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Register a new userEffective chiral theory of large N_C QCD of mesons
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Bing An Li
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En effective chiral theory of large N_C QCD of pseudoscalar, vector, and axial-vector mesons is reviewed.
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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.
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.
We derive the chiral effective Lagrangian for excited heavy-light mesons from QCD under proper approximations. We focus on the chiral partners with $j_l^P=frac{3}{2}^+$ and $j_l^P=frac{3}{2}^-$ which amounts to ($1^+,2^+$) and ($1^-,2^-$) states respectively. The low energy constants including the masses of the chiral partners are calculated. The calculated spectrum for the excited mesons are found roughly consistent with experimental data. In addition, our results indicate that quantum numbers of $B_J(5970)$ can be identified with $1^-$ or $2^-$.
An extended $U(3)_Lbigotimes U(3)_R$ chiral theory which includes pseudoscalar and vector meson nonets as dynamic degrees of freedom is presented. We combine a hidden symmetry approach with a general procedure of including the $eta$ meson into chiral theory. The $U(3)_Lbigotimes U(3)_R$ and the SU(3) symmetries are broken by the mechanism based on quark mass matrix. Meson radiative decay widths are parameterized in terms of a single and real $eta-eta$ mixing angle $theta_P$, a U(3)_V symmetry breaking scale parameter c_W, and the radiative decay constants $F_pi, F_K, F_eta, F_{eta}$, for the $pi, eta$, K, $eta $ mesons, respectively. Taking $F_pi = 93 MeV$, a global fit to decay width data yields F_K/F_pi = 1.16 pm 0.11, F_eta/F_pi = 1.14pm 0.04, F_{eta}/F_pi = 1.09 pm 0.04, c_W = -0.19 pm0.03, theta_P =-(15.4 pm 1.8)^o.
As a successive work to [Phys.Rev.D 102 (2020), 034034], we derive the $1/m_Q$ corrections to chiral effective Lagrangian for heavy-light mesons from QCD under proper approximations. The low energy constants in the effective Lagrangian are expressed in terms of the light quark self-energy and heavy quark mass $m_Q$. Numerical results of the low energy constants with $1/m_Q$ corrections are given. We find that the results of pion decay constant and the masses of heavy-light mesons are improved coherently compared to that obtained in the heavy quark limit.
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