[Paper Review] Quarkonium-Nucleus Bound States from Lattice QCD

Silas R. Beane, Emmanuel Chang+6 more|DSpace@MIT (Massachusetts Institute of Technology)|Oct 26, 2014

Cold Atom Physics and Bose-Einstein Condensates4 citations

TL;DR

This lattice QCD study computes quarkonium-nucleus bound states at the SU(3) flavor-symmetric point, finding significant binding for both charmonium and strangeonium with light nuclei (A=1–4), with extrapolated binding energy to nuclear matter estimated at $ B^\text{NM}_\text{phys} \lesssim 40~\text{MeV} $ at physical quark masses. The results demonstrate the existence of color van der Waals forces via multi-gluon exchange, with binding arising from chromo-polarizability effects in hadronic systems without shared valence quarks.

ABSTRACT

Quarkonium-nucleus systems are composed of two interacting hadronic states without common valence quarks, which interact primarily through multi-gluon exchanges, realizing a color van der Waals force. We present lattice QCD calculations of the interactions of strange and charm quarkonia with light nuclei. Both the strangeonium-nucleus and charmonium-nucleus systems are found to be relatively deeply bound when the masses of the three light quarks are set equal to that of the physical strange quark. Extrapolation of these results to the physical light-quark masses suggests that the binding energy of charmonium to nuclear matter is B < 40 MeV.

Motivation & Objective

• To investigate the existence and properties of quarkonium-nucleus bound states in quantum chromodynamics (QCD) using nonperturbative lattice field theory.
• To isolate chromo-polarization effects in systems without shared valence quarks, thereby probing the color van der Waals force mediated by multi-gluon exchange.
• To determine whether charmonium and strangeonium form bound states with light nuclei and nuclear matter at the SU(3) symmetric point and extrapolate to physical quark masses.
• To assess the role of finite-volume effects and scattering state contamination in identifying true bound states from lattice correlation functions.

Proposed method

• Lattice QCD simulations are performed at the SU(3) flavor-symmetric point with pion and kaon masses set to ~805 MeV, using a single lattice spacing with O(a) improved clover action.
• Correlation functions for quarkonium-nucleus systems are computed in multiple spatial volumes (L=24, 32) to distinguish bound states from scattering states via the Lüscher method.
• Energy splittings between ground and excited states are extracted using variational methods on large basis sets of interpolating operators.
• Finite-volume effects are analyzed by comparing energy levels across volumes; binding is inferred from energy shifts below the inelastic threshold.
• Scattering state contamination is assessed by comparing energy differences in different volumes and using the Lüscher formula to estimate mixing.
• Extrapolation to physical quark masses is performed using a leading-order estimate based on the assumption of saturation of binding for A=3 and A=4 systems.

Experimental results

Research questions

• RQ1 Do quarkonium-nucleus systems form bound states in lattice QCD at the SU(3) symmetric point?
• RQ2 What is the magnitude of binding energy for charmonium and strangeonium with light nuclei (A=1 to 4)?
• RQ3 How do finite-volume effects and scattering state contamination affect the identification of true bound states?
• RQ4 Can the binding energy to nuclear matter be estimated from lattice results at unphysical quark masses, and what is its extrapolated value at physical quark masses?

Key findings

• Significant binding is found for both charmonium and strangeonium with light nuclei (A=1 to 4) at the SU(3) symmetric point, with binding energies deeper than 1 MeV.
• The binding energy for charmonium-nucleus systems is estimated to saturate at ~60 MeV in nuclear matter at the unphysical pion mass of 805 MeV.
• Extrapolation to physical quark masses yields an estimated binding energy for charmonium in nuclear matter of $ B^\text{NM}_\text{phys} \lesssim 40~\text{MeV} $, though uncertainties remain unquantified.
• Scattering state contamination is found to be small and consistent with zero, suggesting the observed bound states are robust, though it could only lead to deeper binding if present.
• The results support the existence of color van der Waals forces in quarkonium-nucleus systems, mediated by multi-gluon exchange, with binding arising from chromo-polarizability.
• The study demonstrates that lattice QCD can reliably compute such exotic hadronic molecules, providing a foundation for future high-precision calculations at smaller quark masses and larger nuclei.