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.

arXiv comment39 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 (64)

• An accurate nucleon-nucleon potential with charge-independence breaking
• The equation of state for nucleon matter and neutron star structure
• Modern Theory of Nuclear Forces
• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Chiral effective field theory and nuclear forces
• Construction of high-quality Nucleon-Nucleon potential models
• Ab-initio Determination of Light Hadron Masses
• Realistic models of pion-exchange three-nucleon interactions
• Nuclear Force from Lattice QCD
• Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice
• Nuclear effective field theory: status and perspectives
• Ab initio calculation of the neutron-proton mass difference
• Three-Body Interactions Among Nucleons and Pions
• Scattering processes and resonances from lattice QCD
• Bound H-dibaryon in Flavor SU(3) Limit of Lattice QCD
• Hadron-Hadron Interactions from Imaginary-time Nambu-Bethe-Salpeter Wave Function on the Lattice
• Reworking the Tucson-Melbourne Three-Nucleon Potential
• Theoretical Foundation of the Nuclear Force in QCD and its applications to Central and Tensor Forces in Quenched Lattice QCD Simulations
• 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?
• Two-particle multichannel systems in a finite volume with arbitrary spin
• Two-Baryon Potentials and H-Dibaryon from 3-flavor Lattice QCD Simulations
• The Deuteron and Exotic Two-Body Bound States from Lattice QCD
• Lattice QCD and Three-particle Decays of Resonances
• $K\to \pi \pi$ Decays in a Finite Volume
• $N\Omega$ dibaryon from lattice QCD near the physical point
• Most Strange Dibaryon from Lattice QCD
• Two Nucleon Systems at $m_{\pi }\sim 450\mathrm{MeV}$ from Lattice QCD
• Helium nuclei, deuteron and dineutron in 2+1 flavor lattice QCD
• Two-Nucleon Higher Partial-Wave Scattering from Lattice QCD
• 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
• I=2 Pion Scattering Length from Two-Pion Wave Functions
• Lattice QCD study of the $H$ dibaryon using hexaquark and two-baryon interpolators
• Two-Nucleon Systems in a Finite Volume: (I) Quantization Conditions
• Spin-2 $N\Omega$ Dibaryon from Lattice QCD
• Unified contraction algorithm for multi-baryon correlators on the lattice
• Exploring Three-Nucleon Forces in Lattice QCD
• Are two nucleons bound in lattice QCD for heavy quark masses? -- Consistency check with Lüscher's finite volume formula --
• Probing $\Omega \Omega$ and $p\Omega$ dibaryons with femtoscopic correlations in relativistic heavy-ion collisions
• Mirage in Temporal Correlation functions for Baryon-Baryon Interactions in Lattice QCD
• Nucleon-Nucleon Potential and its Non-locality in Lattice QCD
• Systematics of the HAL QCD Potential at Low Energies in Lattice QCD
• Spin-Orbit Force from Lattice QCD
• Two-Nucleon Bound States in Quenched Lattice QCD
• Construction of energy-independent potentials above inelastic thresholds in quantum field theories
• Equation of State for Nucleonic Matter and its Quark Mass Dependence from the Nuclear Force in Lattice QCD
• Consistency between Lüscher's finite volume method and HAL QCD method for two-baryon systems in lattice QCD
• Nuclear Force from Lattice QCD
• Asymptotic behavior of Nambu-Bethe-Salpeter wave functions for multi-particles in quantum field theories
• Baryon interactions from lattice QCD with physical quark masses -- Nuclear forces and $\Xi \Xi$ forces --
• Relation between scattering amplitude and Bethe-Salpeter wave function in quantum field theory
• Partial wave decomposition on the lattice and its applications to the HAL QCD method
• Doubly magic nuclei from Lattice QCD forces at $M_{PS}=$469 MeV/c${}^2$
• Baryon-baryon interactions at short distances -- constituent quark model meets lattice QCD
• Medium-heavy nuclei from nucleon-nucleon interactions in lattice QCD
• $I=2$ $\pi \pi$ scattering phase shift from the HAL QCD method with the LapH smearing
• Strange Nuclear Physics from QCD on Lattice
• Comment on "Relation between scattering amplitude and Bethe-Salpeter wave function in quantum field theory"
• Derivative Expansion of Wave Function Equivalent Potentials
• Asymptotic behavior of Nambu-Bethe-Salpeter wave functions for scalar systems with a bound state
• Hermitizing the HAL QCD potential in the derivative expansion

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• 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
• Probing Nucleon-${\Omega }_{\mathrm{ccc}}$Interaction via Lattice QCD at Physical Quark Masses
• Coupled-channel ${\Lambda }_c{K}^{+}-p{D}_s$ Interaction in Flavor $\text{SU}\left(3\right)$ Limit of Lattice QCD
• Reconstructing rare particle source by femtoscopic correlations
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• Two-Pion Exchange Paradigm in Hadron-Hadron Interactions from Lattice QCD