Lattice QCD and baryon-baryon interactions: HAL QCD method

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 Lüscher'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.

39 pages, 20 figures, Contribution to Frontiers in Physics (Research topic) "The Long-Lasting Quest for Nuclear Interactions: The Past, the Present and the Future", Published version

References in corpus (16)

• Chiral effective field theory and nuclear forces
• Ab-initio Determination of Light Hadron Masses
• Nuclear Force from Lattice QCD
• Ab initio calculation of the neutron-proton mass difference
• A relativistic, model-independent, three-particle quantization condition
• Light Nuclei and Hypernuclei from Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry
• Evidence for a Bound H-dibaryon from Lattice QCD
• ABC Effect in Basic Double-Pionic Fusion --- Observation of a new resonance?
• Baryon-Baryon Interactions in the Flavor SU(3) Limit from Full QCD Simulations on the Lattice
• Baryon-Baryon Interactions and Spin-Flavor Symmetry from Lattice Quantum Chromodynamics
• Spin-2 $N\Omega$ Dibaryon from Lattice QCD
• Unified contraction algorithm for multi-baryon correlators on the lattice
• Construction of energy-independent potentials above inelastic thresholds in quantum field theories
• Nuclear Force from Lattice QCD
• Relation between scattering amplitude and Bethe-Salpeter wave function in quantum field theory
• Medium-heavy nuclei from nucleon-nucleon interactions in lattice QCD

Cited by in corpus (31)

• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Doubly Charmed Tetraquark $T_{cc}^{+}$ from Lattice QCD near Physical Point
• Dibaryon with highest charm number near unitarity from lattice QCD
• What is ab initio in nuclear theory?
• QCD and the Strange Baryon Spectrum
• Femtoscopic study of coupled-channel $N\Xi$ and $\Lambda \Lambda$ interactions
• Attractive $N$-$\varphi$ Interaction and Two-Pion Tail from Lattice QCD near Physical Point
• A variational study of two-nucleon systems with lattice QCD
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Little-Bang and Femto-Nova in Nucleus-Nucleus Collisions
• Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875{)}^{+}$ from finite volume energy levels
• Low-energy Scattering and Effective Interactions of Two Baryons at $m_{\pi }\sim 450$ MeV from Lattice Quantum Chromodynamics
• Strongly Bound Dibaryon with Maximal Beauty Flavor from Lattice QCD
• Nucleon-charmonium interactions from lattice QCD
• $d^{\ast }(2380)$ dibaryon from lattice QCD
• Dibaryon resonances and short-range $NN$ interaction
• Emergence of the $\rho$ resonance from the HAL QCD potential in lattice QCD
• Optimized Two-Baryon Operators in Lattice QCD
• Quark-diquark potential and diquark mass from Lattice QCD
• Nonperturbative two-pion exchange contributions to the nucleon-nucleon interaction in covariant baryon chiral perturbation theory
• The negative-parity spin-1/2 $\Lambda$ baryon spectrum from lattice QCD and effective theory
• Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states
• Hadron-hadron potentials coupled to quark degrees of freedom for exotic hadrons
• Inverse scattering problem with a bare state
• Toward nuclear physics from lattice QCD on quantum computers
• Lattice QCD and Baryon-Baryon Interactions
• Di-nucleons do not form bound states at heavy pion mass
• Coupled-channel ${\Lambda }_c{K}^{+}-p{D}_s$ Interaction in Flavor $\text{SU}\left(3\right)$ Limit of Lattice QCD
• Probing Nucleon-${\Omega }_{\mathrm{ccc}}$Interaction via Lattice QCD at Physical Quark Masses
• Wavefunction-based operator optimization for two-hadron systems in lattice QCD
• Reconstructing rare particle source by femtoscopic correlations