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 Lüscher’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.
Highlights
To study the hadron interactions in lattice QCD, both the direct method [1] and the HAL QCD method [2] are employed
In the previous studies at heavier quark masses, both dineutron and deuteron are bound in the direct method [3,4,5,6,7,8,9,10,11], while they are unbound in the HAL QCD method [12, 13]
We reveal the origin of the fake plateau in the temporal correlator quantitatively, and demonstrate that correct plateaux emerge for both the ground and the 1st excited states if temporal correlation functions are projected to eigenstates of the HAL QCD potential
Summary
To study the hadron interactions in lattice QCD, both the direct method [1] and the HAL QCD method [2] are employed. In the series of papers [14,15,16,17], we pointed out that the discrepancies come from the misidentification of the energy eigenstate (“mirage” of the true plateau) in the direct method due to the contamination of excited (scattering) states. The manifestation of this problem can be exposed by a “sanity (consistency) check” [16, 17] using the Lüscher’s formula [18] and source/sink operator dependences of the plateaux [14,15,16]. We reveal the origin of the fake plateau in the temporal correlator quantitatively, and demonstrate that correct plateaux emerge for both the ground and the 1st excited states if temporal correlation functions are projected to eigenstates of the HAL QCD potential
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