Finite volume analysis on systematics of the derivative expansion in HAL QCD method

TL;DR

This study assesses the convergence of the derivative expansion in the HAL QCD method using finite volume analysis on lattice QCD data for $ ext{ΩΩ}$ and $ ext{Ω}_{ccc} ext{Ω}_{ccc}$ systems, demonstrating reliable extraction of binding energies.

Contribution

It provides the first explicit evidence that the HAL QCD method's derivative expansion converges well and can accurately determine ground state binding energies from excited state dominated correlators.

Findings

Derivative expansion is well converged in studied systems.

Eigenmode projection yields spectra consistent with HAL QCD potentials.

HAL QCD method reliably extracts binding energies from excited state dominated correlators.

Abstract

We study the convergence of the derivative expansion in HAL QCD method from the finite volume analysis. Employing the (2+1)-flavor lattice QCD data obtained at nearly physical light quark masses $(m_\pi, m_K) \simeq (146, 525)$ MeV and the physical charm quark mass, we study two representative systems, $\Omega\Omega$ and $\Omega_{ccc}\Omega_{ccc}$ in the $^1S_0$ channel, where both systems were found to have a shallow bound state in our previous studies. The HAL QCD potentials are determined at the leading-order in the derivative expansion, from which finite-volume eigenmodes are obtained. Utilizing the eigenmode projection, we find that the correlation functions are dominated by the ground state (first excited state) in the case of $\Omega\Omega$ ($\Omega_{ccc}\Omega_{ccc}$). In both $\Omega\Omega$ and $\Omega_{ccc}\Omega_{ccc}$, the spectra obtained from eigenmode-projected temporal correlators are found to be consistent with those from the HAL QCD potential for both the ground and first excited state. These results show that the derivative expansion is well converged in these systems, and also provide a first explicit evidence that the HAL QCD method enables us to reliably extract the binding energy of the ground state even from the correlator dominated by excited scattering states.