A new-old approach to composite scalars with chiral fermion constituents

Journal Article · Fri Dec 27 00:00:00 EST 2024 · Nucl.Phys.B

DOI:https://doi.org/10.1016/j.nuclphysb.2024.116788· OSTI ID:2477418

Hill, Christopher T. ^[1]

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1. Fermilab; Wisconsin U., Madison

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, $\varphi \left(r\right)$ , which satisfies a Schrödinger-Klein-Gordon (SKG) equation with eigenvalue ${\mu }^2$ . For super-critical coupling, $g_0^2>g_{0c}^2$ , we have ${\mu }^2<0$ leading to spontaneous symmetry breaking. The binding of chiral fermions is semiclassical, 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, $\varphi \left(\overrightarrow{r}\right)$ , remains spatially extended and dilutes $\varphi \left(0\right)$ . 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.

• Research Organization: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Wisconsin U., Madison
• Sponsoring Organization: US Department of Energy
• Grant/Contract Number: 89243024CSC000002; AC02-07CH11359
• OSTI ID: 2477418
• Report Number(s): FERMILAB-PUB-24-0720-T; oai:inspirehep.net:2838376; arXiv:2410.06887
• Journal Information: Nucl.Phys.B, Journal Name: Nucl.Phys.B Vol. 1011
• Country of Publication: United States
• Language: English

Related Subjects

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