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Register a new userBaryon magnetic moment in large-$N_c$ chiral perturbation theory: Complete analysis for $N_c=3$
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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.
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We present a calculation of the $eta$-$eta$ mixing in the framework of large-$N_c$ chiral perturbation theory. A general expression for the $eta$-$eta$ mixing at next-to-next-to-leading order (NNLO) is derived, including higher-derivative terms up to fourth order in the four momentum, kinetic and mass terms. In addition, the axial-vector decay constants of the $eta$-$eta$ system are determined at NNLO. The numerical analysis of the results is performed successively at LO, NLO, and NNLO. We investigate the influence of one-loop corrections, OZI-rule-violating parameters, and $mathcal{O}(N_c p^6)$ contact terms.
We consider the chiral Lagrangian for baryon fields with J^P =frac{1}{2}^+ or J^P =frac{3}{2}^+ quantum numbers as constructed from QCD with up, down and strange quarks. The specific class of counter terms that are of chiral order Q^3 and contribute to meson-baryon interactions at the two-body level is constructed. Altogether we find 24 terms. In order to pave the way for realistic applications we establish a set of 22 sum rules for the low-energy constants as they are implied by QCD in the large-N_c limit. Given such a constraint there remain only 2 independent unknown parameters that need to be determined by either Lattice QCD simulations or directly from experimental cross section measurements. At subleading order we arrive at 5 parameters.
En effective chiral theory of large N_C QCD of pseudoscalar, vector, and axial-vector mesons is reviewed.
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.
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.
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