(In)stability of the Higgs vacuum from the $\textrm{O}(N)$ model at large $N$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917916646047744 |
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| author | Weller, Ryan Su, Chun-Wei |
| author_facet | Weller, Ryan Su, Chun-Wei |
| contents | The theory of an independent Higgs field is given by an $\textrm{O}(N)$ model with an $N$-component scalar $\vecϕ$ and a quartic $λ(\vecϕ\cdot\vecϕ)^2$ potential when $N=4$. The phase structure of the theory can be studied analytically for all values of the coupling $λ$ using the large-$N$ limit, both at zero and finite temperature. However, authors in the 70s and 80s argued the theory at large $N$ was "sick" and "futile", and dismissed the theory. This was based on two points: (1) a failure to identify the stable phases and vacuum of the theory and (2) the issue of a negative bare coupling $λ<0$ in the UV. We provide evidence that the theory is not, in fact, "sick". Issue (2) is dealt with through the modern understanding of $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian theories with "wrong-sign" couplings. Issue (1) is resolved by realizing that the true vacuum has no spontaneous symmetry breaking (SSB) and that the SSB phase only becomes preferred at high temperatures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01232 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | (In)stability of the Higgs vacuum from the $\textrm{O}(N)$ model at large $N$ Weller, Ryan Su, Chun-Wei High Energy Physics - Theory High Energy Physics - Phenomenology The theory of an independent Higgs field is given by an $\textrm{O}(N)$ model with an $N$-component scalar $\vecϕ$ and a quartic $λ(\vecϕ\cdot\vecϕ)^2$ potential when $N=4$. The phase structure of the theory can be studied analytically for all values of the coupling $λ$ using the large-$N$ limit, both at zero and finite temperature. However, authors in the 70s and 80s argued the theory at large $N$ was "sick" and "futile", and dismissed the theory. This was based on two points: (1) a failure to identify the stable phases and vacuum of the theory and (2) the issue of a negative bare coupling $λ<0$ in the UV. We provide evidence that the theory is not, in fact, "sick". Issue (2) is dealt with through the modern understanding of $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian theories with "wrong-sign" couplings. Issue (1) is resolved by realizing that the true vacuum has no spontaneous symmetry breaking (SSB) and that the SSB phase only becomes preferred at high temperatures. |
| title | (In)stability of the Higgs vacuum from the $\textrm{O}(N)$ model at large $N$ |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2410.01232 |