Abstract
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 such as QCD. 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 formulate 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 combined with the naive plateau fitting for the finite volume energies in the literature 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 (central) nuclear force, tensor force, 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.
Highlights
How do nuclear many-body systems emerge from the fundamental degrees of freedom, quarks and gluons? It has been a long-standing problem to establish a connection between nuclear physics and the fundamental theory of strong interaction, quantum chromodynamics (QCD)
We have reviewed the recent progress in lattice QCD study of baryon-baryon interactions by the HAL QCD method
The key observation is that the Nambu-Bethe-Salpeter (NBS) wave functions contain the information of scattering phase shifts below inelastic threshold in their asymptotic behaviors outside the range of the interactions
Summary
How do nuclear many-body systems emerge from the fundamental degrees of freedom, quarks and gluons? It has been a long-standing problem to establish a connection between nuclear physics and the fundamental theory of strong interaction, quantum chromodynamics (QCD). Lattice QCD and Baryon-Baryon Interactions from a viewpoint of chiral symmetry in QCD [4,5,6,7,8], whose unknown low-energy constants, cannot be determined within its framework but are obtained only by the fit to the experimental data. Under these circumstances, it is most desirable to determine nuclear forces as well as general baryon-baryon interactions from first-principles calculations of QCD, the lattice QCD method. The outcome is expected to make a significant impact on our understanding of nuclear astrophysical phenomena, such as supernovae, binary neutron star merges and nucleosynthesis
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