Electromagnetic form factors of spin-$1/2$ doubly charmed baryons

We study the electromagnetic form factors of the doubly charmed baryons, using covariant chiral perturbation theory within the extended on-mass-shell scheme. Vector-meson contributions are also taken into account. We present results for the baryon magnetic moments, charge, and magnetic radii. While some of the chiral Lagrangian parameters could be set to values determined in previous works, the available lattice results for ${\mathrm{\Xi }}_{cc}^{+}$ and ${\mathrm{\Omega }}_{cc}^{+}$ only allow for robust constraints on the low-energy constant combination, $c_{89}(=-\frac{1}{3}{c}_8+4c_9)$. The couplings of the doubly charmed baryons to the vector mesons have been estimated assuming the Okubo-Zweig-Iizuka rule. We also give the expressions for the form factors of the double-beauty baryons considering the masses predicted in the framework of quark models. A comparison of our results with those obtained in heavy baryon chiral perturbation theory at the same chiral order is made.

Figure 1

Feynman diagram of the vector-meson contribution to the form factor.

Figure 2

Feynman diagrams contributing to the electromagnetic form factors up to order $O(q^3)$. Wiggly, dashed, and solid lines correspond to photon, mesons, and baryons, respectively. The numbers in the circles show the chiral order of the vertices.

Figure 3

Magnetic and electric form factor fit results compared to the lattice data from Refs. [33, 34] and [35], denoted as L1, L2 and L3, respectively. We show the results for four different pion mass configurations: at the physical point (dotted line), at $M_{\pi }=0.3\mathrm{GeV}$ (blue), $M_{\pi }=0.41\mathrm{GeV}$ (red), $M_{\pi }=0.57\mathrm{GeV}$ (green). The data points for $M_{\pi }=0.3\mathrm{GeV}$ ($M_{\pi }=0.57\mathrm{GeV}$) were shifted to the left(right) for better visibility, but they all correspond to the same $Q^2$ value as those for $M_{\pi }=0.41\mathrm{GeV}$.