The kaon electromagnetic mass difference in AdS/QCD

Abstract

In this thesis, a holographic model for quantum chromodynamics (QCD) is used to estimate the electromagnetic contribution to the kaon mass difference. The principal ideas of the model are inspired by the AdS/CFT correspondence, which is believed to be exact. The calculation is first performed theoretically, highlighting the expansion of the result into a diagrammatic structure referred to as Witten diagrams, and similar to that of Feynman diagrams of perturbative quantum field theory. To this end, several relations between the propagators are derived. An outline of the full theoretical calculation is given before proceeding to attempt to evaluate numerically the electromagnetic mass difference to first loop order. This calculation is done in Euclidean space, and the results are fitted to analytical formulae to extrapolate to Minkowski space. The final values are off by several orders of magnitude, which is believed to be in part due to an unidentified numerical glitch, but the overall expected physical behaviour, near the mass pole, is reproduced correctly by the model.

Popular Abstract

Quantum field theory is the framework of the very successful Standard Model of particle physics, our best description yet of the behaviour of the elementary particles that we believe our world is made up of. It is therefore the language in which the subjacent ideas to this theory are univocally expressed, without the disputable interpretations that translating to our normal language requires. The Standard Model is split up into different sectors that each describe one or more of the four currently accepted fundamental interactions of nature. The two most important sectors are the electroweak sector and quantum chromodynamics (QCD). The electroweak sector is a unified theory of the electromagnetic and weak interactions, the first of which is responsible for cohesion of matter on our scale, and the latter can be used to explain radioactive reactions. Quantum chromodynamics, on the other hand, describes the strong-interaction responsible for the cohesion of the atomic nucleus.
Now, understanding how the world works on the scale of elementary particles may seem something of a curiosity at most, but it is exactly those theoretical advances that lead us to many of the electronic devices that are currently pullulating in our everyday lives. Besides, some of the large scale particle accelerators that we use to study this science have found applications in all sorts of unrelated domains, even in medicine!
Unfortunately quantum field theory is not perfect: there are practical issues that make some direct calculations extremely difficult; this is especially the case for QCD. In light of this, physicists often need to be creative in finding other ways to get at results. In particular, it is sometimes possible to find a way to map a difficult problem onto another, if possible, simpler one. When this is possible the problems are said to be dual; a simple example of this can be found in many optimisation problems, where minimising problems can be transformed into maximisation problems and vice versa.
Such an approach is adopted in this work, where we make use of an extension of the so-called AdS/CFT correspondence proposed by Juan Maldacena in 1997. In its original form, it relates a theory of gravity to a quantum field theory. In practice, this means that one can do calculations in the theory of gravity and deduce results in the quantum field theory or vice versa. As of yet, the correspondence is still formally at the stage of conjecture but given the empirical evidence for it, physicists would be extremely surprised if it turned out to be false.
Unfortunately however, the above correspondence cannot be exploited in its original form. This is because it postulates a relationship between two very particular theories pos- sessing extremely stringent symmetry properties. Whilst symmetry often helps simplify the resolution of a problem, those in question here are not shared by realistic theories. For instance, the symmetry properties of these theories would forbid the existence of a mass scale; which is manifestly false. Nevertheless, some physicists hope that the correspondence still holds, at least in an approximate form, if some of the symmetries are removed in someway so that the resulting field theory displays characteristics of one of the more realistic theories, namely in the case of this thesis, quantum chromodynamics. Two kinds of approaches are possible at this point, the first, which is theoretically more satisfying, would be to propose a scheme describing explicitly how the symmetry should be broken and then show that the resulting theory has all the characteristics of quantum chromodynamics; this however is extremely difficult with our current understanding of the AdS/CFT correspondence. The second approach is much more phenomenological: it consists in starting from QCD, postulating that a correspondence holds by providing a so-called “dictionary”, and then fitting parameters in the model to reproduce known experimental/ theoretical results; the model used in the present work was obtained in this way. The aim of this thesis is to use a model, obtained using the phenomenological approach described above, to calculate a particular physical observable known as the ‘kaon electromagnetic mass difference’ in order to ascertain whether the prediction differs from other models. In turn, this could allow us to understand more about the workings of the strong interaction and provide further ways of testing the extremely successful Standard Model, hence pushing back in a tiny way the boundaries of human ignorance.

• author: Borthwick, Jack
• 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: particle physics, AdS/QCD, AdS/CFT, kaon, electromagnetic mass difference, quantum field theory
• language: English
• id: 8878371
• date added to LUP: 2016-06-14 14:01:00
• date last changed: 2016-06-14 14:01:00