Exploring quark mass dependent three-nucleon forces in medium-mass nuclei

TL;DR

This study investigates the role of quark-mass dependent three-nucleon forces, focusing on the dominant term $F_2$, within chiral EFT for medium-mass nuclei. By combining the $F_2$ interaction with established 3N forces up to $N^{2}$LO/$N^{3}$LO and employing two fitting strategies—one using only few-body data and another including $^{16}$O observables—the authors assess whether $F_2$ improves predictions for energies and radii. They find that $F_2$ mainly affects short-range couplings through the few-body fits, while its direct contribution to heavier nuclei remains small; the strategy based on $^{16}$O observables can achieve good agreement, but the inclusion of $F_2$ does not systematically enhance the description nor resolve discrepancies in charge radii, arguing against promoting $F_2$ to a lower order in Weinberg power counting. Overall, the results suggest that $F_2$ acts largely as a reparametrization of short-range 3N couplings rather than new physics, informing future discussions on power counting and the treatment of quark-mass dependent forces in nuclear structure.

Abstract

Recently, new quark mass dependent three-nucleon (3N) forces have been identified, whose contributions in nuclear matter exceed expectations of Weinberg power-counting arguments. In this work, we investigate the impact of the most dominant new interaction term, characterized by the coupling $F_2$, in ab initio calculations of medium-mass nuclei. For this, we combine the new $F_2$ interaction with established 3N interactions up to next-to-next-to-leading order (N$^2$LO) and next-to-next-to-next-to-leading order (N$^3$LO) in chiral effective field theory. We explore two fit strategies for the low-energy couplings. The first is based only on few-body observables, while the second also incorporates information from $^{16}$O. Generally, we find that the $F_2$ interaction has a significant impact on energies and radii, however mainly due to changes in the short-range couplings. Overall, we do not find systematic improvements in the reproduction of medium-mass nuclei when the additional $F_2$ interaction is included.

Figures (7)

• Figure 1: Combinations of 3N LECs $c_D$ and $c_E$ that reproduce the $^{3}\text{H}$ binding energy for the EMN $\text{N}^{2}\text{LO}$ 450 MeV interaction for different values of $F_2$. Dashed lines correspond to unevolved Hamiltonians and solid lines to low-resolution NN+3N interactions at the NN SRG resolution scale $\lambda_{\text{SRG}}=1.8$ fm$^{-1}$. The symbols indicate the fitted values using $^3$H half-life (circles) and $^{16}$O binding energy plus charge radius (diamond). See main text and Table \ref{['tab:interactions']} for details.
• Figure 2: Difference of the calculated $^{16}$O charge radius (top panel) and ground-state energy (bottom panel) to the experimental values as a function of $c_D$ for the EMN $\text{N}^{2}\text{LO}$ 450 evolved interaction at different values of $F_2$. The blue diamond indicates the $c_D$ value that simultaneously reproduces both observables to good approximation for $F_2=0.05$, see also Fig. \ref{['fig:GT_fit_N2LO']} and Table \ref{['tab:interactions']}.
• Figure 3: Difference of the calculated $^{16}$O charge radius (top panel) and ground-state energy (bottom panel) to the experimental values as a function of $c_D$ for the EMN 450 evolved (solid lines) and bare interactions (dashed lines) at $\text{N}^{2}\text{LO}$ and $\text{N}^{3}\text{LO}$. Note the small plot scale for both observables. The diamonds again indicate the fitted interactions listed in Table \ref{['tab:interactions']} and used in Sec. \ref{['sec:results']}.
• Figure 4: Decomposition of the exact $^{3}\text{H}$ and Hartree-Fock $^{16}\text{O}$ ground-state energies into individual 3N and $F_2$ contributions at N$^2$LO. The purple triangles show the results of a reference interaction with $F_2 = 0$, $c_D = 5.0$, and the $c_E$ value fitted to the $^3$H binding energy. The orange triangles correspond to an interaction with $F_2 = 0.05$ added, but without refitting $c_E$. The refitted interaction corresponding to the blue diamonds is specified in Table. \ref{['tab:interactions']}. The $^{3}\text{H}$ expectation values were obtained from solutions of the Faddeev equations. For the Hartree-Fock calculations of $^{16}\text{O}$$E_{3\text{max}} = 16$ was used.
• Figure 5: Ground-state energy per particle (top panels) and charge radius (bottom panels) of closed-shell oxygen (left) and calcium (right) isotopes based on bare and evolved EMN $\text{N}^{2}\text{LO}$ 450 interactions for different $F_2$ values, following the "GT" fitting strategy (see Table \ref{['tab:interactions']}). Experimental data for ground-state energies are taken from Wang_2021, $^{16}\text{O}$ radius from ANGELI201369, and calcium radii from GarciaRuiz2016.