Triton binding energy with realistic precision

TL;DR

This paper calculates the triton binding energy considering uncertainties from nucleon-nucleon scattering data, revealing that current data uncertainties dominate over experimental precision and highlighting the need for improved data and computational methods.

Contribution

It provides a realistic estimate of the triton binding energy with quantified uncertainties directly from NN scattering data, emphasizing the impact of data uncertainties on theoretical precision.

Findings

Statistical error in binding energy is about 15 keV.

Data uncertainties exceed experimental precision by over two orders of magnitude.

Reducing numerical precision could improve computational efficiency.

Abstract

We compute the binding energy of triton with realistic statistical errors stemming from NN scattering data uncertainties and the deuteron and obtain $E_t=-7.638(15) \, {\rm MeV}$. Setting the numerical precision as $\Delta E_t^{\rm num} \lesssim 1 \, {\rm keV}$ we obtain the statistical error $\Delta E_t^{\rm stat}= 15(1) \, {\rm keV}$ which is mainly determined by the channels involving relative S-waves. This figure reflects the uncertainty of the input NN data, more than two orders of magnitude larger than the experimental precision $\Delta E_t^{\rm exp}= 0.1 \, {\rm keV}$ and provides a bottleneck in the realistic precision that can be reached. This suggests an important reduction in the numerical precision and hence in the computational effort.