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Register a new userCombined large-N_c and heavy-quark operator analysis for the chiral Lagrangian with charmed baryons
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The chiral $SU(3)$ Lagrangian with charmed baryons of spin $J^P=1/2^+$ and $J^P=3/2^+$ is analyzed. We consider all counter terms that are relevant at next-to-next-to-next-to-leading order (N$^3$LO) in a chiral extrapolation of the charmed baryon masses. At N$^2$LO we find 16 low-energy parameters. There are 3 mass parameters for the anti-triplet and the two sextet baryons, 6 parameters describing the meson-baryon vertices and 7 symmetry breaking parameters. The heavy-quark spin symmetry predicts four sum rules for the meson-baryon vertices and degenerate masses for the two baryon sextet fields. Here a large-$N_c$ operator analysis at NLO suggests the relevance of one further spin-symmetry breaking parameter. Going from N$^2$LO to N$^3$LO adds 17 chiral symmetry breaking parameters and 24 symmetry preserving parameters. For the leading symmetry conserving two-body counter terms involving two baryon fields and two Goldstone boson fields we find 36 terms. While the heavy-quark spin symmetry leads to $36-16=20$ sum rules, an expansion in $1/N_c$ at next-to-leading order (NLO) generates $36-7= 29$ parameter relations. A combined expansion leaves 3 unknown parameters only. For the symmetry breaking counter terms we find 17 terms, for which there are $17-9=8$ sum rules from the heavy-quark spin symmetry and $17-5=12 $ sum rules from a $1/N_c$ expansion at NLO.
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The chiral SU(3) Lagrangian with pseudoscalar and vector $D$ mesons and with the octet and decuplet baryons is considered. The leading two-body counter terms involving two baryon fields and two $D$ meson fields are constructed in the open-charm sector. There are 26 terms. A combined expansion in the inverse of the charm quark mass and in the inverse of the number of colors provides sum rules that reduce the number of free parameter down to 5 only. Our result shows the feasibility of a systematic computation of the open-charm baryon spectrum based on coupled-channel dynamics.
The chiral effective meson-baryon Lagrangian for the description of interactions between the doubly charmed baryons and Goldstone bosons is constructed up to the order of $q^{4}$. The numbers of linearly independent invariant monomials of $mathcal{O}(q^2)$, $mathcal{O}(q^3)$ and $mathcal{O}(q^4)$ are 8, 32 and 218, in order. The obtained Lagrangian can be used to study the chiral dynamics and relevant phenomenology of the doubly charmed baryons at complete one-loop level in future. For completeness, the non-relativistic reduction of the Lagrangian is also discussed.
Baryon magnetic moments are computed in baryon chiral perturbation theory in the large-$N_c$ limit at one-loop order, where $N_c$ is the number of color charges. Orders $mathcal{O}(m_q^{1/2})$ and $mathcal{O}(m_q ln m_q)$ corrections are both evaluated including all the operator structures that participate at the physical value $N_c=3$. The complete expressions for octet and decuplet baryon magnetic moments in addition to decuplet-octet baryon transition moments are thus compared to their available counterparts obtained in heavy baryon chiral perturbation theory for degenerate intermediate baryons in the loops. Theoretical expressions fully agree at the physical values $N_c=3$ and $N_f=3$ flavors of light quarks. Some numerical evaluations are produced via a least-squares fit to explore the free parameters in the analysis. Results point out the necessity of incorporating the effects of non-degenerate intermediate baryons in the loops for a consistent determination of these free parameters.
Both unitary chiral theories and lattice QCD simulations show that the $DK$ interaction is attractive and can form a bound state, namely, $D^*_{s0}(2317)$. Assuming the validity of the heavy antiquark-diquark symmetry (HADS), the $Xi_{cc}bar{K}$ interaction is the same as the $DK$ interaction, which implies the existence of a $Xi_{cc}bar{K}$ bound state with a binding energy of $49-64$ MeV. In this work, we study whether a $Xi_{cc}Xi_{cc}bar{K}$ three-body system binds. The $Xi_{cc}Xi_{cc}$ interaction is described by exchanging $pi$, $sigma$, $rho$, and $omega$ mesons, with the corresponding couplings related to those of the $NN$ interaction via the quark model. We indeed find a $Xi_{cc}Xi_{cc}bar{K}$ bound state, with quantum numbers $J^P=0^-$, $I=frac{1}{2}$, $S=1$ and $C=4$, and a binding energy of $80-118$ MeV. It is interesting to note that this system is very similar to the well-known $NNbar{K}$ system, which has been studied extensively both theoretically and experimentally. Within the same framework, we show the existence of a $NNbar{K}$ state with a binding energy of $35-43$ MeV, consistent with the results of other theoretical works and experimental data, which serves as a consistency check on the predicted $Xi_{cc}Xi_{cc}bar{K}$ bound state.
We study charmed baryon resonances that are generated dynamically from a coupled-channel unitary approach that implements heavy-quark symmetry. Some states can already be identified with experimental observations, such as $Lambda_c(2595)$, $Lambda_c(2660)$, $Sigma_c(2902)$ or $Lambda_c(2941)$, while others need a compilation of more experimental data as well as an extension of the model to include higher order contributions. We also compare our model to previous SU(4) schemes.
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