# Johan Bijnens

Professor

## Renormalization in Effective Field Theory and Hidden Radiation

Author

## Summary, in English

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.

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.

Department/s

- Theoretical Particle Physics

Publishing year

2011

Language

English

Full text

Document type

Dissertation

Publisher

Department of Astronomy and Theoretical Physics, Lund University

Topic

- Subatomic Physics

Keywords

- Renormalization
- Effective theories
- Phenomenological Models
- Hidden Sectors

Status

Published

Supervisor

- Johan Bijnens

ISBN/ISSN/Other

- ISBN: 978-91-7473-075-3

Defence date

25 March 2011

Defence time

10:15

Defence place

Sal F, Teoretisk Fysik

Opponent

- Per Osland (Prof.)