Non-linearly realized discrete symmetries
- PDF / 1,074,852 Bytes
- 21 Pages / 595.276 x 841.89 pts (A4) Page_size
- 54 Downloads / 218 Views
Springer
Received: July 21, 2020 Accepted: August 23, 2020 Published: October 12, 2020
Saurav Das and Anson Hook Maryland Center for Fundamental Physics, University of Maryland, College Park, MD 20742, U.S.A.
E-mail: [email protected], [email protected] Abstract: While non-linear realizations of continuous symmetries feature derivative interactions and have no potential, non-linear realizations of discrete symmetries feature nonderivative interactions and have a highly suppressed potential. These Goldstone bosons of discrete symmetries have a non-zero potential, but the potential generated from quantum corrections is inherently very highly suppressed. We explore various discrete symmetries and to what extent the potential is suppressed for each of them. Keywords: Discrete Symmetries, Beyond Standard Model, Global Symmetries ArXiv ePrint: 2006.10767
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)071
JHEP10(2020)071
Non-linearly realized discrete symmetries
Contents 1 Introduction
1
2 Explicit example
4
3 Analysis using invariant theory
8 10
5 Conclusions
13
A More details on the A4 invariant potential
14
B Platonic solids B.1 Tetrahedron B.2 Cube B.3 Octahedron B.4 Icosahedron
14 15 16 17 17
1
Introduction
Non-linear realizations of continuous symmetries, Nambu Goldstone bosons (NGBs), often appear in particle physics models. Perhaps the most famous example of a pseudo-Nambu Goldstone boson (pNGB) appears in the Standard Model and is the pion. Exact Goldstone bosons are highly constrained by their continuous shift symmetry so that they are derivatively coupled and do not have a potential. Goldstone bosons are interesting objects and there exists a vast literature studying them [1–13]. While interesting in their own right, the symmetries of a Goldstone boson are often too restrictive to be useful and they are often made into pNGBs by explicitly breaking their exact shift symmetry. The breaking of the exact shift symmetry can reintroduce unwanted features such as a large mass term, typically referred to as the Hierarchy Problem. Unsurprisingly, many of the features discussed below will have analogues with various solutions to the Hierarchy problem that we will only briefly touch upon, as there exists a whole class of models where the Higgs is a pNGB [14–18]. In addition to solutions to Hierarchy problems, discrete symmetries are also ubiquitous in models of flavor, see e.g. refs. [19–21] and references therein. These flavor models use group theoretic properties to explain various observed properties of the quark and lepton mass matrices. These models typically involve spontaneous breaking of the discrete symmetries, leading to their non-linear realizations. The results discussed in this paper will help explain features such as anomalously light scalars that appear in these models.
–1–
JHEP10(2020)071
4 Exchange representation
In this article, we initiate a study of the non-linear realizations of discrete symmetries, objects we dub “discrete” NGBs. We fi
Data Loading...
