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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2410.06887 |
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| _version_ | 1866914987137564672 |
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| author | Hill, Christopher T. |
| author_facet | Hill, Christopher T. |
| contents | We develop a dynamical, Lorentz invariant theory of composite scalars in configuration space consisting of chiral fermions, interacting by the perturbative exchange of a massive "gluon" of coupling $g_0$ and mass $M_0^2$ (the coloron model). The formalism is inspired by, but goes beyond, old ideas of Yukawa and the Nambu-Jona-Lasinio (NJL) model. It yields a non-pointlike internal wave-function of the bound state, $ϕ(r)$, which satisfies a Schrödinger-Klein-Gordon (SKG) equation with eigenvalue $μ^2$. For super-critical coupling, $g_0 >g_{0c}$, we have $μ^2< 0$ leading to spontaneous symmetry breaking. The binding of chiral fermions is semiclassical, and not loop-level as in NJL. The mass scale is determined by the interaction as in NJL. We mainly focus on the short-distance, large $M_0^2$ limit, yielding an NJL pointlike interaction, but the bound state internal wave-function, $ϕ(r)$, remains spatially extended and dilutes $ϕ(0)$. This leads to power-law suppression of the induced Yukawa and quartic couplings and requires radically less fine-tuning of a hierarchy than does the NJL model. We include a discussion of loop corrections of the theory. A realistic top--condensation model appears possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06887 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A New-Old Approach to Composite Scalars with Chiral Fermion Constituents Hill, Christopher T. High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Theory Nuclear Theory We develop a dynamical, Lorentz invariant theory of composite scalars in configuration space consisting of chiral fermions, interacting by the perturbative exchange of a massive "gluon" of coupling $g_0$ and mass $M_0^2$ (the coloron model). The formalism is inspired by, but goes beyond, old ideas of Yukawa and the Nambu-Jona-Lasinio (NJL) model. It yields a non-pointlike internal wave-function of the bound state, $ϕ(r)$, which satisfies a Schrödinger-Klein-Gordon (SKG) equation with eigenvalue $μ^2$. For super-critical coupling, $g_0 >g_{0c}$, we have $μ^2< 0$ leading to spontaneous symmetry breaking. The binding of chiral fermions is semiclassical, and not loop-level as in NJL. The mass scale is determined by the interaction as in NJL. We mainly focus on the short-distance, large $M_0^2$ limit, yielding an NJL pointlike interaction, but the bound state internal wave-function, $ϕ(r)$, remains spatially extended and dilutes $ϕ(0)$. This leads to power-law suppression of the induced Yukawa and quartic couplings and requires radically less fine-tuning of a hierarchy than does the NJL model. We include a discussion of loop corrections of the theory. A realistic top--condensation model appears possible. |
| title | A New-Old Approach to Composite Scalars with Chiral Fermion Constituents |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2410.06887 |