Magnetic moments of the spin-$\frac{1}{2}$ singly charmed baryons in chiral perturbation theory

We systematically derive the analytical expressions of the magnetic moments of the spin-$\frac{1}{2}$ singly charmed baryons to the next-to-next-to-leading order in the heavy baryon chiral perturbation theory (HBChPT). We discuss the analytical relations between the magnetic moments. We estimate the low-energy constants (LECs) in two scenarios. In the first scenario, we use the quark model and Lattice QCD simulation results as input. In the second scenario, the heavy quark symmetry is adopted to reduce the number of the independent LECs, which are then fitted using the data from the Lattice QCD simulations. We give the numerical results to the next-to-leading order for the antitriplet charmed baryons and to the next-to-next-to-leading order for the sextet states.

Figure 1

The blue and black triangles denote the heavy baryons in the ${\overline{3}}_f$ and the $6_f$ flavor representations, respectively. $[\dots ]$ and $\{\dots \}$ denotes the two light quarks are antisymmetric and symmetric in the flavor space, respectively.

Figure 2

The loop diagrams contribute to the magnetic moments of the heavy baryons up to $\mathcal{O}(p^3)$. The solid dot represents the $\mathcal{O}(p^2)$ vertex. The single and double lines denote the spin-$\frac{1}{2}$ and spin-$\frac{3}{2}$ heavy baryons, respectively.