Dependence of nuclear binding on hadronic mass variation

TL;DR

This study investigates how variations in hadronic masses affect nuclear binding energies, providing derivatives that help evaluate implications for big bang nucleosynthesis and lattice QCD extrapolations.

Contribution

It offers a quantitative analysis of nuclear binding dependence on hadronic mass variations using Dyson-Schwinger and Faddeev equations, linking microscopic quark mass changes to nuclear stability.

Findings

Nuclear binding decreases with increasing quark mass.

Deuteron becomes unbound if pion mass increases by ~60%.

Dineutron becomes bound if pion mass decreases by ~15%.

Abstract

We examine how the binding of light ($A\leq 8$) nuclei depends on possible variations of hadronic masses, including meson, nucleon, and nucleon-resonance masses. Small variations in hadronic masses may have occurred over time; the present results can help evaluate the consequences for big bang nucleosynthesis. Larger variations may be relevant to current attempts to extrapolate properties of nucleon-nucleon interactions from lattice QCD calculations. Results are presented as derivatives of the energy with respect to the different masses so they can be combined with different predictions of the hadronic mass-dependence on the underlying current-quark mass $m_q$. As an example, we employ a particular set of relations obtained from a study of hadron masses and sigma terms based on Dyson-Schwinger equations and a Poincar\'{e}-covariant Faddeev equation for confined quarks and diquarks. We find that nuclear binding decreases moderately rapidly as the quark mass increases, with the deuteron becoming unbound when the pion mass is increased by $\sim$60% (corresponding to an increase in $X_q=m_q/\Lambda_{QCD}$ of 2.5). In the other direction, the dineutron becomes bound if the pion mass is decreased by $\sim$15% (corresponding to a reduction of $X_q$ by $\sim$30%). If we interpret the disagreement between big bang nucleosynthesis calculations and measurements to be the result of variation in $X_q$, we obtain an estimate $\delta X_q/X_q=K \cdot (0.013 \pm 0.002)$ where $K \sim 1$ (the expected accuracy in $K$ is about a factor of 2). The result is dominated by $^7$Li data.