$I=2$ $\pi \pi$ potential in the HAL QCD method with all-to-all propagators

Abstract

In this paper, we perform the first application of the hybrid method (exact low modes plus stochastically estimated high modes) for all-to-all propagators to the HAL QCD method. We calculate the HAL QCD potentials in the $I=2$ $\pi \pi$ scattering in order to see how statistical fluctuations of the potential behave under the hybrid method. All of the calculations are performed with the 2+1 flavor gauge configurations on $16^3\times 32$ lattice at the lattice spacing $a\approx 0.12$ fm and $m_{\pi }\approx 870$ MeV. It is revealed that statistical errors for the potential are enhanced by stochastic noises introduced by the hybrid method, which, however, are shown to be reduced by increasing the level of dilutions, in particular, that of space dilutions. From systematic studies, we obtain a guiding principle for a choice of dilution types/levels and a number of eigenvectors to reduce noise contaminations to the potential while keeping numerical costs reasonable. We also confirm that we can obtain the scattering phase shifts for the $I=2$ $\pi \pi$ system by the hybrid method within a reasonable numerical cost, which are consistent with the result obtained with the conventional method. The knowledge we obtain in this study will become useful to investigate hadron resonances which require quark annihilation diagrams such as the $\rho$ meson by the HAL QCD potential with the hybrid method.

arXiv comment20 pages, 10 figures, published version in PTEP

References in corpus (38)

• Observation of $J/\psi p$ resonances consistent with pentaquark states in ${\Lambda }_b^0\to J/\psi K^{-}p$ decays
• Heavy-Quark QCD Exotica
• Observation of a narrow pentaquark state, $P_c(4312{)}^{+}$, and of two-peak structure of the $P_c(4450{)}^{+}$
• Nuclear Force from Lattice QCD
• Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice
• A novel quark-field creation operator construction for hadronic physics in lattice QCD
• Scattering processes and resonances from lattice QCD
• Multiple-channel generalization of Lellouch-Luscher formula
• Bound H-dibaryon in Flavor SU(3) Limit of Lattice QCD
• Practical all-to-all propagators for lattice QCD
• Hadron-Hadron Interactions from Imaginary-time Nambu-Bethe-Salpeter Wave Function on the Lattice
• Theoretical Foundation of the Nuclear Force in QCD and its applications to Central and Tensor Forces in Quenched Lattice QCD Simulations
• Coupled $\pi \pi ,K\overline{K}$ scattering in $P$-wave and the $\rho$ resonance from lattice QCD
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Two-Baryon Potentials and H-Dibaryon from 3-flavor Lattice QCD Simulations
• Lattice QCD Calculation of the $\rho$ Meson Decay Width
• $N\Omega$ dibaryon from lattice QCD near the physical point
• Charmed Tetraquarks Tcc and Tcs from Dynamical Lattice QCD Simulations
• Most Strange Dibaryon from Lattice QCD
• Isoscalar $\pi \pi ,K\overline{K},\eta \eta$ scattering and the $\sigma ,f_0,f_2$ mesons from QCD
• Fate of the Tetraquark Candidate Zc(3900) from Lattice QCD
• Hyperon-nucleon force from lattice QCD
• $P$-wave $\pi \pi$ scattering and the $\rho$ resonance from lattice QCD
• Spin-2 $N\Omega$ Dibaryon from Lattice QCD
• 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 --
• 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
• Coupled channel approach to strangeness S = -2 baryon-bayron interactions in Lattice QCD
• Spin-Orbit Force from Lattice QCD
• ${\Lambda }_{c}N$ interaction from lattice QCD and its application to ${\Lambda }_c$ hypernuclei
• Hadron interactions in lattice QCD
• Polynomial Hybrid Monte Carlo algorithm for lattice QCD with an odd number of flavors
• Consistency between Lüscher's finite volume method and HAL QCD method for two-baryon systems in lattice QCD
• The Tetraquark Candidate Zc(3900) from Dynamical Lattice QCD Simulations
• Asymptotic behavior of Nambu-Bethe-Salpeter wave functions for multi-particles in quantum field theories
• $\Omega \Omega$ interaction from 2+1 flavor lattice QCD

Cited by in corpus (7)

• Two- and three-pion finite-volume spectra at maximal isospin from lattice QCD
• A cross-channel study of pion scattering from lattice QCD
• Glueball scattering cross section in lattice SU(2) Yang-Mills theory
• Determination of crossing-symmetric $\pi \pi$ scattering amplitudes and the quark mass evolution of the $\sigma$ constrained by lattice QCD
• Emergence of the $\rho$ resonance from the HAL QCD potential in lattice QCD
• The HAL QCD potential in $I=1$ $\pi \pi$ system with the $\rho$ meson bound state
• S-wave kaon-nucleon potentials with all-to-all propagators in the HAL QCD method