Abstract
We use lattice QCD to investigate the spectrum of the $\bar{b} \bar{b} u d$ four-quark system with quantum numbers $I(J^P) = 0(1^+)$. We use five different gauge-link ensembles with $2+1$ flavors of domain-wall fermions, including one at the physical pion mass, and treat the heavy $\bar{b}$ quark within the framework of lattice nonrelativistic QCD. Our work improves upon previous similar computations by considering in addition to local four-quark interpolators also nonlocal two-meson interpolators and by performing a L\"uscher analysis to extrapolate our results to infinite volume. We obtain a binding energy of $(-128 \pm 24 \pm 10) \, \textrm{MeV}$, corresponding to the mass $(10476 \pm 24 \pm 10) \, \textrm{MeV}$, which confirms the existence of a $\bar{b} \bar{b} u d$ tetraquark that is stable with respect to the strong and electromagnetic interactions.
Highlights
Mesons, i.e., hadrons with integer spin, were first envisioned by Gell-Mann and Zweig [1,2] to be built from one, two or more quark-antiquark pairs
Exotic mesons can be characterized as having JPC quantum numbers that cannot be constructed in the simple quark-antiquark model, or as having a manifestly exotic quark flavor content
We used the conjugate gradient (CG) solver combined with low-mode deflation, where in the case of the approximate propagators the CG iteration count is fixed to a smaller value, NCG;sl, than needed for the exact propagators
Summary
I.e., hadrons with integer spin, were first envisioned by Gell-Mann and Zweig [1,2] to be built from one, two or more quark-antiquark pairs. In this paper we perform a lattice QCD study of the bb ̄ ud four-quark system with quantum numbers IðJPÞ 1⁄4 0ð1þÞ, using NRQCD bquarks and domain-wall light quarks We make use of both local interpolating fields (in which the four quarks are jointly projected to zero momentum) and nonlocal interpolating fields (in which each of the two quark-antiquark pairs forming a color-singlet is projected to zero momentum individually) It has been shown in previous studies of other systems [44,45] that including both types of interpolating fields is required to reliably determine ground-state energies in exotic channels.
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