Two applications of effective field theory: factorisation of gg→h in SCET & flavour physics of ALPs
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Abstract
The Standard Model of Particle Physics has been confirmed by numerous measurements
verifying its predictions. However, there are multiple direct and indirect hints pointing towards physics beyond the Standard Model. Two possibilities where new physics could
show up are deviations of theory prediction and experiment in high-precision observables
or direct detection of new particles, for instance at colliders or in particle transitions forbidden in the Standard Model. In this thesis, we approach both possibilities in two separate projects that are linked in their use of methodology rooted in the framework of effective field theories.
In the first project we study gluon-gluon to Higgs boson fusion via a light quark loop
in the context of soft-collinear effective theory (SCET) at next-to-leading order in SCET
power counting. Generalising the refactorisation-based subtraction scheme to regulate endpoint divergences to non-abelian final states, we are able to derive a factorisation theorem consisting of convolutions of hard Wilson coefficients and jet and soft functions that is endpoint divergence-free and UV finite. We demonstrate that even though regularisation and renormalisation do not commute in general, all mismatching terms can be absorbed into a redefinition of Wilson coefficients. After deriving the renormalisation group (RG) equations, we solve them iteratively to predict the leading large logarithmic corrections in the three-loop gg → h form factor. Eventually, we solve the RG equations for the leading contribution jet and soft function to RG-improved leading order. This allows us to resum the three leading towers of large logarithms in the form factor to all orders of perturbation theory.
In the second project we investigate how flavour physics experiments can constrain
parameter space of axion-like particle (ALP) models. First, we present how couplings at
the high-energy scale evolve to low energies. We show that independent of the specific
UV coupling, couplings to all Standard Model particles are generated through a series of
RG running and matching effects. This also includes effective flavour-changing couplings. Furthermore, we explain how to consistently implement ALPs in the weak chiral and nuclear Lagrangian, thereby freeing the formula for the branching ratio of the important K → πa decay from a long-standing inconsistency. We then explore the bounds on ALPs from quark and lepton flavour experiments in four benchmark scenarios, where we assume that only a certain coupling is present at the UV scale, and all other couplings are generated via evolution effects.