Abstract
Inspired by the discovery of the spin-$\frac{1}{2}$ doubly charmed baryon ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}$ and the subsequent theoretical studies of its magnetic moments, we study the magnetic moments of its spin-$\frac{3}{2}$ heavy quark spin symmetry counterparts, up to the next-to-leading order in covariant baryon chiral perturbation theory with the extended-on-mass-shell renormalization scheme. With the tree-level contributions fixed by the quark model while the two low energy constants $C$ and $H$ controlling the loop contributions determined in two ways: the quark model (case 1) and lattice QCD simulations together with the quark model (case 2), we study the quark mass dependence of the magnetic moments and compare them with the predictions of the heavy baryon chiral perturbation theory. It is shown that the difference is sizable in case 1, but not in case 2 due to the smaller low energy constants $C$ and $H$, similar to the case of spin-$\frac{1}{2}$ doubly charmed baryons. Second, we predict the magnetic moments of the spin-$\frac{3}{2}$ doubly charmed baryons and compare them with those of other approaches. The predicted magnetic moments in case 2 for the spin-$\frac{3}{2}$ doubly charmed baryons are closer to those of other approaches. In addition, the large differences in case 1 and case 2 for the predicted magnetic moments may indicate the inconsistency between the quark model and the lattice QCD simulations, which should be checked by future experimental or more lattice QCD data.
Highlights
One of the spin-12 doubly charmed baryons, Ξþcc, was first reported by the SELEX Collaboration [1]
With the tree-level contributions fixed by the quark model while the two low energy constants C and H controlling the loop contributions determined in two ways: the quark model and lattice QCD simulations together with the quark model, we study the quark mass dependence of the magnetic moments and compare them with the predictions of the heavy baryon chiral perturbation theory
We turn to the quark model, where the magnetic moments can be calculated from the sum of the magnetic moments of the three constituent quarks, i.e., μq
Summary
One of the spin-12 doubly charmed baryons, Ξþcc, was first reported by the SELEX Collaboration [1]. The magnetic moments of spin-32 doubly charmed baryons have been examined in a variety of phenomenological models [21,22,23,24,25,26,27], the LCSR [28], the HB χPT [29], and lattice QCD simulations [30]. In addition to predicting the physical magnetic moments, we study their light-quark mass dependence such that they can be used to extrapolate future lattice QCD simulations to the physical point.
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