AUTHOR=Aoki Sinya , Doi Takumi 

TITLE=Lattice QCD and Baryon-Baryon Interactions: HAL QCD Method

JOURNAL=Frontiers in Physics

VOLUME=Volume 8 - 2020

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00307

DOI=10.3389/fphy.2020.00307

ISSN=2296-424X

ABSTRACT=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.