Calculation of size for bound-state constituents

Abstract

Elements are given of a calculation that identifies the size of a proton in the Schroedinger 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 that the smaller the lepton mass the larger the proton size extracted from the same observable bound-state energy splitting. In comparison of 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 currently discussed proton-size differences in leptonic atoms. Calculations using the RGPEP of higher order than second are required for a precise interpretation of the energy splittings in terms of the proton size in the Schroedinger equation. Such calculations should resolve the conceptual discrepancy between two conditions: that the renormalization group scale required for high accuracy calculations based on the Schroedinger 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 ignoring corrections due to the effective nature of constituents in the Schrödinger equation.

arXiv comment31 pages, plain latex, 2 figures

References in corpus (16)

• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• Dyson-Schwinger Equations and the Application to Hadronic Physics
• Complete Tenth-Order QED Contribution to the Muon g-2
• High-precision determination of the electric and magnetic form factors of the proton
• Hadronic Spectrum of a Holographic Dual of QCD
• Muonic hydrogen and the proton radius puzzle
• Nonperturbative Light-Front QCD
• Proton structure effects in muonic hydrogen
• Higher-order effective Hamiltonian for light atomic systems
• Sixth-Order Vacuum-Polarization Contribution to the Lamb Shift of the Muonic Hydrogen
• Reinterpretation of gluon condensate in dynamics of hadronic constituents
• Harmonic oscillator force between heavy quarks
• Model of the AdS/QFT duality
• Optimization of perturbative similarity renormalization group for Hamiltonians with asymptotic freedom and bound states
• The Lamb Shift in a Light Front Hamiltonian Approach
• Fermion mass mixing and vacuum triviality in the renormalization group procedure for effective particles

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• Proton radius puzzle in Hamiltonian dynamics