Combined large-N_c and heavy-quark operator analysis for the chiral Lagrangian with charmed baryons

Abstract

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.

34 pages - one table - corrections applied

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• Charmed-Baryon Spectroscopy from Lattice QCD with N_f=2+1+1 Flavors
• DN interaction from meson exchange
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• Large-N_c operator analysis of 2-body meson-baryon counterterms in the chiral Lagrangian
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Cited by in corpus (11)

• Reconciling threshold and subthreshold expansions for pion-nucleon scattering
• On chiral extrapolations of charmed meson masses and coupled-channel reaction dynamics
• On the convergence of the chiral expansion for the baryon ground-state masses
• On kinematical constraints in the hadrogenesis conjecture for the baryon resonance spectrum
• Large-N_c sum rules for charmed baryons at subleading orders
• A framework for the chiral extrapolation of the charmed baryon ground-state masses
• Chiral dynamics of S-wave baryon resonances
• Constraints from a large-N_c analysis on meson-baryon interactions at chiral order Q^3
• Relations for low-energy coupling constants in baryon chiral perturbation theory derived from the chiral quark model
• Low-energy constants from charmed baryons on QCD lattices
• Combined heavy-quark symmetry and large-$N_c$ operator analysis for 2-body counterterms in the chiral Lagrangian with $D$ mesons and charmed baryons