Are two nucleons bound in lattice QCD for heavy quark masses? -- Consistency check with Lüscher's finite volume formula --

Abstract

On the basis of the Lüscher's finite volume formula, a simple test (consistency check or sanity check) is introduced and applied to inspect the recent claims of the existence of the nucleon-nucleon ($NN$) bound state(s) for heavy quark masses in lattice QCD. We show that the consistency between the scattering phase shifts at $k^2>0$ and/or $k^2<0$ obtained from the lattice data and the behavior of phase shifts from the effective range expansion (ERE) around $k^2=0$ exposes the validity of the original lattice data, otherwise such information is hidden in the energy shift $\Delta E$ of the two nucleons on the lattice. We carry out this sanity check for all the lattice results in the literature claiming the existence of the $NN$ bound state(s) for heavy quark masses, and find that (i) some of the $NN$ data show clear inconsistency between the behavior of ERE at $k^2>0$ and that at $k^2<0$, (ii) some of the $NN$ data exhibit singular behavior of the low energy parameter (such as the divergent effective range) at $k^2<0$, (iii) some of the $NN$ data have the unphysical residue for the bound state pole in S-matrix, and (iv) the rest of the $NN$ data are inconsistent among themselves. Furthermore, we raise a caution of using the ERE in the case of the multiple bound states. Our finding, together with the fake plateau problem previously pointed out by the present authors, brings a serious doubt on the existence of the $NN$ bound states for pion masses heavier than 300 MeV in the previous studies.

39 pages, 16 figures, and 11 tables, title changed, references and comment added

References in corpus (9)

• Nuclear Force from Lattice QCD
• Light Nuclei and Hypernuclei from Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry
• Hyperon-nucleon force from lattice QCD
• Spin-2 $N\Omega$ Dibaryon from Lattice QCD
• Nuclear Force from Monte Carlo Simulations of Lattice Quantum Chromodynamics
• Mirage in Temporal Correlation functions for Baryon-Baryon Interactions in Lattice QCD
• Construction of energy-independent potentials above inelastic thresholds in quantum field theories
• Signatures of S-wave bound-state formation in finite volume
• Recent results on the meson and baryon spectrum from lattice QCD

Cited by in corpus (52)

• Scattering processes and resonances from lattice QCD
• $N\Omega$ dibaryon from lattice QCD near the physical point
• Most Strange Dibaryon from Lattice QCD
• Lattice QCD investigation of a doubly-bottom $\bar{b}\bar{b}ud$ tetraquark with quantum numbers $I(J^P)=0(1^{+})$
• Evidence for charm-bottom tetraquarks and the mass dependence of heavy-light tetraquark states from lattice QCD
• Baryon-Baryon Interactions and Spin-Flavor Symmetry from Lattice Quantum Chromodynamics
• Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
• Lattice QCD study of the $H$ dibaryon using hexaquark and two-baryon interpolators
• Heavy hadronic molecules with pion exchange and quark core couplings: a guide for practitioners
• Numerical study of the relativistic three-body quantization condition in the isotropic approximation
• Towards grounding nuclear physics in QCD
• Weakly bound $H$ dibaryon from SU(3)-flavor-symmetric QCD
• Lattice QCD and baryon-baryon interactions: HAL QCD method
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• Two-nucleon S-wave interactions at the $SU(3)$ flavor-symmetric point with $m_{ud}\simeq m_s^{\mathrm{phys}}$: a first lattice QCD calculation with the stochastic Laplacian Heaviside method
• Systematics of the HAL QCD Potential at Low Energies in Lattice QCD
• $DK$ $I=0,$ $D\bar{K}$ $I=0,1$ scattering and the $D_{s0}^{\ast }(2317)$ from lattice QCD
• New Ideas in Constraining Nuclear Forces
• ${\Lambda }_{c}N$ interaction from lattice QCD and its application to ${\Lambda }_c$ hypernuclei
• Glueball scattering cross section in lattice SU(2) Yang-Mills theory
• A variational study of two-nucleon systems with lattice QCD
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Low-energy Scattering and Effective Interactions of Two Baryons at $m_{\pi }\sim 450$ MeV from Lattice Quantum Chromodynamics
• Consistency between Lüscher's finite volume method and HAL QCD method for two-baryon systems in lattice QCD
• The Tetraquark Candidate Zc(3900) from Dynamical Lattice QCD Simulations
• Turning the nuclear energy density functional method into a proper effective field theory: reflections
• Shallow Bound States and Hints for Broad Resonances with Quark Content $\bar{b}\bar{c}ud$ in $B$-$\bar{D}$ and $B^{\ast }$-$\bar{D}$ Scattering from Lattice QCD
• Charmonium resonances with $J^{PC}=1^{--}$ and $3^{--}$ from $\bar{D}D$ scattering on the lattice
• Baryon interactions from lattice QCD with physical quark masses -- Nuclear forces and $\Xi \Xi$ forces --
• Partial wave decomposition on the lattice and its applications to the HAL QCD method
• Singlet channel scattering in a Composite Higgs model on the lattice
• $d^{\ast }(2380)$ dibaryon from lattice QCD
• Excited $J^{--}$ meson resonances at the SU(3) flavor point from lattice QCD
• Pion-mass dependence of the nucleon-nucleon interaction
• Charmonium-nucleon interactions from the time-dependent HAL QCD method
• Optimized Two-Baryon Operators in Lattice QCD
• $I=2$ $\pi \pi$ potential in the HAL QCD method with all-to-all propagators
• Strange Nuclear Physics from QCD on Lattice
• Phenomenological view on baryon-baryon potentials from lattice QCD simulations
• Two-baryon systems from HAL QCD method and the mirage in the temporal correlation of the direct method
• The HAL QCD potential in $I=1$ $\pi \pi$ system with the $\rho$ meson bound state
• Lattice QCD and Baryon-Baryon Interactions
• Asymptotic behavior of Nambu-Bethe-Salpeter wave functions for scalar systems with a bound state
• Di-nucleons do not form bound states at heavy pion mass
• Coupled-channel ${\Lambda }_c{K}^{+}-p{D}_s$ Interaction in Flavor $\text{SU}\left(3\right)$ Limit of Lattice QCD
• Renormalization of a Contact Interaction on a Lattice
• Hermitizing the HAL QCD potential in the derivative expansion
• Hyperon-Nucleon Interaction from Lattice QCD at $(m_{\pi },m_K)\approx (146,525)$ MeV
• ${\eta }_c{\eta }_c$ and $J/\psi J/\psi$ scatterings from lattice QCD
• The one-pion-exchange potential with contact terms from lattice QCD simulations
• Wavefunction-based operator optimization for two-hadron systems in lattice QCD
• Lattice results on dibaryons and baryon--baryon interactions