Springer : Phases of Pseudo-Nambu-Goldstone Bosons

Koutroulis, Fotis; Sakurai, Kazuki; Merchand, Marco; McCullough, Matthew; Pokorski, Stefan

doi:10.1007/JHEP05(2024)095

Article
Report number	arXiv:2309.15749
Title	Phases of Pseudo-Nambu-Goldstone Bosons
Author(s)	Koutroulis, Fotis (Warsaw U.) ; McCullough, Matthew (CERN) ; Merchand, Marco (Warsaw U. ; Royal Inst. Tech., Stockholm ; Stockholm U., OKC) ; Pokorski, Stefan (Warsaw U.) ; Sakurai, Kazuki (Warsaw U.)
Publication	2024-05-09
Imprint	2023-09-27
Number of pages	29
In:	JHEP 2405 (2024) 095
DOI	10.1007/JHEP05(2024)095
Subject category	astro-ph.CO ; Astrophysics and Astronomy ; hep-ph ; Particle Physics - Phenomenology
Abstract	We study the vacuum dynamics of pseudo-Nambu-Goldstone bosons (pNGBs) for $SO(N+1) \rightarrow SO(N)$ spontaneous and explicit symmetry breaking. We determine the magnitude of explicit symmetry breaking consistent with an EFT description of the effective potential at zero and finite temperatures. We expose and clarify novel additional vacuum transitions that can arise for generic pNGBs below the initial scale of $SO(N+1) \rightarrow SO(N)$ spontaneous symmetry breaking, which may have phenomenological relevance. In this respect, two phenomenological scenarios are analyzed: thermal and supercooled dark sector pNGBs. In the thermal scenario the vacuum transition is first-order but very weak. For a supercooled dark sector we find that, depending on the sign of the explicit symmetry breaking, one can have a symmetry-restoring vacuum transition $SO(N-1) \rightarrow SO(N)$ which can be strongly first-order, with a detectable stochastic gravitational wave background signal.
Copyright/License	publication: © 2024 The Authors (License: CC-BY-4.0), sponsored by SCOAP³ preprint: (License: CC BY 4.0)

$\it A cartoon picture showing the functional form of the Gegenbauer thermal effective potential given by \eq{eq:highT}, for the temperature asymptotics $T = 0 $ and $T \gg 0$, when the symmetry-breaking parameter, $\ve_n$, is either positive or negative. The high-temperature limit terminates below the radial mode mass $M$, otherwise the original, approximate, symmetry is restored and the effective description of the model in terms of pNGBs is lost. Cooling down will lead to $SO(N)$ symmetry restoration or breaking depending on the sign of $\ve_n$.$ $\it Schematic phase diagram for radiatively and thermally stable pNGB potentials, for $\ve_n >0$ (left) and $\ve_n<0$ (right). Throughout there is explicit breaking $\SONp\to\SON$. At high temperatures, above the mass of the radial mode, an approximate $\SONp$ is restored. For $\ve_n >0$ at lower temperatures, $\SONp$ is spontaneously broken and at some lower temperature the exact $\SON$ is also spontaneously broken. Whereas for $\ve_n <0$ at lower temperatures, $\SONp$ is spontaneously broken to $\SONm$ and at some lower temperature the exact $\SON$ is restored.$ $\it Successive tunneling towards the true vacuum for the benchmark scenario $n = 15, N =4$. The colouring shows that we move from a higher $\braket{\Pi}$ ({\color{violet} purple} dot) down to smaller values until the DS reaches the deepest minimum ({\color{red} red} dot).$ Show more plots

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Record created 2023-10-18, last modified 2024-05-22

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