Experimental Exploration of the Yang–Mills Mass Gap through Stochastic Particle Dynamics

Experimental Exploration of the Yang–Mills Mass Gap through Stochastic Particle Dynamics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Experimental Exploration of the Yang–Mills Mass Gap through Stochastic Particle Dynamics ZONGO Abel, KABORE Franck, BAZIE Ywo Josué This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8662692/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The Yang–Mills mass gap problem remains one of the deepest unsolved challenges in modern mathematical physics. In this work, we propose an experimental mathematical approach to explore the emergence of the mass gap through stochastic particle dynamics inspired by particle swarm optimization (PSO) and stochastic approximation theory. By modeling the evolution of gauge field energy configurations as interacting stochastic particles, we perform large-scale simulations to investigate how energy fluctuations stabilize toward nonzero vacuum expectation values, suggesting a natural gap in the spectrum. The resulting trajectories reveal self-organizing patterns analogous to confinement phenomena in non-Abelian gauge theories. From the empirical evidence, we formulate conjectures on the probabilistic structure of energy minima and derive semi-analytical approximations linking stochastic stability and spectral gaps. This work illustrates how stochastic dynamical systems can serve as an experimental framework for probing nonperturbative aspects of the Yang–Mills theory, bridging computational experimentation and mathematical insight. Applied Mathematics Yang–Mills theory mass gap stochastic processes particle swarm optimization experimental mathematics gauge field dynamics Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8662692","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":578312872,"identity":"4d3ce260-ef3a-4a22-bfdd-7943a8a8077f","order_by":0,"name":"ZONGO Abel","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"ZONGO","middleName":"","lastName":"Abel","suffix":""},{"id":578312873,"identity":"be9d6338-6bc9-43f6-981a-6b1fe905ee35","order_by":1,"name":"KABORE Franck","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"KABORE","middleName":"","lastName":"Franck","suffix":""},{"id":578312930,"identity":"bb9656c7-5156-4f50-8dbd-10d428a8c759","order_by":2,"name":"BAZIE Ywo Josué","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1klEQVRIiWNgGAWjYBACxgYow4AdxDKwIEULzwEQKUGCdQYSCSCKCC3M7e3PJD62HZYzl3x+dcOPAgkG/vbuBPwO6zljJjmz7bCx5eycsps9QIdJnDm7Ab+WGTls0rxttxM33M5Ju8ED1GIgkUtIS/oz6b8gLTfPpN38Q5yWBDNpRpCWG+zHbhNnS88ZY8uec/+BRA7bbRkDCR6CfjFsb39440dZmpw5+/FnN9/8sZHjb+8loKUBZBUbiMljACbxKgcBeTD5B0SwPyCoehSMglEwCkYmAADyOkqaWs4QPAAAAABJRU5ErkJggg==","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"BAZIE","middleName":"Ywo","lastName":"Josué","suffix":""}],"badges":[],"createdAt":"2026-01-21 18:09:03","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-8662692/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8662692/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":100860623,"identity":"07bf3dbc-1ae8-49f6-9633-039117761df2","added_by":"auto","created_at":"2026-01-22 07:40:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":578523,"visible":true,"origin":"","legend":"","description":"","filename":"ExperimentalExplorationoftheYangMillsMassGapthroughStochasticParticleDynamicsYJB.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8662692/v1_covered_469d6af5-13d3-4e3b-8231-b43aacac78f8.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eExperimental Exploration of the Yang–Mills Mass Gap through Stochastic Particle Dynamics\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Yang–Mills theory, mass gap, stochastic processes, particle swarm optimization, experimental mathematics, gauge field dynamics","lastPublishedDoi":"10.21203/rs.3.rs-8662692/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8662692/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe Yang–Mills mass gap problem remains one of the deepest unsolved challenges in modern mathematical physics. 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