Di-nucleons do not form bound states at heavy pion mass

TL;DR

This work investigates whether di-nucleons bind in QCD at a heavy pion mass by performing high-statistics lattice QCD calculations with $m_π = m_K ≈ 714$ MeV. It employs both the Lüscher finite-volume QC2 method and the HAL QCD potential approach on the same SU(3) symmetric ensembles, cross-checking results across operator bases, including hexaquark interpolators. The analyses find no bound deuteron or dineutron state; the deuteron exhibits a virtual bound-state behavior, and the dineutron shows a similar pattern, with scattering parameters extracted via effective-range fits. The study also demonstrates that off-diagonal correlators with HX operators do not reveal hidden bound states and that previous claims likely stem from plateau misidentification. Together, the results corroborate the absence of di-nucleon binding at this mass point and highlight the need to move to lighter pion masses to approach the physical point.

Abstract

We perform a high-statistics lattice QCD calculation of the low-energy two-nucleon scattering amplitudes. In order to address discrepancies in the literature, the calculation is performed at a heavy pion mass in the limit that the light quark masses are equal to the physical strange quark mass, $m_π= m_K \simeq 714 $ MeV. Using a state-of-the-art momentum space method, we rule out the presence of a bound di-nucleon in both the isospin 0 (deuteron) and 1 (di-neutron) channels, in contrast with many previous results that made use of compact hexaquark creation operators. In order to diagnose the discrepancy, we add such hexaquark interpolating operators to our basis and find that they do not affect the determination of the two-nucleon finite volume spectrum, and thus they do not couple to deeply bound di-nucleons that are missed by the momentum-space operators. Further, we perform a high-statistics calculation of the HAL QCD potential on the same gauge ensembles and find qualitative agreement with our main results. We conclude that di-nucleons do not form bound states at heavy pion masses and that previous identification of deeply bound di-nucleons must have arisen from a misidentification of the spectrum from off-diagonal elements of a correlation function.

Figures (32)

• Figure 1: Effective mass of the pion (left) and nucleon (middle) as a function of $N_{\rm ev}$ at two different choices of total momentum of the correlators. The effective mass is constructed as $m_{\rm eff}(t_s) = \ln(C(t_s-0.5) / C(t_s+0.5))$ in both cases for $t_s=2.5$. The smearing profile of the quark source is plotted in the right panel for different numbers of $N_{\rm ev}$.
• Figure 2: Comparison of the ground state NN energy and energy shift in the $T_{1g}$ channel using the conspiracy (C) and agnostic (A) models (top). For the former, we show the preferred final model while for the latter, we vary the number of exponentials used to model the single ($n$) and NN ($nn$) correlators. The band and dashed lines are from the conspiracy model with 3-states for the single nucleon, to guide the eye. The relative probability for a given model ($w_{\rm model})$ at each $t_{\rm min}$ is determined from the Bayes Factor. We also show stability of the conspiracy model with respect to the number of states used to describe the single nucleon correlators (bottom). The $Q$-value factor is similar to the frequentist $P$-value but uses the augmented $\chi^2/{\rm dof}$Lepage:2001ym.
• Figure 3: Stability of the ground state interaction energy, ${\delta} E_{00}$, for all 15 irreps/levels used in this work for the deuteron. Note that the two levels in $A_2(1)$ have overlapping values of ${\delta} E_{00}$.
• Figure 4: Resulting phase shift expressed as $q\cot{\delta}$ (top) and ${\delta}$ in degrees (bottom) from the single-channel QC2 analysis after irrep averaging. The solid points are used in the analysis. The open data are the original results before irrep averaging. The dotted line in the $q\cot{\delta}$ plot is $\sqrt{-q^2}$, i.e. the virtual bound state condition. A crossing between the $q\cot\delta$ and this curve implies the presence of a virtual bound state. The NN ONLINE - PWA phase shift is obtained from http://nn-online.org using the Partial Wave Analysis of experimental data Stoks:1993tb.
• Figure 5: Stability of the ground state interaction energy , ${\delta} E_{00}$ for all 8 irreps/levels used in this work in the di-neutron channel.