Electromagnetic form factors and structure of the $T_{bb}$ tetraquark from lattice QCD

Abstract

We present the first lattice QCD determination of the electromagnetic form factors of the exotic tetraquark $T_{bb} \ (bb \bar u \bar d)$ with quantum numbers $I( J^P ) = 0( 1^+ )$. The extracted form factors encode information about its internal structure, including the charge distribution and the magnetic dipole moments, determined separately for the light and heavy quarks. Our results provide evidence in favor of it being a bound state consisting of a compact heavy diquark $[bb]$ in a color-antitriplet with spin one, and a light antidiquark $[\bar u \bar d]$ in a color-triplet with spin zero. The charge radius of $T_{bb}$ is found to be significantly smaller than the combined charge radii of $B$ and $B^*$ mesons. These two comprise the lowest-lying threshold $BB^*$ in the channel we are considering, and their electric charge form factors are also determined. The computations were performed on a single CLS ensemble with $N_f = 2+1$ dynamical quarks and a lattice spacing of approximately $a \approx0.064 \ \mathrm{fm}$ at the pion mass $m_π\approx 290 \ \mathrm{MeV}$.

Figures (3)

• Figure 1: a) Example of a connected Wick contraction diagram generated by the $T_{bb}$ three-point correlator \ref{['eq:threept_corr']}, while disconnected diagrams were not computed in this study. b) Pictorial representation of the resulting distributions for light and heavy quarks.
• Figure 2: a) Comparison of charge form factors $F_C (Q^2)$ of hadrons $h = T_{bb}, B(b\bar{u}), B^*(b\bar{u}), \pi(d \bar{u})$, shown as a function of $Q^2$. Discrete markers show lattice data, while the bands represent the $z-$expansion fits. Second order expansion (up to and including $n\!=\!2$ in eq. \ref{['eq:zexp']}) was used to parametrize $T_{bb}, \ B, \ B^*$ electric form factors, while a first order expansion sufficed for an adequate parametrization of the pion form factor. b) Position-space charge densities $\rho(r)$, represented in the form of $-\tfrac{\mathrm{d}e}{\mathrm{d}r}=-4\pi r^2\rho$, related to the form factors via a Fourier transform. Negative values of charge form factors and distributions are shown, given that considered hadrons have negative charge.
• Figure 3: Form factors of the $T_{bb}$. Each of the subplots shows the total value of the form factors with separate contributions yielded by the light current $\hat{\jmath}_{u/d}^\mu$ and the heavy current $\hat{\jmath}_b^{\mu}$. The shaded vertical bands at $Q^2 = 0$ in b) and c) indicate the values of the magnetic dipole moments $2m_{T_{bb}}\cdot \mu$ and electric quadrupole moments $m_{T_{bb}}^2 \cdot \cal Q$, respectively, also found in Table \ref{['tab:tbb_moments']}. The points on the rightmost plot have been slightly displaced horizontally for improved visibility.