Muonic-hydrogen Lamb shift: Dispersing the nucleon-excitation uncertainty with a finite-energy sum rule

We assess the two-photon exchange contribution to the Lamb shift in muonic hydrogen with forward dispersion relations. The subtraction constant T̄(0,Q²) that is necessary for a dispersive evaluation of the forward doubly virtual Compton amplitude, through a finite-energy sum rule, is related to the fixed $J=0$ pole generalized to the case of virtual photons. We evaluated this sum rule using excellent virtual photoabsorption data that are available. We find that the ``proton polarizability correction'' to the Lamb shift in muonic hydrogen is -(40±5)0.28em0exμeV. We conclude that nucleon structure-dependent uncertainty by itself is unlikely to resolve the large (300 μeV) discrepancy between direct measurement of the Lamb shift in μH and expectations based on conventional hydrogen measurements.