Nucleon-nucleon potentials from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math>-full chiral effective-field-theory and implications
Y. Nosyk, D. R. Entem, R. Machleidt
Abstract
We closely investigate $NN$ potentials based upon the $\mathrm{\ensuremath{\Delta}}$-full version of chiral effective-field-theory. We find that recently constructed $NN$ potentials of this kind, which (when applied together with three-nucleon forces) were presented as predicting accurate binding energies and radii for a range of nuclei from $A=16$ to $A=132$ and providing accurate equations of state for nuclear matter, yield a ${\ensuremath{\chi}}^{2}/\mathrm{datum}$ of 60 for the reproduction of the $pp$ data below 100 MeV laboratory energy. This ${\ensuremath{\chi}}^{2}$ is more than three times what the Hamada-Johnston potential of the year of 1962 achieved already some 60 years ago. We perceive this historical fact as concerning in view of the current emphasis on precision. We are able to trace the very large ${\ensuremath{\chi}}^{2}$ as well as the apparent success of the potentials in nuclear structure to unrealistic predictions for $P$-wave states, in which the $\mathrm{\ensuremath{\Delta}}$-full next-to-next-to-leading order (NNLO) potentials are off by up to 40 times the NNLO truncation errors. In fact, we show that the worse the description of the $P$-wave states, the better the predictions in nuclear structure. Thus, these potentials cannot be seen as the solution to the outstanding problems in current microscopic nuclear structure physics.