Sum rules across the unpolarized Compton processes involving generalized polarizabilities and moments of nucleon structure functions

Abstract

We derive two new sum rules for the unpolarized doubly virtual Compton scattering process on a nucleon, which establish novel low-Q 2 relations involving the nucleon's generalized polarizabilities and moments of the nucleon's unpolarized structure functions F 1 (x, Q 2 ) and F 2 (x, Q 2 ). These relations facilitate the determination of some structure constants which can only be accessed in off-forward doubly virtual Compton scattering, not experimentally accessible at present. We perform an empirical determination for the proton and compare our results with a next-to-leading-order chiral perturbation theory prediction. We also show how these relations may be useful for a model-independent determination of the low-Q 2 subtraction function in the Compton amplitude, which enters the two-photon-exchange contribution to the Lamb shift of (muonic) hydrogen. An explicit calculation of the ∆(1232)-resonance contribution to the muonic-hydrogen 2P − 2S Lamb shift yields −1 ± 1 µeV, confirming the previously conjectured smallness of this effect. Contents

Low-energy doubly virtual Compton scattering from dilepton electroproduction on a nucleon

“…Values of the Q 4 term of the subtraction function T 1 (0, Q 2 ) (second column) and of the dVCS low-energy constant b 3,0 (third column), both in units 10 −4 fm 5 , in different theoretical approaches [20]. The indicated range for the HBChPT result corresponds with the range given by Eq.…”

“…8in Ref. [20] for the corresponding expressions. Furthermore, in (4), the invariant amplitudes B i are functions of four Lorentz invariants, with ν ≡ q • P/M, where P ≡ (p + p )/2.…”

“…(8) in Ref. [20]. The non-Born part of the dVCS amplitudes, denoted asB i , can be expanded for small values of q 2 , q 2 , q • q and ν, with coefficients given by polarizabilities.…”

“…As the ν dependence can be fully reconstructed up to at most one subtraction, through a dispersion relation, we only need to discuss the amplitudes entering the subtraction function. To determineT 1 (0, Q 2 ) up to the Q 4 term, we use the low-energy expansion in k ∈ {q, q } [20]:…”

“…At second order in the photon virtuality, this function is constrained by the magnetic polarizability, which is determined experimentally [19]. To fourth order in the photon virtuality, one low-energy constant in this subtraction function is at present empirically unconstrained [20], and one relies on chiral effective field theory calculations [17,21] or phenomenological estimates. We demonstrate in this work that this low-energy constant can be accessed experimentally through the forward-backward asymmetry in the e − p → e − p e − e + process.…”