Dependence of nuclear binding on hadronic mass variation

We examine how the binding of light ($A⩽8$) 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 Poincaré-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 $~60\%$ (corresponding to an increase in $X_q=m_q/{\Lambda }_{\mathrm{QCD}}$ of 2.5). In the other direction, the dineutron becomes bound if the pion mass is decreased by $~15\%$ (corresponding to a reduction of $X_q$ by $~30\%$). 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 $\delta X_q/X_q=K·(0.013\pm 0.002)$ where $K~1$ (the expected accuracy in $K$ is about a factor of 2). The result is dominated by ${}^7\mathrm{Li}$ data.

Figure 1

Variation of two-nucleon energies with current-quark mass variation from DSE calculation: full calculation (solid lines) and with OPE modification only (dashed lines) for three different Argonne Hamiltonians. Virtual bound state energies are plotted as positive quantities; $m_{q0}$ is the physical current-quark mass.

Figure 2

Variation of multinucleon energies with current-quark mass variation from DSE calculation for AV14 Hamiltonian.

Figure 3

Variation of nuclear energies with current-quark mass variation from DSE calculation for AV18+UIX Hamiltonian.