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Isospin breaking at two loops in three-flavour Chiral Perturbation Theory

Yu, Hanchen LU (2024) FYTM06 20232
Particle and nuclear physics
Department of Physics
Abstract
In this thesis, we first give an introduction to the framework of Chiral Perturbation Theory. Following this, we proceed to conduct a detailed two-loop order calculation within Chiral Perturbation Theory, aimed at analyzing pseudoscalar meson masses and decay constants while incorporating isospin breaking effects. Our calculations account for both quark mass and charge isospin breaking effects in determining the masses, while focusing solely on quark mass correction for the decay constants. Throughout this work, we provide explicit expressions for both the masses and decay constants.
Popular Abstract
In the vast landscape of quantum field theories, such as the electroweak theory and quantum chromodynamics (QCD), lies a fundamental question: how do we effectively describe phenomena at lower energy scales when the true nature of high-energy physics remains elusive? This puzzle is elegantly addressed by Effective Field Theories (EFT), which sift through the complexities of high-energy interactions to focus on the essential physics at play in the low-energy realm.

Think of EFT as a skilled cartographer simplifying a map: just as cities are represented by dots, EFT distills the behavior of particles and forces to their most relevant aspects. This approach allows physicists to zoom in on specific features, separating the essential from... (More)
In the vast landscape of quantum field theories, such as the electroweak theory and quantum chromodynamics (QCD), lies a fundamental question: how do we effectively describe phenomena at lower energy scales when the true nature of high-energy physics remains elusive? This puzzle is elegantly addressed by Effective Field Theories (EFT), which sift through the complexities of high-energy interactions to focus on the essential physics at play in the low-energy realm.

Think of EFT as a skilled cartographer simplifying a map: just as cities are represented by dots, EFT distills the behavior of particles and forces to their most relevant aspects. This approach allows physicists to zoom in on specific features, separating the essential from the extraneous much like examining a map in detail.

Take, for instance but also what we investigate in this thesis, the realm of QCD, where the coupling constant decreases as energy scale increases. This characteristic enables the use of perturbation theory at high energies. However, in the low-energy domain, where the coupling constant becomes much bigger than one, perturbation theory fails to suffice. The non-perturbative nature of QCD in the low-energy region is actually not difficult to understand, here, the degrees of freedom shift from quarks and gluons to hadrons, similar to focusing on cities rather than the intricate details of their architecture.

The low-energy behavior of QCD can be understood through the lens of Chiral Perturbation Theory (ChPT), an effective field theory specifically tailored to describe the interactions of hadrons. ChPT is constructed such that its shares the same approximate chiral symmetry as QCD, just as the spatial arrangement of cities is preserved in the distribution of points on a map.

As technological advancements propel experiments probing low-energy QCD to unprecedented precision, the need for equally precise theoretical calculations intensifies. Despite past research yielding invaluable insights, there are still some uncertainties that persist, particularly the isospin breaking effects, which stem from differences in masses and charges between $u$ and $d$ quarks. In this work, we've incorporated these effects and corrected the calculations for the masses and decay rates of particles, thereby establishing formulas to predict these observable properties more accurately. (Less)
Please use this url to cite or link to this publication:
author
Yu, Hanchen LU
supervisor
organization
course
FYTM06 20232
year
type
H2 - Master's Degree (Two Years)
subject
keywords
chiral perturbation theory, two-loop, meson masses, meson decay constants
language
English
id
9160128
date added to LUP
2024-06-11 13:55:22
date last changed
2024-07-03 09:42:01
@misc{9160128,
  abstract     = {{In this thesis, we first give an introduction to the framework of Chiral Perturbation Theory. Following this, we proceed to conduct a detailed two-loop order calculation within Chiral Perturbation Theory, aimed at analyzing pseudoscalar meson masses and decay constants while incorporating isospin breaking effects. Our calculations account for both quark mass and charge isospin breaking effects in determining the masses, while focusing solely on quark mass correction for the decay constants. Throughout this work, we provide explicit expressions for both the masses and decay constants.}},
  author       = {{Yu, Hanchen}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Isospin breaking at two loops in three-flavour Chiral Perturbation Theory}},
  year         = {{2024}},
}