Low-energy γp scattering and determination of proton polarizabilities

Abstract

For the first time an analysis of all experimental data on the differential cross section of elastic γp scattering at photon energies ω < 150 MeV is performed in order to determine the electric (α p ) and magnetic (β p ) polarizabilities of the proton. A fit of these data with the two free parameters, α p and β p , embedded into a theoretical cross section obtained on the basis of finite-energy s-channel dispersion relations gives the following world-average values of the proton polarizabilities (in units of 10 −4 fm 3 ): α exp p = 11.7 ± 0.8 (stat. + sys.) ± 0.7 (model), β exp p = 2.3 ± 0.9 (stat. + sys.) ± 0.7 (model), where the first error takes into account statistical and systematic errors of the experimental cross sections and the second error does model uncertainties in the theoretical cross section.

Erratum: Compton scattering from the proton at fourth order NLO in the chiral expansion [Phys. Rev. C63, 064608 (2001)]

“…Above the threshold the good agreement at forward angles continues, while the lack of agreement at backward angles is dramatically worse. [24,22], Hallin, Saskatoon (black squares) [25], MacGibbon, Saskatoon (red circles) [26], Olmos de León, Mainz (magenta diamonds) [27] and various earlier experiments, listed by Baranov (cyan pentagons) [22]. Cross sections are in units of nb/sr, and energies in MeV.…”

Proton Compton scattering in a unified proton-Δ+model

“…We did not attempt to rescale the data of each experiment within its own systematical uncertainty to see if it would lead to better consistency between datasets as it was done in [53]. The optimal set of parameters was found to be:…”

“…For the peak range, we use only the MAMI(2001) experiment [10], which contains 436 data points with photon incident energy ranging from 260MeV to 455MeV. A good fit is achieved at systematical uncertainty which tends to be large [53].…”

Compton scattering by the nucleon

“…αp βp αp + βp 11.7 ± 1.1 2.3 ± 1.1 14.0 ± 1.6 [9] 11.9 ± 1.4 1.2 ± 0.8 13.1 ± 1.6 [10] 11.8 ± 0.9 1.6 ± 0.6 13.6 ± 1.1 a)…”

“…In case of fixed-θ dispersion theory (α − β) t-miss p is compatible with zero. Table 7 Predicted information (α − β) calc p on the polarizability difference compared with the experimental result (α−β) exp p = 10.5 ± 1.1 [10] or (α − β) exp p = 10.1 ± 0.9 (adopted average including all existing data [9,10]). In fixed-t dispersion theory the prediction (α − β) calc p corresponds to the integral part (α − β) int p , in fixed-θ dispersion theory (α − β) calc p is either chosen to be the s-channel contribution only (line 3) or the predicted s-channel contribution supplemented by the predicted γγ → ππ → NN t-channel contribution according to the BEFT sum rule (line 4).…”