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Spin-dependent interactions and fine structure in negative-parity singly heavy baryons

Zhen-Yu Li ^1,*, Guo-Liang Yu ^2,†, Zhi-Gang Wang ^2,‡, and Jian-Zhong Gu ^3,§

¹School of Physics and Electronic Science, Guizhou Education University, Guiyang 550018, China
²Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China
³China Institute of Atomic Energy, Beijing 102413,China

^*Contact author: zhenyvli@163.com
^†Contact author: yuguoliang2011@163.com
^‡Contact author: zgwang@aliyun.com
^§Contact author: gujianzhong2000@aliyun.com

Phys. Rev. D 114, 074039 – Published 16 October, 2026

DOI: https://doi.org/10.1103/wg7b-mlfp

Abstract

In order to meet the high-precision measurement of the current baryon spectroscopy, for the first time, we rigorously analyze the spin-dependent interactions and the fine structure of the negative-parity singly heavy baryons in the relativized quark model, which was previously unfeasible in the three-quark system. This gains access to the exploration of the strong interactions dominated by the nonperturbative QCD, and reveals how the various forms of strong interactions in a baryon compete with each other, affect the evolution of the energy levels, cause the energy level splitting, and contribute to the mixing effect responsible for the formation of the fine structures. It is shown that the rigorous calculation can nicely reproduce the data; the averaged deviation between the calculated and experimental energy levels is less than 5 MeV for the negative-parity singly heavy baryons. This confirms the reliability of the calculation and also helps make reasonable assignments for the observed negative-parity baryons. The large amount of data obtained by the rigorous calculations contains a wealth of interaction information and is helpful for both of the theoretical and experimental studies. The key to the rigorous calculation in this work is the proposal of a new method, namely the two-step Gaussian expansion method. This new method not only overcomes the long-standing unresolved problem in the relativized quark model, but also provides an effective approach for the high-precision calculation of other few-body systems such as the compact tetraquarks and pentaquarks, especially for the treatment of spin-orbit interactions and tensor interactions which actually appear ubiquitously in all of quantum many-body systems.

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Phys. Rev. D 114, 074039– Published 16 October, 2026

Vol. 114, Iss. 7 — 1 October 2026

Received 27 May 2026
Accepted 21 September 2026

DOI: https://doi.org/10.1103/wg7b-mlfp

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Spin-dependent interactions and fine structure in negative-parity singly heavy baryons

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