[Paper Review] Baryon interactions from lattice QCD with physical masses -- $S=-2$ sector --

Kenji Sasaki, Sinya Aoki+9 more|arXiv (Cornell University)|Feb 21, 2017

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This study computes strangeness $S=-2$ baryon-baryon interactions directly from lattice QCD using the HAL QCD method with physical masses on a large $(8.1\text{fm})^4$ lattice. It reveals flavor-, spin-, and isospin-dependent potentials with short-range repulsion and long-range attraction, indicating significant $N\Xi$ and $\Lambda\Sigma$ channel coupling, and finds stronger attraction in the $I=0$ $N\Xi$ channel, suggesting suppressed decay widths and potential for bound states.

ABSTRACT

The strangeness $S=-2$ baryon-baryon interaction is investigated directly from the fundamental theory of the strong interaction, QCD. The HAL QCD method enables us to extract baryon interactions from the Nambu-Bethe-Salpeter wave functions without using any experimental information. We present our latest result on the $S = -2$ baryon interactions and discuss the H-dibaryon state using potentials which are calculated by using the (almost) physical point gauge configurations with large lattice volume of$(8.1{ m{fm}})^4$ generated on the K-computer.

Motivation & Objective

• To compute $S=-2$ baryon-baryon interactions from first principles in lattice QCD without relying on experimental data.
• To investigate the role of $SU(3)$ flavor symmetry breaking and Pauli blocking in $BB$ potentials using the HAL QCD method.
• To assess the existence and properties of exotic states such as the H-dibaryon and the $N\Xi$ interaction in coupled channels.
• To determine the isospin and spin dependence of $N\Xi$ and $\Sigma\Sigma$ potentials for understanding hypernuclear decay and binding.

Proposed method

• The HAL QCD method extracts energy-independent, non-local potentials from the Nambu-Bethe-Salpeter (NBS) wave functions obtained via four-point correlation functions in a finite box.
• The method uses time-dependent Schrödinger-like equations to derive potentials from the temporal and spatial correlations of baryon four-point functions.
• A derivative expansion up to leading order is applied to handle non-locality, with potentials expressed as $U^{c}_{c'}(\vec{r},\vec{r}') \simeq V^{\text{LO}}_{c'c}(\vec{r}) \delta(\vec{r}-\vec{r}')$.
• The calculation employs $N_f=2+1$ dynamical gauge configurations with physical pion and kaon masses on a $96^3 \times 96$ lattice at $a \simeq 0.085$ fm.
• Coupled-channel potentials are constructed for $N\Xi$, $\Lambda\Sigma$, and $\Sigma\Sigma$ systems in various spin-isospin channels.
• Scattering phase shifts and bound state spectra are extracted by solving the Schrödinger equation with the derived potentials in infinite space.

Experimental results

Research questions

• RQ1 What is the nature of the $S=-2$ baryon-baryon interaction at physical quark masses, as derived directly from QCD?
• RQ2 How do isospin and spin quantum numbers influence the $N\Xi$ and $\Sigma\Sigma$ potentials in the $S=-2$ sector?
• RQ3 To what extent is the $N\Xi$ potential modified by Pauli blocking and $SU(3)$ flavor symmetry breaking?
• RQ4 What is the role of off-diagonal couplings between $N\Xi$, $\Lambda\Sigma$, and $\Sigma\Sigma$ channels in determining the scattering and binding properties?
• RQ5 Is there evidence for a bound state or resonance in the $N\Xi$ system, particularly in the $I=0$ channel?

Key findings

• All diagonal $BB$ potentials in the $S=-2$ sector exhibit a short-range repulsive core whose strength depends strongly on flavor, spin, and isospin quantum numbers.
• The $N\Xi$ potential in the $I=0$ channel is more attractive and has a weaker repulsive core than in the $I=1$ channel, indicating significant isospin dependence.
• The off-diagonal potential $V^{N\Xi}_{\Lambda\Sigma}$ is comparable in magnitude to the diagonal elements, indicating strong coupling between $N\Xi$ and $\Lambda\Sigma$ channels.
• The $\Sigma\Sigma$ potential in the $^{1}S_0(I=2)$ channel shows long-range attraction and short-range repulsion, with a weaker repulsive core than the $N\Xi$ potential in the $^{3}S_1(I=0)$ channel.
• The $N\Xi$ potential in the $^{3}S_1(I=0)$ channel has a shallow attractive well surrounding a weak repulsive core, suggesting possible bound state formation.
• The strong decay of $N\Xi$ into $\Lambda\Lambda$ is suppressed due to the small off-diagonal potential in the $^{1}S_0(I=0)$ channel, consistent with long-lived $\Xi$-hypernuclei.