Year: 2025
Type: preprint
Abstract: Various approximate symmetries exist in nature. For example, the flavor $SU(4)$ symmetry involving the $up/down/strange/charm$ quarks is severely broken, the flavor $SU(3)$ symmetry involving the $up/down/strange$ quarks is moderately broken, and the isospin $SU(2)$ symmetry involving the $up/down$ quarks is slightly broken. These broken symmetries are primarily governed by the strong interaction, making them an ideal platform for investigating the general behavior of approximate symmetries. To explore the application of the flavor $SU(4)$ group to ground-state baryons, we systematically calculate the transition matrices associated with various flavor $SU(4)$ representations as well as the matrices that describe their connections. These matrices are then employed to analyze the mass spectrum of ground-state baryons. Our results indicate that these states can be described as mixtures of various flavor representations, such as $Σ_c/Ξ_c^\prime/Ω_c \sim \mathbf{20_M} \oplus \mathbf{20_S}\oplus \mathbf{\bar{4}_A}~[SU(4)]$, $Ξ_c/Ξ_c^\prime \sim \mathbf{\bar 3_A} \oplus \mathbf{6_S}~[SU(3)]$, $Λ^0/Σ^0 \sim \mathbf{1_A} \oplus \mathbf{3_S}~[SU(2)]$, where the subscripts $\mathbf{S}$, $\mathbf{A}$, and $\mathbf{M}$ denote the symmetric, antisymmetric, and mixed flavor wave functions, respectively. Our results also indicate that the flavor symmetries, as they break, necessitate the mixing of these flavor representations according to specific rules. Together with a complementary analysis of vector mesons, these results motivate a general group-expansion picture in which the effective Hamiltonian evolves order by order as flavor symmetries are broken.
Source: arXiv (Cornell University)
Author: Chen, Hua-Xing
Institution: Southeast University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G7452539093
OpenAlex ID: W4415145772
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