  The possible involvement of weakly bound three-body systems in the muonic
hydrogen spectroscopy experiment [1], which could resolve the current
discrepancy between determinations of the proton radius, is investigated. Using
variational calculations with complex coordinate rotation, it is shown that the
$p\mu e$ ion, which was recently proposed as a possible candidate [2], has no
resonant states in the energy region of interest. QED level shifts are included
phenomenologically by including a Yukawa potential in the three-body Coulomb
Hamiltonian before diagonalization. It is also shown that the $pp\mu$ molecular
ion cannot play any role in the observed line.
