Binding energy of the $T_{bb}$ tetraquark from lattice QCD with relativistic and nonrelativistic heavy-quark actions

Abstract

We present a new determination of the $\bar b \bar b u d$ ($J^P=1^+$, $I=0$) tetraquark binding energy using lattice QCD with domain-wall light quarks and a nonperturbatively tuned three-parameter anisotropic-clover ``relativistic'' action for the $b$ quarks. We also perform a direct comparison with a reanalysis of data generated in prior work using a lattice-NRQCD action for the $b$ quarks and otherwise identical parameters. Using the new data with relativistic $b$ quarks from seven different ensembles with multiple lattice spacings and pion masses, we perform combined chiral and continuum extrapolations and obtain $(m_{T_{bb}}-m_B-m_{B^*})_{\rm RHQ}=(-79 \pm 23)$ MeV. For the NRQCD data from five ensembles, we perform chiral-only extrapolations and obtain $(m_{T_{bb}}-m_B-m_{B^*})_{\rm NRQCD}=(-74 \pm 17 \pm 10)$ MeV. The lower magnitude of the results obtained here, compared to the original analysis in Phys. Rev. D 100, 014503 (2019), is due to the use of the symmetric parts of the correlation matrices with local four-quark operators only.

Figures (12)

• Figure 1: Effective energies of the $B$ and $B^*$ two-point functions from the F006 ensemble for the RHQ action (left) and the NRQCD action (right). The blue and green bands show the model-averaged $B$ and $B^*$ meson energies.
• Figure 2: Chiral-continuum extrapolation of the $B$-meson hyperfine splitting computed using the RHQ action. The curves show the fit model (\ref{['eq:HFSchiralcontinuum']}) evaluated for the three different lattice spacings for which we have data, and in the continuum limit. The dashed vertical line indicates the physical pion mass.
• Figure 3: Effective energies of the $\bar{b}\bar{b}ud$ [$I(J^P)=0(1^+)$] lowest two principal correlators, from the F006 ensemble computed with the RHQ action (left) and the NRQCD action (right). The blue horizontal band represents the model-averaged ground-state energy. Corresponding plots from the other ensembles are shown in Figs. \ref{['fig:EffNRQCD']} and \ref{['fig:EffRHQ']}.
• Figure 4: Upper panels: the $T_{bb}$ binding energies $\Delta E_0$ as a function of the value of $t_{\text{min}}/a$ used in the fit of the $T_{bb}$ lowest principal correlator (computed using the model-averaged $B$ and $B^*$ energies), along with the binding energy computed using the model-averaged $T_{bb}$, $B$, and $B^*$ energies. Lower panels: the normalized model weights for the fits to the $T_{bb}$ lowest principal correlator and for the fits to the $B$ and $B^*$ two-point functions, as a function of $t_{\text{min}}/a$. The left and right panels show the results from the RHQ and NRQCD actions, respectively. All results shown here are from the F006 ensemble. Corresponding plots for the other ensembles are shown in Figs. \ref{['fig:DeltaEtminRHQ']} and \ref{['fig:DeltaEtminNRQCD']}.
• Figure 5: Linear (left) and linear+log (right) chiral-only extrapolations of the NRQCD and RHQ results for the $T_{bb}$ binding energies obtained with the $3\times 3$ GEVP. The dashed vertical lines indicate the physical pion mass.