Updating bounds on the low-energy constants of Chiral Perturbation Theory from exact bounds on amplitudes

Abstract

Chiral perturbation theory is an efficient effective theory to describe meson-meson scattering at low energy. An effective theory naturally introduces low energy constants and they are used, for example, to solve the ultraviolet divergences. The aim of this master thesis is to focus on meson-meson scattering to find some theoretical bounds on the coupling constants, based mainly on arguments from analyticity and unitarity. In this work, new bounds have been derived for the two and three flavours cases, at p4. Next, properties of the general N flavours case have been studied and applied to the four flavours case. The contribution of the p6 lagrangian has also been considered to estimate the error in our calculations. Finally, upon all the calculated constraints, one might want to keep only the necessary ones. When the number of coupling constants is high, it is a problematic issue. A way to treat this problem has been developed.

Popular Abstract

Many new physical theories have been developed during the last century. The objects with high velocities are described by Special Relativity, the heavy ones by General Relativity, and the small ones by Quantum Mechanics. All of them show us that physics does not always follow our natural intuitions. Time, space, distance and even shapes appear to be more difficult to define than it sounds. This makes a popular science paper difficult to write. Let us nevertheless try to go down to the world of mesons.

A question of interactions

Physics is governed by four main interactions: Gravitation, which is described by General Relativity; Electromagnetism, the most important one at our scale as most of our devices like computers, phones or lamps are electromagnetic systems; the weak interaction, which can be used, through the natural instability of some materials, to produce energy with nuclear plants and finally, the strong interaction, which makes the atom's nucleus stable. These latter three interactions are described by Quantum Mechanics and Special Relativity, and are unified in the Standard Model.

Standard model

The Standard Model is used to understand low scale physics. The paper you are reading is made of molecules, these molecules, of atoms, an atom of electrons and of a nucleus. The nucleus in turn is made of protons and neutrons, which are both made of 3 quarks. Quarks, of which there are six types, and electrons are the fundamental "bricks" of all the matter. A meson, is a particle made up of two of these quarks.

A question of scale

With a magnet you can attract your keys despite of gravity but not any objects left on the moon. So at our scale, Electromagnetism is the most interesting phenomena, whereas at a bigger range, it becomes negligible with respect to gravity. At each scale, there are preponderant physical phenomena that we can highlight with a particular theory. The same occurs in our study: the Standard Model describes non relevant physics for us, like high energy physics. We use therefore a simplified theory, which introduces "coupling constants" and the more precision we want, the more constants we need. These numbers are really difficult to calculate, and the purpose of this work is to derive some constraints on them.

In the world of light meson particles

Since we want to simplify our problem by getting rid of heavy particles, we first have to look at light mesons. They are, of course, made of the lightest quarks. At the first level of precision we need to introduce two constants, on which constraints have been already found in Vincent Mateu and Aneesh V. Manohar's paper : Dispersion Relation Bounds for pion pion Scattering. We have derived better ones. Next, the numbers of quarks have been increased to 3 and then 4. Then, a procedure was created to organise our results and select the relevant information. Finally, the error has been evaluated inserting experimental values for the coupling constants in the second level of precision.

• author: Alvarez, Benjamin
• supervisor: Johan Bijnens
• organization: Theoretical Particle Physics - Undergoing reorganization; Department of Astronomy and Theoretical Physics - Undergoing reorganization
• course: FYTM01 20161
• year: 2016
• type: H2 - Master's Degree (Two Years)
• subject: Physics and Astronomy
• keywords: Coupling constants, meson-meson scattering, Chiral perturbation theory, constraints.
• language: English
• id: 8887016
• date added to LUP: 2016-07-09 16:21:43
• date last changed: 2016-07-09 16:21:43