Evidence for the existence of $ud\overline{b}\overline{b}$ and the nonexistence of $ss\overline{b}\overline{b}$ and $cc\overline{b}\overline{b}$ tetraquarks from lattice QCD

We combine lattice QCD results for the potential of two static antiquarks in the presence of two quarks $qq$ of finite mass and quark model techniques to study possible existing $qq\overline{b}\overline{b}$ tetraquarks within the Born-Oppenheimer approximation. While there is strong indication for a bound four-quark state for $qq=(ud-du)/\sqrt{2}$, i.e., isospin $I=0$, which is stable with respect to QCD, i.e., can only decay weakly, we find clear evidence against the existence of corresponding tetraquarks with $qq\in \{uu,(ud+du)/\sqrt{2},dd\}$, i.e., isospin $I=1$, $qq=ss$, and $qq=cc$.

Figure 1

At small $\overline{b}\overline{b}$ separations $r$, the heavy antiquarks $\overline{b}\overline{b}$ form an antidiquark, which corresponds to a color triplet. There is essentially no screening of the $\overline{b}\overline{b}$ interaction due to the much farther separated light quarks $qq$.

Figure 2

At large $\overline{b}\overline{b}$ separations $r$, the $qq\overline{b}\overline{b}$ system is essentially a system of two $B_{(s,c)}^{(*)}$ mesons. The color charge of each of the antiquarks $\overline{b}$ is almost completely screened by one of the light quarks $q$. (a) $q\in \{u,d\}$. (b) $q=s$. (c) $q=c$.

Figure 3

Histograms used to estimate systematic errors for $\alpha$ and $d$ for the scalar $u/d$ channel (green, red, and blue bars represent systematic, statistical, and combined errors, respectively).

Figure 4

$\overline{b}\overline{b}$ potentials in the presence of two lighter quarks $qq$ ($qq$ flavor: up/down in green, strange in blue, charm in red; $qq$ spin: $j=0$, i.e., scalar, in the upper line, $j=1$, i.e., vector, in the lower line). The plotted curves with the error bands correspond to Eq. (4) with the parameter sets from Table 3. Vertical lines indicate lattice separations $r=2a,3a,\dots$ of lattice QCD potential results $V^{\mathrm{lat}}(r)$ used to generate the parameter sets from Table 3 via ${\chi }^2$ minimizing fits.

Figure 5

Histogram used to estimate the systematic error for the binding energy $E_B$ for the scalar $u/d$ channel and $m_H=m_B$ (green, red, and blue bars represent systematic, statistical, and combined errors, respectively).

Figure 6

Binding energy isolines $E_B(\alpha ,d)=\text{constant}$ in the $\alpha \text{−}d$-plane for $u/d$, $s$, and $c$ light quarks $qq$, respectively (gray dashed lines: $m_H=m_{B_{(s,c)}}$; gray solid lines: $m_H=m_b$). The red and green dots represent the fits of Eq. (4) to lattice QCD $\overline{b}\overline{b}$ potential results, while the red and green bars are the corresponding combined systematic and statistical errors.