Geometric Constraints on the QCD Scale and Strong Coupling from a QTP-Strong Framework

Geometric Constraints on the QCD Scale and Strong Coupling from a QTP-Strong Framework | 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 Geometric Constraints on the QCD Scale and Strong Coupling from a QTP-Strong Framework Ittipat Roopkom, Pichet Wisartpong, Wirote Jongchanachavawat, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8514132/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 In this paper, we present a geometric framework designed to determine both the strong coupling strength and the QCD scale from a unified mass–charge structure. We introduce a simple, dimensionless mass–charge identity linking the effective strong charge to the neutral–charged pion mass ratio, ( e / g s ) 2 + ( M π 0 / M π ± ) 2 = 1, which defines a strong-sector mixing angle θ S . Based on a discrete hierarchy of effective charges, the framework predicts a geometric angle of θ S ≈ −14.5° (for g s = 4 e ). This prediction accurately reproduces the observed neutral–charged pion mass ratio and geometrically characterizes the strong interaction as a binding-dominated regime. Building on the hierarchy 1 e →2 e →4 e , the strong fine-structure constant is obtained from a universal geometric relation, α = ( q / q pl ) 2 , in agreement with experimental determinations at the percent level without adjustable parameters. Moreover, the confinement mass scale is derived directly from the proton charge radius as m Λ = ℏ/( r p c ) ≈ m p /4, yielding a value consistent with the phenomenological QCD scale Λ QCD . Taken together, these results indicate that the electromagnetic, weak, and strong interactions can be consistently described within a unified geometric framework at the level of coupling strengths and characteristic mass scales. High Energy and Particle Physics Theoretical Physics Nuclear Physics Strong interaction Geometric coupling Mass–charge relation QCD scale Unified alpha 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-8514132","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":569058544,"identity":"4b79500c-9aa9-43c4-a286-b46b102e1d10","order_by":0,"name":"Ittipat Roopkom","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEElEQVRIie3RMUsDMRQH8FcCz+XZroE7Ll8hpaBOfpbCgVMKBRfRosLBOV1dFf0wPQJxKc5CF8HV7aCTFBPvbB1y5yqYPyQE8n7hhQcQEvIHg3YtmnPvFYDHAPR9ST4BiMwR6c7M7px2legnYAk0BHn98i+kL25LPZ19wOFNZs5fZkcEUWEqgmMBolj4iGtM3xkJ8dKcrJSxjcXP6QNBOrzG/riVEErgXB2sFFrC1YgRsLFtTLaTTU1O1WZLrrrJfl4TNsm3RHeQVOr7+Yg4mTSazDmh/UvvUT4Nc1ReIrLyrZquk4TvZWWl1pfJICo0vJ9diAFbeomLm8xuBF/TcYPCtvqG/AjvKA0JCQn5l/kEmgBDd6jgU4sAAAAASUVORK5CYII=","orcid":"","institution":"Faculty of Engineering and Industrial Technology, Phetchaburi Rajabhat University, Phetchaburi, Thailand","correspondingAuthor":true,"prefix":"","firstName":"Ittipat","middleName":"","lastName":"Roopkom","suffix":""},{"id":569058545,"identity":"e0d14cc2-40e9-488b-8923-28edef312c27","order_by":1,"name":"Pichet Wisartpong","email":"","orcid":"","institution":"School of Electrical and Electronic Engineering, Mahanakorn University of Technology, Bangkok, Thailand","correspondingAuthor":false,"prefix":"","firstName":"Pichet","middleName":"","lastName":"Wisartpong","suffix":""},{"id":569058546,"identity":"a7dcdafb-36da-4942-be52-4343aad6467a","order_by":2,"name":"Wirote Jongchanachavawat","email":"","orcid":"","institution":"Faculty of Engineering and Industrial Technology, Phetchaburi Rajabhat University, Phetchaburi, Thailand","correspondingAuthor":false,"prefix":"","firstName":"Wirote","middleName":"","lastName":"Jongchanachavawat","suffix":""},{"id":569058547,"identity":"6a982db1-2927-44be-9151-a4b3fe5434b0","order_by":3,"name":"Beverly F. 