Tetsuo Hatsuda

We derive the one-pion exchange potential (OPEP) in the presence of a homogeneous magnetic field using chiral perturbation theory with nonrelativistic nucleons. Our approach is applicable not only to weak magnetic fields but also to strong ones up to around the pion-mass scale. The Green’s function of charged pions is modified by the magnetic field, leading to changes in the nuclear force. By numerically evaluating the modified OPEP incorporating its spin and isospin dependences, we show that the range of the potential decreases in both directions parallel and perpendicular to the magnetic field as the field strength increases. We also compute the resulting energy shift of the deuteron due to the modified OPEP, which can reach the order of 1 MeV around $|eB| = m_\pi ^2$, which is comparable to the deuteron binding energy.

A systematic way to constructing optimized interpolating operators for two-hadron systems is developed by incorporating inter-hadron spatial wavefunctions. The wavefunctions can be obtained from an iterative process with an appropriate initial guess. To implement these operators, a novel quark smearing technique utilizing $Z_3$ noise vectors is proposed, which allows for effectively incorporating inter-hadron spatial wavefunctions at the source without using all-to-all quark propagators. Proof-of-principle application to the $Ω_{ccc}Ω_{ccc}$ system using physical-point lattice configurations with a large size $La\simeq8.1$~fm shows that optimized operators enables clear identification of states around $2m_{Ω_{ccc}}\simeq 9700$ MeV with the energy gap as narrow as $\sim 5$ MeV. A comparison on correlation functions, effective energies, and HAL QCD potentials between unoptimized operators and optimized operators is given, with a special emphasis on the effects from nearby elastic scattering states. Potential applicability of the optimized operator to various two-hadron systems and its relation to the variational method are also discussed.

A systematic way to constructing optimized interpolating operators strongly coupled to QCD two-particle states is developed, which is achieved by incorporating inter-hadron spatial wavefunctions. To efficiently implement these operators in lattice QCD, a novel quark smearing technique utilizing noise vectors is proposed. Applied to the $Ω_{ccc}Ω_{ccc}$ system, the optimized operators resolve distinct eigenstates separated by only $\sim 5$ MeV near the threshold $2m_{Ω_{ccc}} \simeq 9700$ MeV. This exceptional resolving power opens new possibilities for studies of a wide range of hadronic systems in QCD.

The interaction between nucleon and charmonia ($J/\psi$ and $\eta_c$) is expected to deepen our understanding of various aspects in nonperturbative QCD ranging from the origin of nucleon mass to $J/\psi$ mass modification in nuclear medium and properties of hidden-charm pentaquark states. Here, we present the low-energy $NJ/\psi$ and $N\eta_c$ interactions based on ($2+1$) flavor lattice QCD simulations with nearly physical pion mass $m_\pi=146$ MeV. The interactions, extracted from the spacetime correlations of the nucleon and charmonium system by using the HAL QCD method, are found to be attractive in all distances and manifest a characteristic long-range tail consistent with the two-pion exchange interaction. The resulting scattering lengths are around $0.3$ fm, $0.4$ fm and $0.2$ fm for $NJ/\psi$ with spin $3/2$, with spin $1/2$, and $N\eta_c$, respectively. Our results are orders of magnitude larger than those from the photoproduction experiments assuming the vector meson dominance.

In this study, we develop a deep learning method to learn hadronic interactions unsupervisedly from the correlation functions calculated in lattice QCD simulations. We present our approach of using deep neural networks to model the inter-hadron potentials that are learned from Nambu-Bethe-Salpeter (NBS) wave functions. This enables the incorporation of most general forms of potentials into the Schrodinger-type equation for detailed analysis of hadronic interactions. Our results include validations with separable potentials, as well as the local and non-local potentials for the $\Omega_{ccc}-\Omega_{ccc}$ system. The neural networks accurately capture the essential features of these interactions, providing a reliable tool for predicting and analyzing hadron scattering properties, potentially bridging the experimental observables and lattice QCD data.