THE ROLE OF RESONANCES IN CHIRAL PERTURBATION THEORY

THE ROLE OF RESONANCES IN CHIRAL PERTURBATION THEORY

September 1988 | G. Ecker, J. Gasser, A. Pich, E. de Rafael
This paper investigates the role of meson resonances in chiral perturbation theory (CHPT) for low-energy strong, electromagnetic, and weak interactions. The authors consider the coupling constants of the $ O(p^4) $ effective chiral lagrangian involving pseudoscalar fields, focusing on contributions from meson resonances. They find that these resonance contributions dominate the low-energy coupling constants, even though vector and axial-vector mesons are not treated as gauge bosons of local chiral symmetry. Vector meson dominance emerges as a prominent result of their analysis. The authors calculate the electromagnetic pion mass difference to lowest order in chiral perturbation theory with explicit resonance fields. They show that the electromagnetic pion mass difference is dominated by resonance (loop) contributions, which are consistent with experimental data. The results indicate that the coupling constants $ L_1, \ldots, L_{10} $ are completely dominated by resonance contributions, with vector and axial-vector mesons playing a significant role. The paper also discusses the chiral couplings of meson resonances to Goldstone bosons, showing that these couplings are determined by the transformation properties of the resonances under the chiral group $ SU(3)_L \times SU(3)_R $. The authors derive the effective chiral lagrangian for the case of $ SU(3)_L \times SU(3)_R $, including contributions from vector, axial-vector, scalar, and pseudoscalar mesons. The resonance parameters, such as masses and couplings, are determined using experimental data and theoretical arguments, including Weinberg's sum rules. The authors find that the axial-vector meson octet mass and coupling constants are consistent with experimental values. They also calculate the decay rate for $ a_1 \rightarrow \pi \gamma $, finding agreement with experimental data. The paper concludes that meson resonances play a crucial role in determining the low-energy coupling constants of the effective chiral lagrangian. The results support the idea of resonance dominance in chiral perturbation theory, with vector and axial-vector mesons contributing significantly to the low-energy constants. The electromagnetic pion mass difference is also shown to be dominated by resonance contributions, consistent with experimental observations. The authors emphasize that the results are consistent with the chiral symmetry and the underlying QCD dynamics.This paper investigates the role of meson resonances in chiral perturbation theory (CHPT) for low-energy strong, electromagnetic, and weak interactions. The authors consider the coupling constants of the $ O(p^4) $ effective chiral lagrangian involving pseudoscalar fields, focusing on contributions from meson resonances. They find that these resonance contributions dominate the low-energy coupling constants, even though vector and axial-vector mesons are not treated as gauge bosons of local chiral symmetry. Vector meson dominance emerges as a prominent result of their analysis. The authors calculate the electromagnetic pion mass difference to lowest order in chiral perturbation theory with explicit resonance fields. They show that the electromagnetic pion mass difference is dominated by resonance (loop) contributions, which are consistent with experimental data. The results indicate that the coupling constants $ L_1, \ldots, L_{10} $ are completely dominated by resonance contributions, with vector and axial-vector mesons playing a significant role. The paper also discusses the chiral couplings of meson resonances to Goldstone bosons, showing that these couplings are determined by the transformation properties of the resonances under the chiral group $ SU(3)_L \times SU(3)_R $. The authors derive the effective chiral lagrangian for the case of $ SU(3)_L \times SU(3)_R $, including contributions from vector, axial-vector, scalar, and pseudoscalar mesons. The resonance parameters, such as masses and couplings, are determined using experimental data and theoretical arguments, including Weinberg's sum rules. The authors find that the axial-vector meson octet mass and coupling constants are consistent with experimental values. They also calculate the decay rate for $ a_1 \rightarrow \pi \gamma $, finding agreement with experimental data. The paper concludes that meson resonances play a crucial role in determining the low-energy coupling constants of the effective chiral lagrangian. The results support the idea of resonance dominance in chiral perturbation theory, with vector and axial-vector mesons contributing significantly to the low-energy constants. The electromagnetic pion mass difference is also shown to be dominated by resonance contributions, consistent with experimental observations. The authors emphasize that the results are consistent with the chiral symmetry and the underlying QCD dynamics.
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