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Register a new userChiral effective Lagrangian for doubly charmed baryons up to $mathcal{O}(q^4)$
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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.
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We calculate the masses and sigma terms of the doubly charmed baryons up to next-to-next-to-next-to-leading order (i.e., $mathcal{O}(p^4)$) in a covariant baryon chiral perturbation theory by using the extended-on-mass-shell renormalization scheme. Their expressions both in infinite and finite volumes are provided for chiral extrapolation in lattice QCD. As a first application, our chiral results of the masses are confronted with the existing lattice QCD data in the presence of finite volume corrections. Up to $mathcal{O}(p^3)$ all relevant low energy constants can be well determined. As a consequence, we obtain the physical values for the masses of $Xi_{cc}$ and $Omega_{cc}$ baryons by extrapolating to the physical limit. Our determination of the $Xi_{cc}$ mass is consistent with the recent experimental value by LHCb collaboration, however, larger than the one by SELEX collaboration. In addition, we predict the pion-baryon and strangeness-baryon sigma terms, as well as the mass splitting between the $Xi_{cc}$ and $Omega_{cc}$ states. Their quark mass dependences are also discussed. The numerical procedure can be applied to the chiral results of $mathcal{O}(p^4)$ order, where more unknown constants are involved, when more data are available for unphysical pion masses.
We adopt a covariant version of the naive dimensional analysis and construct the chiral two-nucleon contact Lagrangian constrained by Lorentz, parity, charge conjugation, hermitian conjugation, and chiral symmetries. We show that at $mathcal{O}(q^0)$, $mathcal{O}(q^2)$, $mathcal{O}(q^4)$, where $q$ denotes a generic small quantity, there are 4, 13, and 23 terms, respectively. We find that by performing $1/m_N$ expansions, the covariant Lagrangian reduces to the conventional non-relativistic one, which includes 2, 7, and 15 terms at each corresponding order.
In this work, we evaluate the lifetimes of the doubly charmed baryons $Xi_{cc}^{+}$, $Xi_{cc}^{++}$ and $Omega_{cc}^{+}$. We carefully calculate the non-spectator contributions at the quark level where the Cabibbo-suppressed diagrams are also include
d. The hadronic matrix elements are evaluated in the simple non-relativistic harmonic oscillator model. Our numerical results are generally consistent with that obtained by other authors who used the diquark model. However, all the theoretical predictions on the lifetimes are one order larger than the upper limit set by the recent SELEX measurement. This discrepancy would be clarified by the future experiment, if more accurate experiment still confirms the value of the SELEX collaboration, there must be some unknown mechanism to be explored.
We report results of a study of doubly charmed baryons and charmed strange baryons. The analysis is performed using a 980 fb^-1 data sample collected with the Belle detector at the KEKB asymmetric-energy e^+e^- collider. We search for doubly charmed baryons Xi_cc^+(+) with the Lambda_c^+K^-pi^+(pi^+) and Xi_c^0pi^+(pi^+) final states. No significant signal is observed. We also search for two excited charmed strange baryons, Xi_c(3055)^+ and Xi_c(3123)^+ with the Sigma_c^++(2455)K^- and Sigma_c^++(2520)K^- final states. The Xi_c(3055)^+ signal is observed with a significance of 6.6 standard deviations including systematic uncertainty, while no signature of the Xi_c(3123)^+ is seen. We also study properties of the Xi_c(2645)^+ and measure a width of 2.6 +- 0.2 (stat) +- 0.4 (syst) MeV/c^2, which is the first significant determination.
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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