Quark-Mass Dependence of Light-Nuclei Masses from Lattice QCD and Trace-Anomaly Contributions to Nuclear Bindings

Abstract

We present lattice QCD calculations of the masses of the deuteron, dineutron, Helium-3 and Helium-4 with physical sea quarks and valence quark masses corresponding to pion masses between 140 and 700 MeV. At the physical point, the lowest finite-volume two-nucleon energy levels exhibit the qualitative pattern of a bound deuteron and an unbound dineutron within uncertainties, while at heavier quark masses they indicate the presence of deeply bound states. Compared with expectations from low-energy effective field theories, the observed mass dependence of the binding energies provides first-principles constraints on the quark-mass dependence of two- and three-nucleon interactions. From the quark-mass variation of the nuclear energies, we determine nuclear sigma terms and quantify the response of light-nuclear masses to changes in the light-quark mass. Using the QCD trace anomaly relation, we decompose the nuclear binding energy into quark-mass and gluonic contributions around the deuteron mass scale of $μ=2$ GeV. We find that the quark-mass contribution to the binding energy is small and approximately additive in nucleon number within current precision, whereas the gluonic component provides the dominant contribution and show milder increases with mass number.

Figures (17)

• Figure 1: Summary of $\Delta E_A$ results for two-nucleon systems in the deuteron (top) and dineutron (bottom) channels from various lattice QCD calculations. Results are ordered from top to bottom by increasing valence pion mass. Results from this work are shown by filled red legends: diamonds denote the smeared–point (SP) and squares the smeared–smeared (SS) setups. This work uses physical-mass sea quarks and varying valence pion masses, while all previous studies used both heavy valence and sea pion masses.
• Figure 2: Summary of $\Delta E_A$ results for two-nucleon systems in the $^3$He (top) and $^4$He (bottom) channels from various lattice QCD calculations. Results are ordered from top to bottom by increasing valence pion mass. Results from this work are shown by filled red legends: diamonds denote the smeared–point (SP) and squares the smeared–smeared (SS) setups. This work uses physical-mass sea quarks and varying valence pion masses, while all previous studies used both heavy valence and sea pion masses.
• Figure 3: Lattice QCD results of the energy splitting $\Delta E_{A}$ as a function of nucleon mass $m_N$ compared with several low-energy descriptions for the deuteron (top), $^3$He (middle), and $^4$He (bottom). The curves correspond to the Argonne V18 phenomenological potential (AV18), next-to-leading order partially quenched nucleon–nucleon potential (PQ NN potential), leading-order pionless EFT (pionless EFT and pionless EFT1), and pionless EFT without three-nucleon interactions (pionless EFT NN).
• Figure 4: Comparison of nuclear to nucleon sigma-term ratios for ${}^2\mathrm{H}$, ${}^3\mathrm{He}$, and ${}^4\mathrm{He}$ from this work ((lattice QCD at physical quark masses) with previous lattice-QCD and EFT results: NPLQCD 17 Chang:2017eiq, BCDLS 13 Beane:2013kca, pionless EFT constrained in this work, and the EFT analysis of Ref. Berengut:2013nh. See text for details.
• Figure 5: Decomposition of the binding energy per nucleon $\Delta E/A$ at $\overline{\mathrm{MS}}$=scale $\mu=2~\mathrm{GeV}$ into the quark-mass contribution, $\Delta E_{\sigma}$ (open symbols), and the gluonic trace-anomaly contribution, $\Delta E_{F^2}$ (filled symbols), for ${}^2\mathrm{H}$, ${}^3\mathrm{He}$, and ${}^4\mathrm{He}$. Circle symbols denote the lattice-QCD results, while triangle symbols correspond to the pionless-EFT benchmarks.