Low Energy Chiral Lagrangian in Curved Space-Time from the Spectral Quark Model

Details Low Energy Chiral Lagrangian in Curved Space-Time from the Spectral Quark Model Low Energy Chiral Lagrangian in Curved Space-Time from the Spectral Quark Model

2004-03-12

arxiv.org/abs/hep-ph/0403139v2

Phys.Rev. D70 (2004) 034031

Physics

High Energy Physics

High Energy Physics - Phenomenology

18 pages, no figures

Scientific paper

10.1103/PhysRevD.70.034031

We analyze the recently proposed Spectral Quark Model in the light of Chiral Perturbation Theory in curved space-time. In particular, we calculate the chiral coefficients $L_1, ..., L_{10}$, as well as the coefficients $L_{11}$, $L_{12}$, and $L_{13}$, appearing when the model is coupled to gravity. The analysis is carried for the SU(3) case. We analyze the pattern of chiral symmetry breaking as well as elaborate on the fulfillment of anomalies. Matching the model results to resonance meson exchange yields the relation between the masses of the scalar, tensor and vector mesons, $M_{f_0}=M_{f_2}=\sqrt{2} M_V= 4 \sqrt{3 /N_c} \pi f_\pi$. Finally, the large-$N_c$ limit suggests the dual relations in the vector and scalar channels, $M_V=M_S= 2 \sqrt{6 /N_c} \pi f_\pi $ and $^{1/2}_S = < r^2 >^{1/2}_V = 2 \sqrt{N_c} / f_\pi = 0.59 {\rm fm} $.

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