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

We perform a high-statistics lattice QCD calculation of the low-energy two-nucleon scattering amplitudes. 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, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>m</a:mi> <a:mi>π</a:mi> </a:msub> <a:mo>=</a:mo> <a:msub> <a:mi>m</a:mi> <a:mi>K</a:mi> </a:msub> <a:mo>≃</a:mo> <a:mn>714</a:mn> <a:mspace width="0.28em"/> <a:mi>MeV</a:mi> </a:mrow> </a:math> . 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. 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. Furthermore, 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.