Ben Hörz

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, m π = m K ≃ 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. 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.

We use lattice QCD calculations of the finite-volume spectra of systems of two and three mesons to determine, for the first time, three-particle scattering amplitudes with physical quark masses. Our results are for combinations of π + and K + , at a lattice spacing a = 0.063 fm , and in the isospin-symmetric limit. We also obtain accurate results for maximal-isospin two-meson amplitudes, with those for π + K + and 2 K + being the first determinations at the physical point. Dense lattice spectra are obtained using the stochastic Laplacian-Heaviside method, and the analysis leading to scattering amplitudes is done using the relativistic finite-volume formalism. Results are compared to chiral perturbation theory and to phenomenological fits to experimental data, finding good agreement.

We study the interactions of systems of two and three nondegenerate mesons composed of pions and kaons at maximal isospin using lattice QCD, specifically π⁺K⁺, π⁺π⁺K⁺ and K⁺K⁺π⁺. Utilizing the stochastic LapH method, we determine the spectrum of these systems on two CLS N_f = 2 + 1 ensembles with pion masses of 200 MeV and 340 MeV, and include many levels in different momentum frames. We constrain the K matrices describing two- and three-particle interactions by fitting the spectrum to the results predicted by the finite-volume formalism, including up to p waves. This requires also results for the π⁺π⁺ and K⁺K⁺ spectrum, which have been obtained previously on the same configurations. We explore different fitting strategies, comparing fits to energy shifts with fits to energies boosted to the rest frame, and also comparing simultaneous global fits to all relevant two- and three-particle channels to those where we first fit two-particle channels and then add in the three-particle information. We provide the first determination of the three-particle K matrix in π⁺π⁺K⁺ and K⁺K⁺π⁺ systems, finding statistically significant nonzero results in most cases. We include s and p waves in the K matrix for π⁺K⁺ scattering, finding evidence for an attractive p-wave scattering length. We compare our results to Chiral Perturbation Theory, including an investigation of the impact of discretization errors, for which we provide the leading order predictions obtained using Wilson Chiral Perturbation Theory.

Implementations of measurement kernels in high-level Lattice QCD frameworks enable rapid prototyping, but can leave hardware capabilities significantly underutilized. This is an acceptable tradeoff if the time spent in unoptimized routines is generally small. The computational cost of modern spectroscopy projects however can be comparable to or even exceed the cost of generating gauge configurations and computing solutions of the Dirac equation. One such key kernel in the stochastic LapH method is the computation of baryon blocks; we discuss several implementation strategies and achieve a 7.2x speedup over the current implementation on a system with Intel® Xeon® Platinum 8358 processors, formerly Ice Lake.

Implementations of measurement kernels in high-level Lattice QCD frameworks enable rapid prototyping, but can leave hardware capabilities significantly underutilized. This is an acceptable tradeoff if the time spent in unoptimized routines is generally small. The computational cost of modern spectroscopy projects however can be comparable to or even exceed the cost of generating gauge configurations and computing solutions of the Dirac equation. One such key kernel in the stochastic LapH method is the computation of baryon blocks; we discuss several implementation strategies and achieve a 7.2x speedup over the current implementation on a system with Intel(R) Xeon(R) Platinum 8358 processors, formerly Ice Lake.