collinear-Effective Theory. Also the 2-loop beam functions are derived in
the same framework by a comparison to other works. This framework relies on
rapidity renormalization group equations to resum logarithms, which gives an
improved handling of theoretical uncertainties in the resummation. With our
result, one can perform next-to-next-leading log resummation of the mentioned
observable.

Paper II. In this paper, we show that there is no need to introduce scalar
kinetic mixing for models containing several identical scalar fields. This is
shown by an explicit 1-loop calculation of the renormalization group equations
using a toy model. The calculation is performed in separate renormalization
schemes; with and without kinetic mixing. We also derive the renormalization
scale dependent transformations that relate each of these schemes to one
another.

Paper III. This paper analyzes how breaking an imposed Z2 symmetry spreads
during renormalization group evolution of the CP~conserved Two-Higgs-Doublet
Model. We derive the 2-loop renormalization group equations and perform
numerical parameter scans of several physical scenarios.

Paper IV. This is a manual for the software 2HDME that was developed to
perform the numerical calculations in paper III. The code can evolve any
Two-Higgs-Doublet Model at 2-loop order and perform many tree-level calculations
such as masses and oblique parameters, but also tests of stability and
unitarity.

Paper V. In this paper, we use 2HDME in a similar way to paper III, but
this time with the CP~violating Two-Higgs-Doublet Model. We also implement a
calculation of the electron's electric dipole moment that we use to constrain
the amount of CP~violation. We perform several numerical parameter scans of
scenarios with different levels of Z2 symmetry breaking.