Partial-wave analysis of proton Compton scattering data below the pion-production threshold

Abstract

Low-energy Compton scattering off the proton is used for determination of the proton polarizabilities. However, the present empirical determinations rely heavily on the theoretical description(s) of the experimental cross sections in terms of polarizabilities. The most recent determinations are based on either the fixed-t dispersion relations (DR) or chiral perturbation theory in the single-baryon sector (χPT). The two approaches obtain rather different results for proton polarizabilities, most notably for β M1 (magnetic dipole polarizability). We attempt to resolve this discrepancy by performing a partial-wave analysis of the world data on proton Compton scattering below threshold. We find a large sensitivity of the extraction to a few "outliers", leading us to conclude that the difference between DR and χPT extraction is a problem of the experimental database rather than of "modeldependence". We have specific suggestions for new experiments needed for an efficient improvement of the database. With the present database, the difference of proton scalar polarizabilities is constrained to a rather broad interval: α E1 − β M1 = (6.8 . . . 10.9) × 10 −4 fm 3 , with their sum fixed much more precisely [to 14.0(2)] by the Baldin sum rule. II. MULTIPOLE EXPANSION AND (BI-)LINEAR EMPIRICAL CONSTRAINTSThe general formalism of the multipole expansion for nucleon CS is given in [18,24], and concisely summarized in [5, Sec. 2]. The idea is that, using the rotational and discrete symmetries, the CS helicity amplitudes T σ λ ,σ λ (s,t), with σ (σ ) the helicity of initial (final) photon and λ (λ ) for the helicity arXiv:1712.05349v2 [nucl-th]

Virtual Compton scattering and nucleon generalized polarizabilities

“…An intense effort is ongoing experimentally and theoretically to pin down the RCS polarizabilities; see, e.g., Refs. [9,10,87,90]. Figure 18 displays the data of Table 5 for α E1 (Q 2 ) and β M1 (Q 2 ).…”

“…Nevertheless a consistent behavior tends to emerge from the world data, namely thanks to the precise data points from the MAMI-VI experiment. The low-Q 2 measurements suggest the existence of an extremum of β M1 (Q 2 ), weakly pronounced, in the region near Q 2 = 0.1 GeV 2 ; but the exact shape depends crucially on the actual RCS value, which is under debate [9,10,87,90]. The DR model as shown in Fig.…”

First extraction of the scalar proton dynamical polarizabilities from real Compton scattering data

“…[20], only a relevant progress in both the quality and the quantity of the existing data set will allow to significantly improve this situation.…”

“…More recently, a partial-wave analysis of the unpolarized Compton scattering data has been discussed also in Ref. [20], pointing out the need to improve the accuracy of the experimental data set to pin down the values of the static scalar dipole polarizabilities with more precision.…”

“…We used two different data sets, i.e., all the available experimental data for the unpolarized cross sections below pion-production threshold, denoted as FULL data set 1 (for a total of 150 data points) [26,[31][32][33][34][36][37][38][39][40][41][42], and the data set given by the TAPS experiment alone (55 data points) [26], which is, by far, the most comprehensive available subset. "Improved" data sets have been defined in recent fits of RCS observables, by discarding some data points from different experiments [4,20,43]. Here we do not apply any selection to the data, and we postpone a more detailed discussion of the statistical consistency of the different data subsets to a future work [44], entirely devoted to the extraction of the static scalar dipole polarizabilities from data.…”