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$S$-wave kaon-nucleon interactions from lattice QCD at the physical point

Kotaro Murakami, Sinya Aoki, Takumi Doi, Yan Lyu, Wren Yamada

Abstract

We investigate S-wave kaon-nucleon ($KN$) interactions with strangeness $S=+1$ in lattice QCD using the time-dependent HAL QCD method. Employing the $(2+1)$-flavor gauge configuration with $m_π\approx 137~\textrm{MeV}$ and $m_{K}\approx 502~\textrm{MeV}$, we calculate the $KN$ potentials at the leading order in the derivative expansion. The potentials in both isospin channels ($I=1$ and $I=0$) exhibit repulsion at short distances, while only the $I=0$ potential has a small attractive pocket at intermediate distances. The phase shifts computed from these potentials show no signals corresponding to resonances or bound states in both isospin channels, suggesting the absence of the $Θ^{+}(1540)$ pentaquark in the S-wave $KN$ systems. The scattering lengths result in $a^{I=1}_{0} = -0.226(5)(^{+5}_{-0})~\textrm{fm}$ and $a^{I=0}_{0} = +0.028(61)(^{+3}_{-26})~\textrm{fm}$. Our results of the S-wave cross sections for $I=1$ are consistent with some of the experimental data within $2-3$ $σ$, while they deviate from others. The results for $I=0$, combined with recent studies on chiral perturbation theory, suggest that the scattering amplitudes in this channel are dominated by P-wave components rather than S-wave.

$S$-wave kaon-nucleon interactions from lattice QCD at the physical point

Abstract

We investigate S-wave kaon-nucleon () interactions with strangeness in lattice QCD using the time-dependent HAL QCD method. Employing the -flavor gauge configuration with and , we calculate the potentials at the leading order in the derivative expansion. The potentials in both isospin channels ( and ) exhibit repulsion at short distances, while only the potential has a small attractive pocket at intermediate distances. The phase shifts computed from these potentials show no signals corresponding to resonances or bound states in both isospin channels, suggesting the absence of the pentaquark in the S-wave systems. The scattering lengths result in and . Our results of the S-wave cross sections for are consistent with some of the experimental data within , while they deviate from others. The results for , combined with recent studies on chiral perturbation theory, suggest that the scattering amplitudes in this channel are dominated by P-wave components rather than S-wave.

Paper Structure

This paper contains 12 sections, 17 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. HAL QCD method for systems of octet meson and baryon
  3. Setups
  4. Definition of the correlation functions
  5. Simulation details
  6. Numerical results
  7. $KN$ potentials
  8. $KN$ scattering observables
  9. Discussions on systematic uncertainties
  10. Conclusion
  11. Plots of the comparison of the LO $KN$ potentials between different pion masses
  12. Energy shifts on finite volume from $KN$ temporal correlation functions with optimized operators

Figures (10)

  • Figure 1: Leading-order potentials in $I=1$ (Left panel) and $I=0$ channels (Right panel) at $t/a=12\textrm{--}16$.
  • Figure 2: Fit results for the $I=1$ (Left panel) and $I=0$ channels (Right panel) at $t/a=14$. Teal and orange bands correspond to the fit results using $V^{\textrm{4G}}_{I}(r)$ and $V^{\textrm{3GTPE}}_{I}(r)$, respectively. The red cross plots are the original potential data (same as those in Fig. \ref{['fig:results_pot_orig']}).
  • Figure 3: Phase shifts for the S-wave $KN$ scatterings in $I=1$ (Left panel) and $I=0$ channels (Right panel) at $t/a=12$ (Blue), $14$ (Red), and $16$ (Green). Experimental results are taken from Refs. Goldhaber:1962zz (Circles), Burnstein:1974ax (Crosses), and Cameron:1974xx (Triangles) for $I=1$ channel, and from Refs. PhysRev.134.B1111 (Pentagon and Hexagon) and PhysRevD.15.1200 (Stars) for $I=0$ channel. Dashed, dotted and solid lines depict the results of the energy-dependent partial-wave analysis in Refs. Martin:1975gs, Hyslop:1992cs and Gibbs:2006ab, respectively.
  • Figure 4: $(p^{\ast}\cot{\delta_{0}(p^{\ast})})^{-1}$ for the S-wave $KN$ scatterings in $I=1$ (Left panel) and $I=0$ channels (Right panel) at $t/a=12$ (Blue), $14$ (Red), and $16$ (Green). Experimental results are taken from Refs. Goldhaber:1962zz (Circles), Burnstein:1974ax (Crosses), and Cameron:1974xx (Triangles) for $I=1$ channel, and from Refs. PhysRev.134.B1111 (Pentagon and Hexagon) and PhysRevD.15.1200 (Stars) for $I=0$ channel. Dashed, dotted and solid lines depict the results of the energy-dependent partial-wave analysis in Refs. Martin:1975gs, Hyslop:1992cs and Gibbs:2006ab, respectively. Magenta band located at $(p^{\ast}/m_{\pi})^2=0$ represents the scattering length taken from Dover:1982zh. The phase shift at the ground-state energy on the finite volume is shown as a brown curve.
  • Figure 5: S-wave total cross sections for $KN$ scatterings in $I=1$ (Left panel) and $I=0$ channels (Right panel) at $t/a=12$ (Blue), $14$ (Red), and $16$ (Green). Experimental results are taken from Refs. Goldhaber:1962zz (Circles), Burnstein:1974ax (Crosses), Cameron:1974xx (Triangles), Bowen:1970azd (Diamonds) and Adams:1973elr (Inverted triangles) for the $I=1$ channel, and from Refs. Bowen:1970azd (Diamonds) and Carroll:1973ux (Squares) for the $I=0$ channel.
  • ...and 5 more figures