Analysis of Dalitz decays with intrinsic parity violating interactions in resonance chiral perturbation theory

Abstract

Observables of light hadron decays are analyzed in a model of chiral Lagrangian which includes resonance fields of vector mesons. In particular, transition form factors are investigated for Dalitz decays of $V\to P{l}^{+}{l}^{-}$ and $P\to \gamma l^{+}{l}^{-}$ $(V=1^{-},P=0^{-})$. Moreover, the differential decay width of $P\to {\pi }^{+}{\pi }^{-}\gamma$ and the partial widths of $P\to 2\gamma ,V\to P\gamma ,{\eta }^{\prime }\to V\gamma ,\varphi (1020)\to \omega (782){\pi }^0$ and $V\to 3P$ are also calculated. In this study, we consider a model which contains octet and singlet fields as representation of $SU(3)$. As an extension of chiral perturbation theory, we include 1-loop ordered interaction terms. For both pseudoscalar and vector meson, we evaluate mixing matrices in which isospin/$SU(3)$ breaking is taken into account. Furthermore, intrinsic parity violating interactions are considered with singlet fields. For parameter estimation, we carry out ${\chi }^2$ fittings in which a spectral function of $\tau$ decays, vector meson masses, decay widths of $V\to P\gamma$ and transition form factor of $V\to P{l}^{+}{l}^{-}$ are utilized as input data. Using the estimated parameter region in the model, we give predictions for decay widths and transition form factors of intrinsic parity violating decays. As further model predictions, we calculate the transition form factors of $\varphi (1020)\to {\pi }^0{l}^{+}{l}^{-}$ and ${\eta }^{\prime }\to \gamma l^{+}{l}^{-}$ in the vicinity of resonance regions, taking account of the contribution for intermediate $\rho (770)$ and $\omega (782)$.

Comments: 73 pages, 17 figures, 13 tables. Version accepted in PTEP