Lattice QCD and Baryon-Baryon Interactions

In this chapter, the current status on baryon-baryon interactions such as nuclear forces in lattice Quantum ChromoDynamics (QCD) is reviewed. In studies of baryon-baryon interactions in lattice QCD, the most reliable method so far is the potential method, proposed by the Hadrons to Atomic nuclei from Lattice QCD (HAL QCD) collaboration, whose formulation, properties and extensions are explained in detail. Using the HAL QCD potential method, potentials between nucleons (proton and neutron, denoted by $N$) in the derivative expansion have been extracted in various cases. The lattice QCD results shown in this chapter include a Leading Order (LO) central potential in the parity-even $NN(^1S_0)$ channel, LO central and tensor potentials in the parity-even $NN(^3S_1$-$^3D_1)$ channel, and a Next-to-Leading Order (NLO) spin-orbit potential as well as LO potentials in the parity-odd channels. Preliminary results at the almost physical pion and kaon masses, in addition to exploratory studies on three-nucleon potentials, are presented. Interactions between generic baryons including hyperons, made of one or more strange quarks as well as up and down quarks, have also been investigated. Universal properties of potentials between baryons become manifest in the flavor SU(3) symmetric limit, where masses of three quarks, up, down and strange, are all equal. In particular, it is observed that one bound state, traditionally called the $H$-dibaryon, appears in the flavor singlet representation of SU(3). A fate of the $H$ dibaryon is also discussed with flavor SU(3) breaking taken into account at the almost physical point. Finally, various kinds of dibaryons, bound or resonate states of two baryons, including charmed dibaryons, have been predicted by lattice QCD simulations at the almost physical point.