{"title":"具有贝特-萨尔彼得方程的五体系统","authors":"Gernot Eichmann , M.T. Peña , Raul D. Torres","doi":"10.1016/j.physletb.2025.139525","DOIUrl":null,"url":null,"abstract":"<div><div>We extend the Bethe-Salpeter formalism to systems made of five valence particles. Restricting ourselves to two-body interactions, we derive the subtraction terms necessary to prevent overcounting. We solve the five-body Bethe-Salpeter equation numerically for a system of five scalar particles interacting by a scalar exchange boson. To make the calculations tractable, we implement properties of the permutation group <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msub></math></span> and construct an approximation based on intermediate two- and three-body poles. We extract the five-body ground and excited states along with the spectra obtained from the two-, three-, and four-body equations. In the limit of a massless exchange particle, the two-, three, four- and five-body states coexist within a certain range of the coupling strength, whereas for heavier exchange particles the five-body system becomes Borromean. Our study serves as a building block for the calculation of pentaquark properties using functional methods.</div></div>","PeriodicalId":20162,"journal":{"name":"Physics Letters B","volume":"866 ","pages":"Article 139525"},"PeriodicalIF":4.3000,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Five-body systems with Bethe-Salpeter equations\",\"authors\":\"Gernot Eichmann , M.T. Peña , Raul D. Torres\",\"doi\":\"10.1016/j.physletb.2025.139525\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We extend the Bethe-Salpeter formalism to systems made of five valence particles. Restricting ourselves to two-body interactions, we derive the subtraction terms necessary to prevent overcounting. We solve the five-body Bethe-Salpeter equation numerically for a system of five scalar particles interacting by a scalar exchange boson. To make the calculations tractable, we implement properties of the permutation group <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msub></math></span> and construct an approximation based on intermediate two- and three-body poles. We extract the five-body ground and excited states along with the spectra obtained from the two-, three-, and four-body equations. In the limit of a massless exchange particle, the two-, three, four- and five-body states coexist within a certain range of the coupling strength, whereas for heavier exchange particles the five-body system becomes Borromean. Our study serves as a building block for the calculation of pentaquark properties using functional methods.</div></div>\",\"PeriodicalId\":20162,\"journal\":{\"name\":\"Physics Letters B\",\"volume\":\"866 \",\"pages\":\"Article 139525\"},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2025-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physics Letters B\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0370269325002862\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ASTRONOMY & ASTROPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics Letters B","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0370269325002862","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
We extend the Bethe-Salpeter formalism to systems made of five valence particles. Restricting ourselves to two-body interactions, we derive the subtraction terms necessary to prevent overcounting. We solve the five-body Bethe-Salpeter equation numerically for a system of five scalar particles interacting by a scalar exchange boson. To make the calculations tractable, we implement properties of the permutation group and construct an approximation based on intermediate two- and three-body poles. We extract the five-body ground and excited states along with the spectra obtained from the two-, three-, and four-body equations. In the limit of a massless exchange particle, the two-, three, four- and five-body states coexist within a certain range of the coupling strength, whereas for heavier exchange particles the five-body system becomes Borromean. Our study serves as a building block for the calculation of pentaquark properties using functional methods.
期刊介绍:
Physics Letters B ensures the rapid publication of important new results in particle physics, nuclear physics and cosmology. Specialized editors are responsible for contributions in experimental nuclear physics, theoretical nuclear physics, experimental high-energy physics, theoretical high-energy physics, and astrophysics.