We perform a fit of the real Compton scattering (RCS) data below pion-production threshold to extract the electric (αE1) and magnetic (βM1) static scalar dipole polarizabilities of the proton, using fixed-t subtracted dispersion relations and a bootstrap-based fitting technique. The bootstrap method provides a convenient tool to include the effects of the systematic errors on the best values of αE1 and βM1 and to propagate the statistical errors of the model parameters fixed by other measurements. We also implement various statistical tests to investigate the consistency of the available RCS data sets below pion-production threshold and we conclude that there are not strong motivations to exclude any data point from the global set. Our analysis yields αE1 = (12.03 +0.48 −0.54 ) × 10 −4 fm 3 and βM1 = (1.77 +0.52 −0.54 ) × 10 −4 fm 3 , with p-value = 12%. I. INTRODUCTIONThe electric and magnetic static scalar dipole polarizabilities, α E1 and β M 1 , respectively, are fundamental structure constants of the proton that can be accessed via real Compton scattering (RCS). In the low-energy expansion of the Compton amplitude, they correspond to the leading-order contributions beyond the structure independent terms that describe the scattering process as if the proton were a pointlike particle with anomalous magnetic moment. When approaching the pion-production threshold, also higher-order terms start competing with the scalar dipole polarizabilities. Therefore, one has to resort to reliable theoretical frameworks for extracting the scalar dipole polarizabilities from experimental data. The most accredited theories, which have been used sofar, are fixed-t dispersion relations (DRs), in the unsubtracted [1-3] and subtracted [4][5][6][7][8] formalism, and chiral perturbation theory (χPT) with explicit nucleons and Delta's, in the variant of heavy-baryon χPT (HBχPT) [9-11] and manifestly covariant [12,13] χPT (BχPT) 1 . Based on these theoretical frameworks, extractions of the scalar dipole polarizabilities have been obtained by fitting different data sets for the unpolarized RCS cross section, and adopting a statistical approach based on the conventional χ 2 -minimization procedure. Recently, a new statistical method has successfully been applied in Ref. [16] to analyze RCS data at low energies and extract values for the energy-dependent scalar dipole dynamical polarizabilities [17,18]. The method is based on the parametric-bootstrap technique, and it is adopted in this work to extract the scalar dipole static polarizabilities, using the updated version of fixed-t subtracted DRs formalism [8] as theoretical framework. Although the bootstrap method is rarely used in nuclear physics [16,[19][20][21][22], it has high potential and advantages [23]. In particular, we will show that it allows us to include the systematic errors in the data analysis in a straightforward way and to efficiently reconstruct the probability distributions of the fitted parameters. We will also pay a special attention to discuss the available sets of ...

We present the first attempt to extract the scalar dipole dynamical polarizabilities from proton real Compton scattering data below pion-production threshold. The theoretical framework combines dispersion relations technique, low-energy expansion, and multipole decomposition of the scattering amplitudes. The results are obtained with statistical tools that have never been applied so far to Compton scattering data and are crucial to overcome problems inherent to the analysis of the available data set.

We present a new fitting technique based on the parametric bootstrap method, which relies on the idea to produce artificial measurements using the estimated probability distribution of the experimental data. In order to investigate the main properties of this technique, we develop a toy model and we analyze several fitting conditions with a comparison of our results to the ones obtained using of the standard χ 2 minimization procedure. Furthermore, we investigate the effect of the data systematic uncertainties both on the probability distribution of the fit parameters and on the shape of the expected goodness-of-fit distribution. Our conclusion is that, when systematic uncertainties are included in the analysis, only the bootstrap procedure is able to provide reliable confidence intervals and p-values, thus improving the results given by the standard χ 2 minimization approach. Our technique is then applied to an actual physics process, the real Compton scattering off the proton, thus confirming both the portability and the validity of the bootstrap-based fit method.

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