[Paper Review] Comment on "Are two nucleons bound in lattice QCD for heavy quark masses? - Sanity check with Lüscher's finite volume formula -"

Silas R. Beane, Emmanuel Chang+9 more|arXiv (Cornell University)|May 25, 2017

Quantum Chromodynamics and Particle Interactions9 citations

TL;DR

This comment refutes erroneous claims by the HALQCD collaboration regarding the validity of lattice QCD calculations for two-nucleon bound states at heavy quark masses. Using Lüscher’s finite-volume formalism, the authors demonstrate that independent lattice QCD studies—including their own refined analysis—pass all sanity checks, confirming robust bound states in the $^{1}S_{0}$ and $^{3}S_{1}$ channels at $m_/pi = 806$ MeV.

ABSTRACT

In this comment, we address a number of erroneous discussions and conclusions presented in a recent preprint by the HALQCD collaboration, arXiv:1703.07210. In particular, we demonstrate that lattice QCD determinations of bound states at quark masses corresponding to a pion mass of $m_π= 806$ MeV are robust, and that the phases shifts extracted by the NPLQCD collaboration for these systems pass all of the 'sanity checks' introduced in arXiv:1703.07210.

Motivation & Objective

• To correct misinterpretations and flawed conclusions in the HALQCD preprint (arXiv:1703.07210) regarding the existence of two-nucleon bound states in lattice QCD.
• To validate the robustness of lattice QCD determinations of bound states at $m_\pi = 806$ MeV using Lüscher’s finite-volume formalism.
• To demonstrate that the NPLQCD results for the $^{1}S_{0}$ and $^{3}S_{1}$ channels pass all proposed 'sanity checks' for consistency and reliability.
• To highlight inconsistencies in the HALQCD analysis, particularly regarding source independence and misidentification of excited states.
• To reaffirm the reliability of multiple independent lattice QCD calculations that identify bound states in two-nucleon systems at heavy quark masses.

Proposed method

• Application of Lüscher’s finite-volume formalism to extract infinite-volume energy levels from two-point correlation functions in lattice QCD simulations.
• Use of effective range expansion (ERE) fits to phase shifts extracted from finite-volume energy levels to test consistency with bound state criteria.
• Comparison of ERE fits from the original 2013 NPLQCD analysis (Beane et al.) with a refined 2017 analysis (Wagman et al.) on the same correlation functions.
• Evaluation of source independence by analyzing correlation functions with different interpolating fields, confirming consistent ground-state energy extraction.
• Use of the criterion $k^{*2} = -\kappa^{(\infty)2}$ to test whether extracted phase shifts correspond to bound states in the infinite-volume limit.
• Systematic comparison of results across multiple lattice ensembles and groups, including NPLQCD, PACS-CS, and others, to assess consistency and robustness.

Experimental results

Research questions

• RQ1 Do lattice QCD calculations at $m_\pi = 806$ MeV provide consistent and reliable evidence for two-nucleon bound states in the $^{1}S_{0}$ and $^{3}S_{1}$ channels?
• RQ2 Are the conclusions of the HALQCD collaboration regarding the absence of bound states in these channels valid, given the finite-volume formalism and sanity checks?
• RQ3 How do the results from the refined 2017 NPLQCD analysis (Wagman et al.) compare with the original 2013 analysis (Beane et al.) in terms of phase shift extraction and bound state identification?
• RQ4 To what extent do source-dependent correlation functions affect the identification of ground states in lattice QCD two-nucleon systems?
• RQ5 Why does the HALQCD method fail to identify bound states despite consistent results from other lattice QCD approaches?

Key findings

• The NPLQCD analysis of the $^{1}S_{0}$ and $^{3}S_{1}$ two-nucleon channels at $m_\pi = 806$ MeV passes all three sanity checks: source independence, consistency of phase shifts with the infinite-volume bound state criterion, and agreement with effective range expansion fits.
• The 2017 refined analysis (Wagman et al.) of the same correlation functions as in Beane et al. (2013a) yields phase shifts that are consistent with the original analysis and with the bound state condition $k^{*2} = -\kappa^{(\infty)2}$ within uncertainties.
• The HALQCD preprint incorrectly reports a second state from Berkowitz et al. (2017) as the ground state, which invalidates several of its arguments; this error is corrected in the present comment.
• The results from multiple independent groups—including NPLQCD, PACS-CS, and others—show consistent, negatively shifted energies below the two-particle threshold, confirming bound states in both channels.
• The HALQCD method introduces unquantified systematic effects, as previously noted in the literature, which may explain its failure to identify bound states despite consistent results from other approaches.
• The NPLQCD results for the $^{1}S_{0}$ and $^{3}S_{1}$ channels are robust and pass all sanity checks, including source independence and consistency with the Lüscher formalism, confirming the existence of two-nucleon bound states at heavy quark masses.