When lepton-proton bound-state eigenvalue equations
are derived from a local quantum field theory using
second-order renormalization group procedure for
effective particles (RGPEP) a la QCD for heavy
quarkonia [1], the resulting non-perturbative
corrections to the Schroedinger equation appear
relevant to our understanding of the proton radius
puzzle. The puzzle can be described as a conclusion
that the proton radius in muon-proton bound states
is smaller than in the electron-proton bound states
by about 4% [2]. The RGPEP indicates instead that
the radii ought to be discussed taking into account
the scale difference between the effective theories
required for handling different bound-states using
the same Schroedinger equation [3]. Even more
intriguing, the effective non-relativistic
Schroedinger dynamics for lepton-proton atoms
turns out to be operating in these very low-energy
systems with the same type of momentum variables
that also naturally appear in the light-front
holography for quark-antiquark states [4,5] and
in the interpretation of AdS/QFT duality in terms
of the Ehrenfest theorem [6,7].

[1] E.g., see
   Harmonic oscillator force between heavy quarks,
   S. D. Glazek,
   Phys. Rev. D69, 065002 (2004).

[2] Muonic hydrogen and the proton radius puzzle,
   R. Pohl et al.,
   Ann. Rev. Nucl. Part. Sci. 63, 175 (2013).

[3] Calculation of size for bound-state constituents,
   S. D. Glazek,
   Phys. Rev. D90, 045020, 26p (2014).

[4] Hadronic spectrum of a holographic dual of QCD,
   G. F. de Teramond, S. J. Brodsky,
   Phys. Rev.Lett. 94, 201601 (2005).

[5] Reinterpretation of gluon condensate in
   dynamics of hadronic constituents,
   S. D. Glazek,
   Acta Phys. Pol. B 42, 1933 (2011).

[6] Model of the AdS/QFT duality,
   S. D. Glazek, A. P. Trawinski,
   Phys. Rev. D 88, 105025 (2013).

[7] Effective confining potentials for QCD,
   A. P. Trawinski, S. D. Glazek, S. J. Brodsky,
   G. F. de Téramond, H. G. Dosch,
   Phys. Rev. D 90,  074017 (2014).