Sanity check for $NN$ bound states in lattice QCD with L\"uscher's finite volume formula -- Exposing Symptoms of Fake Plateaux --

TL;DR

This paper critically examines the validity of $NN$ bound state results in lattice QCD, exposing issues like operator dependence and fake plateaux, and challenges recent claims of correct volume independence and effective range expansion fits.

Contribution

It provides further evidence of operator dependence of plateaux and critiques the physical validity of recent lattice QCD analyses of $NN$ bound states.

Findings

Operator dependences of plateaux exist with low P-values.

Volume independence does not confirm correctness.

ERE fits violate the physical pole condition.

Abstract

A sanity check rules out certain types of obviously false results, but does not catch every possible error. After reviewing such a sanity check for $NN$ bound states with the L\"uscher's finite volume formula[1-3], we give further evidences for the operator dependence of plateaux, a symptom of the fake plateau problem, against the claim in [4]. We then present our critical comments on [5] by NPLQCD: (i) Operator dependences of plateaux in NPL2013[6,7] exist with the $P$-values of 4--5%. (ii) The volume independence of plateaux in NPL2013 does not prove their correctness. (iii) Effective range expansion (ERE) fits in NPL2013 violate the physical pole condition. (iv) Ref.[5] is partly based on new data and analysis different from the original ones[6,7]. (v) A new ERE in Refs.[5,8] does not satisfy the L\"uscher's finite volume formula. [1] T. Iritani et al., JHEP 10 (2016) 101. [2] S. Aoki et al., PoS (LATTICE2016) 109. [3] T. Iritani et al., 1703.0720. [4] T. Yamazaki et al., PoS (LATTICE2017) 108. [5] S.R. Beane et al., 1705.09239. [6] S.R. Beane et al., PRD87 (2013) 034506. [7] S.R. Beane et al., PRC88 (2013) 024003. [8] M.L. Wagman et al., 1706.06550.