Lattice QCD and Baryon-Baryon Interactions: HAL QCD Method - Aoki, Sinya; Doi, Takumi (Frontiers in Physics, 2020)
In this article, we review the HAL QCD method to investigate baryon-baryon interactions such as the nuclear forces in lattice QCD. We first explain our strategy to investigate baryon-baryon interactions by defining potentials in field theories such as QCD in detail. We introduce the Nambu-Bethe-Salpeter (NBS) wave functions in QCD for two baryons below the inelastic threshold. We then define the potential from NBS wave functions in terms of the derivative expansion, which is shown to reproduce the scattering phase shifts correctly below the inelastic threshold. Using this definition, we propose a method to extract the potential in lattice QCD. Secondly, we discuss pros and cons of the HAL QCD method, by comparing it with the conventional method, where one directly extracts the scattering phase shifts from the finite volume energies through the L¥"uscher's formula. We give several theoretical and numerical evidences that the conventional method so far fails to work on baryon-baryon interactions due to contaminations of elastic excited states. On the other hand, we show that such a serious problem can be avoided in the HAL QCD method by defining the potential in an energy-independent way. We also discuss systematics of the HAL QCD method, in particular errors associated with a truncation of the derivative expansion. Thirdly, we present several results obtained from the HAL QCD method, which include the (central) nuclear force, the tensor force, the spin-orbital force, and three nucleon force. We finally show the latest results calculated at the nearly physical pion mass, m_¥pi ¥simeq 146 MeV, including hyperon forces which lead to form ¥Omega¥Omega and N¥Omega dibaryons.