New Story
Appendices on Our Dark Matter Study
by Phenomenology TechnologyFebruary 22nd, 2025
Too Long; Didn't Read
Our universe at a large scale can be described well if we assume isotropy and homogeneity of space.Companies Mentioned
Coin Mentioned
Table of Links
2 Dark matter through ALP portal and 2.1 Introduction
2.3 Existing constraints on ALP parameter space
3 A two component dark matter model in a generic 𝑈(1)𝑋 extension of SM and 3.1 Introduction
3.3 Theoretical and experimental constraints
3.4 Phenomenology of dark matter
3.5 Relic density dependence on 𝑈(1)𝑋 charge 𝑥𝐻
4 A pseudo-scalar dark matter case in 𝑈(1)𝑋 extension of SM and 4.1 Introduction
4.3 Theoretical and experimental constraints
Appendices
A Standard model
The kinetic term for the fermions (leptons and quarks) is given by
The Yukawa interactions for the leptons and quarks are given by
B Friedmann equations
Our universe at a large scale can be described well if we assume isotropy and homogeneity of space. The Friedmann-Lemaitre-Robertson-Walker (FLRW) metric hold these assumptions, which is given by,
here p and 𝜌 are the pressure and energy density of the fluid respectively whereas 𝑢𝜇 is the velocity vector in comoving coordinates. One can now derive the Friedmann equations as
Using the above two equations, one can derive the density evolution equation,
where H is the Hubble parameter.
C Type I seasaw mechanism
here subscript c stands for charge conjugation. Now one can write the above expression as follows
One can diagonalize the above mass matrix and can get mass eigenstates corresponding to
This naturally explains the smallness of neutrino masses.
D Feynman diagrams in two-component DM model
The relevant Feynman diagram for relic density analysis of scalar and fermion DM are shown in Figs. D.1 and D.2, respectively.
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This paper is available on arxiv under CC BY 4.0 DEED license.
Author:
(1) Shivam Gola, The Institute of Mathematical Sciences, Chennai.
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