Systematics of the HAL QCD potential at low energies in lattice QCD

Iritani, Takumi; Aoki, Sinya; Doi, Takumi; Gongyo, Shinya; Hatsuda, Tetsuo; Ikeda, Yoichi; Inoue, Takashi; Ishii, Noriyoshi; Nemura, Hidekatsu; Sasaki, Kenji

doi:10.1103/physrevd.99.014514

Cited by 74 publications

(142 citation statements)

References 48 publications

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“…. Since the elastic state saturation can be generally achieved at much smaller t − t 0 than the case of the ground state saturation, we can obtain reliable results from this "time-dependent HAL QCD method" [12,13,14,15].…”

Section: Hal Qcd Methodsmentioning

confidence: 87%

“…In practice, however, this extraction of the NBS wave function from the ground state saturation is very difficult due to increasing statistical noises at large t − t 0 [12,13,14]. Therefore, in Ref.…”

Section: Hal Qcd Methodsmentioning

confidence: 99%

“…where V ( x, ∇) is expanded in terms of ∇ [16]. At low energies, since the leading order (LO) potential of the derivative expansion dominates [15], the interaction for the S-wave spin singlet system is well approximated by the LO central potential given as…”

Section: Hal Qcd Methodsmentioning

confidence: 99%

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Partial wave decomposition on the lattice and its applications to the HAL QCD method

et al. 2020

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The approximated partial wave decomposition method to the discrete data on a cubic lattice, developed by C. W. Misner, is applied to the calculation of S-wave hadron-hadron scatterings by the HAL QCD method in lattice QCD. We consider the Nambu-Bethe-Salpeter (NBS) wave function for the spin-singlet Λ c N system calculated in the (2 + 1)-flavor QCD on a (32a fm) 3 lattice at the lattice spacing a 0.0907 fm and m π 700 MeV. We find that the l = 0 component can be successfully extracted by Misner's method from the NBS wave function projected to A + 1 representation of the cubic group, which contains small l ≥ 4 components. Furthermore, while the higher partial wave components are enhanced so as to produce significant comb-like structures in the conventional HAL QCD potential if the Laplacian applied to the NBS wave function is approximated by the usual second order difference, such structures are found to be absent in the potential extracted by Misner's method, where the Laplacian can be evaluated analytically. Despite the difference in the potentials, two methods give almost identical results on the central values and on the magnitude of statistical errors for the fits of the potentials, and consequently on the scattering phase shifts. This indicates that not only that Misner's method works well in lattice QCD but also the contaminations from higher partial waves in the study of S-wave scatterings are well under control even in the conventional HAL QCD method. It will be of interest to study interactions in higher partial wave channels in Misner's method, where the utility of this method may become clearer.

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Section: Hal Qcd Methodsmentioning

confidence: 87%

Section: Hal Qcd Methodsmentioning

confidence: 99%

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Partial wave decomposition on the lattice and its applications to the HAL QCD method

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“…where α, β and γ are color indices, and q 1 , [15]. Such a wall source is known to have a large overlap with low-lying states [18,19].…”

Section: Coupled-channel Baryon-baryon Interactionmentioning

confidence: 99%

“…See also Ref. [18] for an explicit construction of the higher order terms as well as the convergence test of the derivative expansion.…”

Section: Coupled-channel Baryon-baryon Interactionmentioning

confidence: 99%

ΛΛ and NΞ interactions from lattice QCD near the physical point

et al. 2020

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The S-wave ΛΛ and N Ξ interactions are studied on the basis of the (2+1)-flavor lattice QCD simulations close to the physical point (m π 146MeV and m K 525MeV). Lattice QCD potentials in four different spin-isospin channels are extracted by using the coupled-channel HAL QCD method and are parametrized by analytic functions to calculate the scattering phase shifts. The ΛΛ interaction at low energies shows only a weak attraction, which does not provide a bound or resonant dihyperon. The N Ξ interaction in the spin-singlet and isospin-singlet channel is most attractive and lead the N Ξ system near unitarity. Relevance to the strangeness=−2 hypernuclei as well as to two-baryon correlations in proton-proton, proton-nucleus and nucleus-nucleus collisions is also discussed.

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Lattice QCD and Baryon-Baryon Interactions

Aoki

Doi

2022

Handbook of Nuclear Physics

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In this chapter, the current status on baryon-baryon interactions such as nuclear forces in lattice Quantum ChromoDynamics (QCD) is reviewed. In studies of baryon-baryon interactions in lattice QCD, the most reliable method so far is the potential method, proposed by the Hadrons to Atomic nuclei from Lattice QCD (HAL QCD) collaboration, whose formulation, properties and extensions are explained in detail. Using the HAL QCD potential method, potentials between nucleons (proton and neutron, denoted by N) in the derivative expansion have been extracted in various cases. The lattice QCD results shown in this chapter include a Leading Order (LO) central potential in the parity-even NN( 1 S 0 ) channel, LO central and tensor potentials in the parity-even NN( 3 S 1 -3 D 1 ) channel, and a Next-to-Leading Order (NLO) spin-orbit potential as well as LO potentials in the parity-odd channels. Preliminary results at the almost physical pion and kaon masses, in addition to exploratory studies on three-nucleon potentials, are presented. Interactions between generic baryons including hyperons, made of one or more strange quarks as well as up and down quarks, have also been investigated. Universal properties of potentials between baryons become manifest in the flavor SU(3) symmetric limit, where masses of three quarks, up, down and strange, are all equal. In particular, it is observed that one bound state, traditionally called the H-dibaryon, appears in the flavor singlet representation of SU(3). A fate of the H dibaryon is also discussed with flavor SU(3) breaking taken into account at the almost physical point. Finally, various kinds of dibaryons, bound or resonate states of two baryons, including charmed dibaryons, have been predicted by lattice QCD simulations at the almost physical point.

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Systematics of the HAL QCD potential at low energies in lattice QCD

Cited by 74 publications

References 48 publications

Partial wave decomposition on the lattice and its applications to the HAL QCD method

Partial wave decomposition on the lattice and its applications to the HAL QCD method

ΛΛ and NΞ interactions from lattice QCD near the physical point

Lattice QCD and Baryon-Baryon Interactions

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