Looking for a new Sphaleron in the Weinberg Salam Theory

Dutta, Swapnil (2021) Looking for a new Sphaleron in the Weinberg Salam Theory. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Swapnil Dutta (16MS045)) 16MS045_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (882kB)

Abstract

In this project, we have explored the possibility of existence of new Sphalerons in the Weinberg-Salam theory. It is well known that at least one sphaleron already exists in the Weinberg-Salam theory, which is the electroweak sphaleron, which have been found out by Klinkhamer and Manton[1]. We follow their solution to calculate properties of the already known electroweak sphaleron[1]. We calculated some properties of sphalerons which could not be done in [1] as the precise values of several parameters of the standard model were not known back then in 1984. We also tried a purely numerical solution of the electroweak Sphaleron and found out that our energy upperbound was an improvement over their upper bound. We have also pointed out that the electroweak sphaleron is associated with only one of the possible cases in the topology of Weinberg-Salam (WS) theory that yields a sphaleron and that there are other complementary cases which could yield new sphalerons. We searched for new sphalerons within the realm of those possibilities. We have used various approaches to look for new sphalerons - namely, the techniques of Lagrange multipliers, calculus of variations and a purely numerical technique. However, we have not found any sphaleron in those complementary cases, but have compiled the lessons and conclusions learnt from those attempts. We hope that these no-go attempts will be useful for physicists who wish to search for new sphalerons in WS theory and elsewhere.

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