Model selection for pion photoproduction

Abstract

Partial-wave analysis of meson and photon-induced reactions is needed to enable the comparison of many theoretical approaches to data. In both energy-dependent and independent parametrizations of partial waves, the selection of the model amplitude is crucial. Principles of the S-matrix are implemented to different degree in different approaches; but a many times overlooked aspect concerns the selection of undetermined coefficients and functional forms for fitting, leading to a minimal yet sufficient parametrization. We present an analysis of low-energy neutral pion photoproduction using the Least Absolute Shrinkage and Selection Operator (LASSO) in combination with criteria from information theory and K-fold cross validation. These methods are not yet widely known in the analysis of excited hadrons but will become relevant in the era of precision spectroscopy. The principle is first illustrated with synthetic data; then, its feasibility for real data is demonstrated by analyzing the latest available measurements of differential cross sections (dσ/dΩ), photon-beam asymmetries (Σ), and target asymmetry differential cross sections (dσT /d ≡ T dσ/dΩ) in the lowenergy regime.

Charmonium spectrum with a Dirac potential model in the momentum space

“…Once that 1000 fits have been performed, the uncertainties of the model parameters can be propagated to the charmonium spectrum using bootstrap [65,66]. This method allows us to carry to the spectrum computation the experimental uncertainties together with the correlations among the parameters.…”

“…These uncertainties are exactly propagated to the parameters and to the computed spectrum using the bootstrap technique [65,66]. This method is computationally expensive but allows a rigorous determination, from the statistical point of view, of the parameters of the model and their uncertainties, as well as the propagation of such uncertainties to the computation of the spectrum.…”

Model selection for pion photoproduction

“…We choose an optimal λ = 2.8 which coincides with the minimum of the BIC which is also the last point of the plateau. For the cross validation χ 2 V there is no minimum at all in this case (as there was for B-model [27]). Only an upper bound for λ can be determined continuing the upper end of the error bar at λ = 2.8 to the right as indicated.…”

“…The results of this fit are described in detail in Ref. [27]. Middle, the AIC, AICc and BIC criteria, and, in the bottom, the cross-validation χ 2 V for the analysis of real data.…”

“…[6] were also analyzed in Ref. [27]. The description of the data with the LASSO scan was remarkably good as well.…”