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• W2146697374 abstract "Elements are given of a calculation that identifies the size of a proton in the Schrodinger equation for lepton-proton bound states, using the renormalization group procedure for effective particles (RGPEP) in quantum field theory, executed only up to the second order of expansion in powers of the coupling constant. Already in this crude approximation, the extraction of size of a proton from bound-state observables is found to depend on the lepton mass, so the smaller the lepton mass the larger the proton size extracted from the same observable bound-state energy splitting. In comparing hydrogen and muon-proton bound-state dynamics, the crude calculation suggests that the difference between extracted proton sizes in these two cases can be a few percent. Such values would match the order of magnitude of the currently discussed proton-size differences in leptonic atoms. Calculations using the RGPEP of higher than second order are required for a precise interpretation of the energy splittings in terms of the proton size in the Schrodinger equation. Such calculations should resolve the conceptual discrepancy between two conditions: that the renormalization group scale required for high accuracy calculations based on the Schrodinger equation is much smaller than the proton mass (on the order of a root of the product of reduced and average masses of constituents) and that the energy splittings due to the physical proton size can be interpreted by ignoring corrections due to the effective nature of constituents in the Schrodinger equation." @default.
• W2146697374 created "2016-06-24" @default.
• W2146697374 creator A5052673693 @default.
• W2146697374 date "2014-08-18" @default.
• W2146697374 modified "2023-10-14" @default.
• W2146697374 title "Calculation of size for bound-state constituents" @default.
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• W2146697374 doi "https://doi.org/10.1103/physrevd.90.045020" @default.
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