Magnetic moments of the spin-$\frac{3}{2}$ doubly charmed baryons in covariant baryon chiral perturbation theory

Abstract

Inspired by the discovery of the spin-$\frac{1}{2}$ doubly charmed baryon ${\Xi }_{cc}^{++}$ 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 (BChPT) with the extended-on-mass-shell renormalization (EOMS) scheme. With the tree-level contributions fixed by the quark model while the two low energy constants (LECs) $C$ 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 (HB ChPT). It is shown that the difference is sizable in case 1, but not in case 2 due to the smaller LECs $C$ 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.

a sign problem corrected, and comparion with the lattice QCD data added

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Cited by in corpus (6)

• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Screening of quark charge and mixing effects on transition moments and M1 decay widths of baryons
• Investigating the M1 radiative decay behaviors and the magnetic moments of the predicted triple-charm molecular-type pentaquarks
• Strong decays of the low-lying doubly bottom baryons
• Electromagnetic polarizabilities of the spin-$\frac{1}{2}$ singly heavy baryons in heavy baryon chiral perturbation theory
• Chiral Lagrangians for spin-$\frac{1}{2}$ and spin-$\frac{3}{2}$ doubly charmed baryons