Renormalization in Effective Field Theory and Hidden Radiation

This thesis dealswith the field of high-energy particle physics. It ismainly concernedwith two issues:
the “renormalization of effective field theories” and the “detection of hidden sectors”. The first two
papers are dedicated to the renormalization issue while the second two deal with the hidden sectors.
Renormalization is crucial when one calculates physical observables to a high degree of precision in
quantum field theory using perturbative expansions. The field has lately seen many new developments,
a recent one is the Weinberg-B¨uchler-Colangelo algorithm for calculating so-called Leading
Logarithms (LL). These terms appear at each refinement of the calculation of a physical observable,
i.e. at higher-orders in the perturbative expansion. They can be used to give a rough estimate of the
size of each higher-order correction (refinement), to verify that each new calculation will yield a small
correction to the previous estimate. This way, once the desired precision is reached, one can be sure
that ulterior (often lengthy) calculations will not be necessary.
In paper I we apply the algorithmto the calculation of the mass, in a particularly simple model called
O(N + 1)/O(N) non-linear massive sigma model. Though the model has a simple structure, it has
the interesting feature that for N = 3 it describes two-flavour ChPT (chiral perturbation theory), the
theory for lowenergy particle interactions, like π −π scattering. In paper II we apply the algorithmto
the decay constant, the vacuumexpectation value, the scattering amplitude, the pion scalar and vector
form factors. We perform the calculation to very high precision (the first four or five LLs, depending
on the observable), and showin which cases it is preferable to express the logs in terms of the physical
observables and in which cases in terms of the model parameters. We also solve (part of) the longstanding
problem of summing the contributions of infinite refinements, for all these observables.We
do this in the large number of fields N limit approximation.We prove this to be a poor approximation
of the generic N expressions for most observables.
The second topic deals with the detection of new hypothetical light mass particle sectors, hidden
from ordinary matter by an energy barrier. We exploit the high energies reached by particle colliders
to breach the barrier and observe the deviations from standard particle distributions induced by the
hidden sector. We consider both hadron colliders like LHC in CERN, where protons collide, and
the case of lepton colliders, where electron and positron collide. We develop models and tools to
simulate the effects of these new particles. The tools are inserted in a full scale random Monte Carlo
event generator called PYTHIA 8. This is used to simulate particle collisions, so that one can connect
the probabilities calculated from the theory with the particle distributions observed in the detectors.
In paper III we explore the idea of discovering a new hidden sector charge through the effects of
its radiation on the standard particle kinematics. In paper IV we seek to determine the structure of
said charges, through differences between the induced radiation and hadronization patterns and the
subsequent effects on standard distributions.