On the radiative decays of light vector and axial-vector mesons

Abstract

We study the light vector and axial-vector mesons. According to the hadrogenesis conjecture the nature of the two types of states is distinct. The axial-vector mesons are generated dynamically by coupled-channel interactions based on the chiral Lagrangian written down in terms of the Goldstone bosons and the light vector mesons. We propose a novel counting scheme that arises if the chiral Lagrangian is supplemented by constraints from large-N_c QCD in the context of the hadrogenesis conjecture. The counting scheme is successfully tested by a systematic study of the properties of vector mesons. The spectrum of light axial-vector mesons is derived relying on the leading order interaction of the Goldstone bosons with the vector mesons supplemented by a phenomenology for correction terms. The f_1(1282), b_1(1230), h_1(1386), a_1(1230) and K_1(1272) mesons are recovered as molecular states. Based on those results the one-loop contributions to the electromagnetic decay amplitudes of axial-vector molecules into pseudo-scalar or vector mesons are evaluated systematically. In order to arrive at gauge invariant results in a transparent manner we choose to represent the vector particles by anti-symmetric tensor fields. It is emphasized that there are no tree-level contributions to a radiative decay amplitude of a given state if that state is generated by coupled-channel dynamics. The inclusion of the latter would be double counting. At present we restrict ourselves to loops where a vector and a pseudo-scalar meson couple to the axial-vector molecule. We argue that final and predictive results require further computations involving intermediate states with two vector mesons. The relevance of the latter is predicted by our counting rules.

added appendix concerning double-counting issues

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• Dalitz plots and lineshape of $a_1(1260)$ from a relativistic three-body unitary approach
• Reactions with pions and vector mesons in the sector of odd intrinsic parity
• Photon-fusion reactions from the chiral Lagrangian with dynamical light vector mesons
• Hadronic three-body decays of light vector mesons
• Anomalous thresholds in $B\to (P,V){\gamma }^{\ast }$ form factors
• $f_1(1285)\to e^{+}{e}^{-}$ decay and direct $f_1$ production in $e^{+}{e}^{-}$ collisions
• Renormalization and additional degrees of freedom within the chiral effective theory for spin-1 resonances
• Chiral behavior of vector meson self energies
• On light vector mesons and chiral SU(3) extrapolations
• Theoretical description of the $\mathbf{J}/\mathbf{\psi }\to \mathbf{\eta }({\mathbf{\eta }}^{\prime }){\mathbf{h}}_1(1380)$, $\mathbf{J}/\mathbf{\psi }\to \mathbf{\eta }({\mathbf{\eta }}^{\prime }){\mathbf{h}}_1(1170)$ and $\mathbf{J}/\mathbf{\psi }\to {\mathbf{\pi }}^0{\mathbf{b}}_1(1235{)}^0$ reactions
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• Information on the structure of the rho meson from the pion form-factor
• Renormalisation of the low-energy constants of chiral perturbation theory from loops with dynamical vector mesons
• The vertex corrections due to the triangle singularity mechanism in the light axial vector meson couplings to $K^{\ast }\bar{K}+c.c.$
• Electromagnetic Transition Form Factors of Mesons
• The role of long distance contribution to the $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$ in the Standard Model
• On kinematical constraints in the hadrogenesis conjecture for the baryon resonance spectrum
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• Estimates for Parameters and Characteristics of the Confining SU(3)-gluonic Field in $\varphi$-meson from Leptonic Widths
• Towards an effective field theory for vector mesons
• High order chiral Lagrangians with vector mesons in different approaches
• Amplitude Analysis of the Isospin-Violating Decay $J/\psi \to \gamma \eta {\pi }^0$