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Single state saturation of the temporal correlation function is a key condition to extract physical observables such as energies and matrix elements of hadrons from lattice QCD simulations. A method commonly employed to check the saturation is to seek for a plateau of the observables for large Euclidean time. Identifying the plateau in the cases having nearby states, however, is non-trivial and one may even be misled by a fake plateau. Such a situation takes place typically for the system with two or more baryons. In this study, we demonstrate explicitly the danger from a possible fake plateau in the temporal correlation functions mainly for two baryons ($XiXi$ and $NN$), and three and four baryons ($^3{rm He}$ and $^4{rm He})$ as well, employing (2+1)-flavor lattice QCD at $m_{pi}=0.51$ GeV on four lattice volumes with $L=$ 2.9, 3.6, 4.3 and 5.8 fm. Caution is given for drawing conclusion on the bound $NN$, $3N$ and $4N$ systems only based on the temporal correlation functions.
In this article, we review the HAL QCD method to investigate baryon-baryon interactions such as nuclear forces in lattice QCD. We first explain our strategy in detail to investigate baryon-baryon interactions by defining potentials in field theories
We report the recent progress on the determination of three-nucleon forces (3NF) in lattice QCD. We utilize the Nambu-Bethe-Salpeter (NBS) wave function to define the potential in quantum field theory, and extract two-nucleon forces (2NF) and 3NF on
A systematic analysis of the structure of single-baryon correlation functions calculated with lattice QCD is performed, with a particular focus on characterizing the structure of the noise associated with quantum fluctuations. The signal-to-noise pro
We present first results for two-baryon correlation functions, computed using $N_f=2$ flavours of O($a$) improved Wilson quarks, with the aim of explaining potential dibaryon bound states, specifically the H-dibaryon. In particular, we use a GEVP to
Nuclear forces and hyperon forces are studied by lattice QCD. Simulations are performed with (almost) physical quark masses, $m_pi simeq 146$ MeV and $m_K simeq 525$ MeV, where $N_f=2+1$ nonperturbatively ${cal O}(a)$-improved Wilson quark action wit