Various types of theoretical uncertainties by example of the elastic nucleon-deuteron scattering spin correlation coefficient Cz,x

Yu Volkotrub,J Golak,H Witała,K Topolnicki,R Skibiński,A Wrońska,A Magiera,W Przygoda

doi:10.1051/epjconf/201919905006

Yu Volkotrub, J Golak + Show 6 more

Open Access

https://doi.org/10.1051/epjconf/201919905006

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Abstract

The elastic nucleon-deuteron scattering process can be used to study three-nucleon dynamics, but in order to draw reliable conclusions based on the comparison of theoretical predictions and data, an estimation of theoretical uncertainties is necessary. We consider the statistical errors arising from a propagation of uncertainties of the two-nucleon interaction parameters to the three-nucleon system, truncation errors, regulator dependencies, and uncertainties arising from using the formalism of partial waves. We give an example of the nucleon-deuteron spin correlation coefficient Cz,x, obtained within the Faddeev approach, to discuss magnitudes of the above mentioned theoretical uncertainties. We find that using various models of the nuclear forces results in the dominant theoretical uncertainty for the nucleon-deuteron elastic scattering observables.

Highlights

The elastic nucleon-deuteron scattering process can be used to study three-nucleon dynamics, but in order to draw reliable conclusions based on the comparison of theoretical predictions and data, an estimation of theoretical uncertainties is necessary
The possible sources of theoretical uncertainties in the fewnucleon sector are the statistical errors arising from a propagation of uncertainties of free parameters of the 2N interaction to the 3N system, the truncation errors related to neglecting the higher orders of chiral expansions, the dependence on regulator functions, the numerical uncertainties as well as the uncertainties bound to the computational scheme used, and last but not least the uncertainty arising from using the various models of nuclear interaction
Summarizing, we applied the OPE-Gaussian force to study the propagation of uncertainties of 2N interaction parameters to 3N observables

Summary

Introduction - problem and solution method

The necessity of reliable theoretical errors estimation steams from the growing precision of experimental data as well as from the fact that nowadays we are aiming to study details of the underlying physics. The important feature of the OPE-Gaussian potential is that the values of its parameters (a, Vk,n) and their covariance matrix are known This allows us to use a statistical approach to estimate some theoretical uncertainties. We regard two models of the chiral interaction at the fifth order of the chiral expansion (N4LO): one with the semi-local regularization in coordinate space [7] and one using the nonlocal regularization in momentum space [11] In both cases the regulator function depends on one parameter whose range has been proposed by the authors of Refs. To calculate 3N observables we use the formalism of Faddeev equations which is a standard technique used to investigate nucleon-deuteron scattering This framework as well as our numerical performance is described in detail e.g. in [6]. As mentioned above our numerical solution is obtained by using 3N partial waves, and we take into account all states with the two-body angular momentum j up to jmax and the three-body total angular momentum

Results for nucleon-deuteron spin correlation coefficient

Summary