A Universal Geometric Invariant Linking the Fine-Structure Constant to Lepton and Nucleon Magnetic Moments

A Universal Geometric Invariant Linking the Fine-Structure Constant to Lepton and Nucleon Magnetic Moments | 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 Article A Universal Geometric Invariant Linking the Fine-Structure Constant to Lepton and Nucleon Magnetic Moments Ittipat Roopkom, Pichet Wisartpong, Wirote Jongchanachavawat, and 3 more This is a preprint; it has not been peer reviewed by a journal.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-8186891/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 fine-structure constant, α, has remained one of the most persistent mysteries in modern physics: a dimensionless constant that governs electromagnetic interaction strength yet lacks a definitive theoretical origin. In this work, we introduce the QTP–α framework, a geometric–dynamic model in which α emerges from a universal invariant quantity QTP = πmpllpl, together with a particle-specific confinement factor satisfying QTP = γimiri. When applied to the electron, the relation yields α = π/γe without renormalization, relying solely on the experimentally determined confinement radius and mass. A second outcome is a universal γ-series for the anomalous magnetic moment of elementary fermions and nucleons, ai = [(afactor)^–1] ∑_(n=1)^∞[(1/γi n)〗^n. This series reproduces measured values with high accuracy, naturally distinguishing elementary fermions (afactor = 2) from composite nucleons (𝑎factor ≈ ±1) via their structural normalization. These results suggest that mass, charge, and spin are organized by a deeper structural invariant connecting Planck-scale geometry to atomic observables. Physical sciences/Physics/Particle physics/Theoretical particle physics Physical sciences/Physics/Nuclear physics/Theoretical nuclear physics Fine-structure constant Anomalous magnetic moment Planck scale geometry Unified scaling laws Full Text Additional Declarations There is NO Competing Interest. 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8186891","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":552069909,"identity":"c954dedd-c3c6-4211-abaa-ad9ed64f63b8","order_by":0,"name":"Ittipat 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In this work, we introduce the QTP–α framework, a geometric–dynamic model in which α emerges from a universal invariant quantity QTP = πmpllpl, together with a particle-specific confinement factor satisfying QTP = γimiri. When applied to the electron, the relation yields α = π/γe without renormalization, relying solely on the experimentally determined confinement radius and mass. A second outcome is a universal γ-series for the anomalous magnetic moment of elementary fermions and nucleons, ai = [(afactor)^–1]*∑_(n=1)^∞[(1/γi*n)〗^n. This series reproduces measured values with high accuracy, naturally distinguishing elementary fermions (afactor = 2) from composite nucleons (𝑎factor ≈ ±1) via their structural normalization. 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