Abstract
The proton-polarizability contribution to the muonic-hydrogen Lamb shift is a major source of theoretical uncertainty in the extraction of the proton charge radius. An empirical evaluation of this effect, based on the proton structure functions, requires a systematically improvable calculation of the “subtraction function”, possibly using lattice QCD. We consider a different subtraction point, with the aim of accessing the subtraction function directly in lattice calculations. A useful feature of this subtraction point is that the corresponding contribution of the structure functions to the Lamb shift is suppressed. The whole effect is dominated by the subtraction contribution, calculable on the lattice.
Highlights
The nucleon structure functions are used as input in calculations of the nuclear structure effects in precision atomic spectroscopy
Some efforts in this direction have already been made [10,11,12,13] In the present work we propose an unconventional choice of the subtraction point, which, first of all, is directly accessible in lattice calculations, and secondly, diminishes the structure-function contribution
Concerning the transverse contributions, note that for the conventional subtraction at 0 they cancel between the subtraction and inelastic contributions, whereas for the subtraction at iQ they are absent from the subtraction function and cancel between the structure functions within the inelastic contribution
Summary
The nucleon structure functions are used as input in calculations of the nuclear structure effects in precision atomic spectroscopy (see [1,2,3,4] for reviews). One should aim at calculating the subtraction-function contribution in lattice QCD (LQCD). While T2 is fully determined by the empirical proton structure function F2(x, Q2), the amplitude T1 is determined by F1(x, Q2) only up to the subtraction function. We find that the subtraction at ν = iQ leads to interesting ramifications for the μH Lamb-shift evaluation In this case, for example, the so-called “inelastic contribution” (i.e., the contributions of inelastic structure functions F1 and F2) becomes negligible. We go through the main steps of the formulae, present numerical results based on the Bosted-Christy parametrization of proton structure functions [15], and discuss the prospects for future lattice calculations of these effects
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