Abstract
We investigate the HAL QCD potential in $I=1$$\pi \pi$ scattering using the hybrid method for all-to-all propagators, in which a propagator is approximated by low eigenmodes, and the ...remaining high-eigenmode part is stochastically estimated. To verify the applicability of the hybrid method to systems containing quark creation$/$annihilation contributions such as the $\rho$ meson, we calculate the $I=1$$\pi\pi$ potential with the $(2+1)$-flavor gauge configurations on a $16^3 \times 32$ lattice with lattice spacing $a \approx 0.12$ fm and $(m_{\pi},m_{\rho}) \approx (870, 1230)$ MeV, in which the $\rho$ meson appears as a deeply bound state. While we find that the naive stochastic evaluations for quark creation$/$annihilation contributions lead to extremely large statistical fluctuations, additional noise reduction methods enable us to obtain a sufficiently precise potential, which shows a strong attractive force. We also confirm that the binding energy and $k^3 \cot \delta$ obtained from our potential are roughly consistent with an existing $\rho$ meson bound state, within the large systematic error associated with our calculation, whose possible origin is also discussed.
Baryon–baryon interactions with strangeness
$S=-2$
with flavor SU(3) breaking are calculated for the first time by using the HAL QCD method extended to the coupled-channel system in lattice QCD. The ...potential matrices are extracted from the Nambu–Bethe–Salpeter wave functions obtained by the
$2+1$
-flavor gauge configurations of the CP-PACS
$/$
JLQCD Collaborations with a physical volume of
$(1.93~{\rm fm})^3$
and with
$m_{\pi }/m_K=0.96, 0.90, 0.86$
. The spatial structure and the quark mass dependence of the potential matrix in the baryon basis and in the SU(3) basis are investigated.
Exotic pentaquark baryon with strangeness +1, Θ+, is studied in the QCD sum rule approach. We derive sum rules for the positive and negative parity baryon states with J=12 and I=0. It is found that ...the standard values of the QCD condensates predict a negative parity Θ+ of mass ≃1.5 GeV, while no positive parity state is found. We stress the roles of chiral-odd condensates in determining the parity and mass of Θ+.
Abstract
We study decuplet baryons from meson–baryon interactions in lattice quantum chromodynamics (QCD), in particular, Δ and Ω baryons from P-wave I = 3/2 Nπ and I = 0 $\Xi \bar{K}$ interactions, ...respectively. Interaction potentials are calculated in the HAL QCD method using 3-quark-type source operators at mπ ≈ 410 MeV and mK ≈ 635 MeV, where Δ as well as Ω baryons are stable. We use the conventional stochastic estimate of all-to-all propagators combined with the all-mode averaging to reduce statistical fluctuations. We have found that the $\Xi \bar{K}$ system has a weaker attraction than the Nπ system while the binding energy from the threshold is larger for Ω than Δ. This suggests that an inequality $m_{N}+m_{\pi }-m_{\Delta }\lt m_{\Xi }+m_{\bar{K}}-m_{\Omega }$ comes mainly from a smaller spatial size of a $\Xi \bar{K}$ bound state due to a larger reduced mass, rather than its interaction. Root-mean-square distances of bound states in both systems are small, indicating that Δ and Ω are tightly bound states and thus can be regarded qualitatively as composite states of three quarks. Results of binding energies agree with those obtained from temporal two-point functions within large systematic errors, which arise dominantly from the lattice artifact at short distances.
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 \(NN(^1S_0)\) channel, LO central and tensor potentials in the parity-even \(NN(^3S_1\)-\(^3D_1)\) 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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