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Framework\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Faculty of Engineering and Industrial Technology, Phetchaburi Rajabhat University, Phetchaburi, Thailand","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"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":"Strong interaction, Geometric coupling, Mass–charge relation, QCD scale, Unified alpha","lastPublishedDoi":"10.21203/rs.3.rs-8514132/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8514132/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we present a geometric framework designed to determine both the strong coupling strength and the QCD scale from a unified mass\u0026ndash;charge structure. We introduce a simple, dimensionless mass\u0026ndash;charge identity linking the effective strong charge to the neutral\u0026ndash;charged pion mass ratio, (\u003cem\u003ee\u003c/em\u003e/\u003cem\u003eg\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e)\u003csup\u003e2\u003c/sup\u003e + (\u003cem\u003eM\u003c/em\u003e\u003csub\u003eπ\u003c/sub\u003e\u003csup\u003e0\u003c/sup\u003e/\u003cem\u003eM\u003c/em\u003e\u003csub\u003eπ\u003c/sub\u003e\u003csup\u003e\u0026plusmn;\u003c/sup\u003e)\u003csup\u003e2\u003c/sup\u003e = 1, which defines a strong-sector mixing angle \u003cem\u003eθ\u003c/em\u003e\u003csub\u003e\u003cem\u003eS\u003c/em\u003e\u003c/sub\u003e. Based on a discrete hierarchy of effective charges, the framework predicts a geometric angle of \u003cem\u003eθ\u003c/em\u003e\u003csub\u003e\u003cem\u003eS\u003c/em\u003e\u003c/sub\u003e \u0026asymp; \u0026minus;14.5\u0026deg; (for \u003cem\u003eg\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e = 4\u003cem\u003ee\u003c/em\u003e). This prediction accurately reproduces the observed neutral\u0026ndash;charged pion mass ratio and geometrically characterizes the strong interaction as a binding-dominated regime. Building on the hierarchy 1\u003cem\u003ee\u003c/em\u003e\u0026rarr;2\u003cem\u003ee\u003c/em\u003e\u0026rarr;4\u003cem\u003ee\u003c/em\u003e, the strong fine-structure constant is obtained from a universal geometric relation, \u003cem\u003eα\u003c/em\u003e = \u003cb\u003e(\u003c/b\u003e\u003cem\u003eq\u003c/em\u003e/\u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003epl\u003c/em\u003e\u003c/sub\u003e\u003cb\u003e)\u003c/b\u003e\u003csup\u003e2\u003c/sup\u003e, in agreement with experimental determinations at the percent level without adjustable parameters. Moreover, the confinement mass scale is derived directly from the proton charge radius as \u003cem\u003em\u003c/em\u003e\u003csub\u003eΛ\u003c/sub\u003e = ℏ/(\u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e\u003cem\u003ec\u003c/em\u003e\u003cb\u003e)\u003c/b\u003e \u0026asymp; \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e/4, yielding a value consistent with the phenomenological QCD scale Λ\u003csub\u003eQCD\u003c/sub\u003e. Taken together, these results indicate that the electromagnetic, weak, and strong interactions can be consistently described within a unified geometric framework at the level of coupling strengths and characteristic mass scales.\u003c/p\u003e","manuscriptTitle":"Geometric Constraints on the QCD Scale and Strong Coupling\nfrom a QTP-Strong Framework","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-07 05:21:14","doi":"10.21203/rs.3.rs-8514132/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"c3e48523-7387-4a16-8b46-6401d872f016","owner":[],"postedDate":"January 7th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":60549071,"name":"High Energy and Particle Physics"},{"id":60549072,"name":"Theoretical Physics"},{"id":60549073,"name":"Nuclear Physics"}],"tags":[],"updatedAt":"2026-01-07T05:21:14+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-07 05:21:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8514132","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8514132","identity":"rs-8514132","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}