Regular Article - Theoretical Physics
The solution to the ‘1/2 vs 3/2’ puzzle
Department of Physics, Hebei University, 071002, Baoding, China
2 Key Laboratory of High-precision Computation and Application of Quantum Field Theory of Hebei Province, 071002, Baoding, China
3 School of Physical Science and Technology, Northwestern Polytechnical University, 710072, Xi’an, China
4 School of Physics, Harbin Institute of Technology, 150001, Harbin, China
5 Department of Physics, Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, 401331, Chongqing, China
6 Institute of Theoretical Physics, Chinese Academy of Science, 100190, Beijing, China
7 CCAST (World Laboratory), P.O. Box 8730, 100190, Beijing, China
Accepted: 1 November 2022
Published online: 15 November 2022
Using an almost complete relativistic method based on the Bethe–Salpeter equation, we study the mixing angle , the mass splitting , the strong decay widths and the weak production rates of the and . We find there is the strong cancellation between the and partial waves in with , which leads to the ‘1/2 vs 3/2’ puzzle. The puzzle can not be overcome by adding only relativistic corrections since in a large parameter range where is linear varying and not small, the , and remain almost unchanged but conflict with data. While in a special range around the mass inverse point where and , they change rapidly but we find the windows where , and are all consistent with data. The small confirmed by experiment, is crucial to solve the ‘1/2 vs 3/2’ puzzle.
© The Author(s) 2022
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.