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Register a new userMagnetic moments of the spin-$frac{3}{2}$ doubly charmed baryons in covariant baryon chiral perturbation theory
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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.
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We have systematically investigated the magnetic moments of spin-$frac{1}{2}$ doubly charmed baryons in the framework of the heavy baryon chiral perturbation theory. In this paper, one loop corrections with intermediate spin-$frac{1}{2}$ and spin-$frac{3}{2}$ doubly charmed baryon states are considered. The numerical results are calculated to next-to-leading order: $mu_{Xi^{++}_{cc}}=0.35mu_{N}$, $mu_{Xi^{+}_{cc}}=0.62mu_{N}$, $mu_{Omega^{+}_{cc}}=0.41mu_{N}$. Our results may be useful for future experiment and chiral extrapolation of the lattice QCD.
We calculate the octet baryon magnetic moments in covariant baryon chiral perturbation theory with the extended-on-mass-shell renormalization scheme up to next-to-next-to-leading order. At this order, there are nine low-energy constants, which cannot be uniquely determined by the seven experimental data alone. We propose two strategies to circumvent this problem. First, we assume that chiral perturbation theory has a certain convergence rate and use this as one additional constraint to fix the low-energy constants by fitting to the experimental data. Second, we fit to lattice QCD simulations to determine the low-energy constants. We then compare the resulting predictions of the light and strange quark mass dependence of the octet baryon magnetic moments by the three mostly studied formulations of baryon chiral perturbation theory, namely, the extended-on-mass-shell, the infrared, and the heavy baryon approach. It is shown that once more precise lattice data become available, one will learn more about the convergence pattern of baryon chiral perturbation theory.
The chiral corrections to the magnetic moments of the spin-$frac{1}{2}$ doubly charmed baryons are systematically investigated up to next-to-next-to-leading order with heavy baryon chiral perturbation theory (HBChPT). The numerical results are calculated up to next-to-leading order: $mu_{Xi^{++}_{cc}}=-0.25mu_{N}$, $mu_{Xi^{+}_{cc}}=0.85mu_{N}$, $mu_{Omega^{+}_{cc}}=0.78mu_{N}$. We also calculate the magnetic moments of the other doubly heavy baryons, including the doubly bottomed baryons (bbq) and the doubly heavy baryons containing a light quark, a charm quark and a bottom quark (${bc}q$ and $[bc]q$): $mu_{Xi^{0}_{bb}}=-0.84mu_{N}$, $mu_{Xi^{-}_{bb}}=0.26mu_{N}$, $mu_{Omega^{-}_{bb}}=0.19mu_{N}$, $mu_{Xi^{+}_{{bc}q}}=-0.54mu_{N}$, $mu_{Xi^{0}_{{bc}q}}=0.56mu_{N}$, $mu_{Omega^{0}_{{bc}q}}=0.49mu_{N}$, $mu_{Xi^{+}_{[bc]q}}=0.69mu_{N}$, $mu_{Xi^{0}_{[bc]q}}=-0.59mu_{N}$, $mu_{Omega^{0}_{[bc]q}}=0.24mu_{N}$.
We obtain leading- and next-to-leading order predictions of chiral perturbation theory for several prominent moments of nucleon structure functions. These free-parameter free results turn out to be in overall agreement with the available empirical information on nearly all of the considered moments, in the region of low-momentum transfer ($Q^2 < 0.3$ GeV$^2$). Especially surprising is the situation for the spin polarizability $delta_{LT}$, which thus far was not reproducible in chiral perturbation theory for proton and neutron simultaneously. This problem, known as the $delta_{LT}$ puzzle, is not seen in the present calculation.
We investigate the electromagnetic transitions of the singly charmed baryons with spin 3/2, based on a pion mean-field approach, also known as the chiral quark-soliton model, taking into account the rotational $1/N_c$ corrections and the effects of flavor SU(3) symmetry breaking. We examine the valence- and sea-quark contributions to the electromagnetic transition form factors and find that the quadrupole form factors of the sea-quark contributions dominate over those of the valence-quark ones in the smaller $Q^2$ region, whereas the sea quarks only provide marginal contributions to the magnetic dipole transition form factors of the baryon sextet with spin 3/2. The effects of the flavor SU(3) symmetry breaking are in general very small except for the forbidden transition $Xi_c^0gammato Xi_c^{*0}$ by $U$-spin symmetry. We also discuss the widths of the radiative decays for the baryon sextet with spin 3/2, comparing the present results with those from other works.
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