Momentum transfer dependence of the proton’s electric and magnetic polarizabilities

Abstract

The Q 2 -dependence of the sum of the electric and magnetic polarizabilities of the proton is calculated over the range 0 ≤ Q 2 ≤ 6 GeV 2 using the generalized Baldin sum rule. Employing a parametrization of the F1 structure function valid down to Q 2 = 0.06 GeV 2 , the polarizabilities at the real photon point are found by extrapolating the results of finite Q 2 to Q 2 = 0 GeV 2 . We determine the evolution over four-momentum transfer to be consistent with the Baldin sum rule using photoproduction data, obtaining α + β = 13.7 ± 0.7 × 10 −4 fm 3 .I.

Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: The subtraction function and moments of unpolarized structure functions

“…Fig. 4), which is also observed in parametrizations of experimental cross sections [66]. Because of cancellations between the πN-loop and the Δ-exchange contributions, the dipole also crucially affects the overall sign of the slope, as can be seen in Fig.…”

Cottingham formula and nucleon polarisabilities

“…As discussed in the text, the picture implies that these parameterisations provide a coherent framework only for Q 2 > 0.5 alities (cf. [71]): (a) The algebraic form of the representation used for σ L implies that the quantityσ L ≡ σ L ν 2 /Q 2 disappears when Q tends to zero instead of approaching a nonzero limiting value. (b) Isospin symmetry implies that the contributions of the resonance (1232) to proton and neutron are the same, but, as noted in [36], the BC-parameterisation does not respect this symmetry to the expected accuracy.…”

“…The cross section integrals are evaluated with the parameterisation specified in Sect. 5.1, except for˜ F1 , where the contribution from the region of the Delta is calculated with BC instead of MD resentations to the amplitudes under consideration we refer to [71,81,82].…”

“…As pointed out in [71], the structure function F 1 (x, Q 2 ) can also be used to continue the integral relevant for the Baldin sum rule to nonzero values of Q 2 :…”

“…In [71], the function F 1 (Q 2 ) is instead evaluated with the BC-parameterisation, also in the region of the -resonance. This leads to the behaviour indicated by the dash-dotted line labelled˜ F 1 .…”