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

Abstract

We present the first lattice QCD calculation of electromagnetic form factors of a tetraquark, focusing on the $T_{bb} = bb\bar u \bar d$ with quantum numbers $I(J^P) = 0(1^+)$. The electromagnetic current probes the charge monopole, magnetic dipole and the electric quadrupole distributions within the tetraquark. From it, we find evidence that its structure consists of a compact heavy diquark $[bb]$ in spin one, color-antitriplet configuration, and a light antidiquark $[\bar u \bar d]$ in spin zero, color-triplet configuration. The computations were performed on a single CLS ensemble with $N_f = 2+1$ dynamical quarks at a lattice spacing $a\approx 0.064$ fm and with a pion mass $m_π\approx 290$ MeV.

Figures (4)

• Figure 1: Generic connected diagram generated by the Wick contractions in the $T_{bb}$ three-point correlator \ref{['eq:3ptformula']}.
• Figure 2: a) Charge form factors of $T_{bb}, B= b\bar{u}, B^* = b\bar{u} , \pi = d \bar{u}$, shown as a function of $Q^2$. Discrete points represent lattice data, while the continuous bands show $z-$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 $-\tfrac{\mathrm{d}e}{\mathrm{d}r}=-4\pi r^2\rho$, are related to the form factors via a Fourier transform. Negative values of charge form factors and distributions are shown, given that considered hadrons are negatively charged.
• Figure 3: Form factors of the $T_{bb}$. Each subfigure 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 crosses in a) mark values to which each of the charge form factors have been normalized at $Q^2=0$, while the shaded vertical bands in b) and c) indicate the values of 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 are slightly horizontally displaced for improved visibility.
• Figure 4: Pictorial representation of the spatial, spin and color composition of the $T_{bb}$, as determined by from its EM form factors.