Two-baryon systems from HAL QCD method and the mirage in the temporal correlation of the direct method

TL;DR

This paper compares the HAL QCD and direct methods for studying two-baryon systems in lattice QCD, identifying the excited state contamination as the cause of the mirage problem in the direct method and validating the HAL QCD approach.

Contribution

It systematically investigates uncertainties in the HAL QCD method and confirms the origin of the mirage in the direct method using the HAL QCD potential.

Findings

The systematic uncertainties in HAL QCD are well controlled.

The mirage plateau in the direct method is caused by excited state contamination.

HAL QCD method is consistent with Lüscher's finite volume formula.

Abstract

Both direct and HAL QCD methods are currently used to study the hadron interactions in lattice QCD. In the direct method, the eigen-energy of two-particle is measured from the temporal correlation. Due to the contamination of excited states, however, the direct method suffers from the fake eigen-energy problem, which we call the "mirage problem," while the HAL QCD method can extract information from all elastic states by using the spatial correlation. In this work, we further investigate systematic uncertainties of the HAL QCD method such as the quark source operator dependence, the convergence of the derivative expansion of the non-local interaction kernel, and the single baryon saturation, which are found to be well controlled. We also confirm the consistency between the HAL QCD method and the L\"uscher's finite volume formula. Based on the HAL QCD potential, we quantitatively confirm that the mirage plateau in the direct method is indeed caused by the contamination of excited states.