$a_1(1260),a_1(1420)$ and the production in heavy meson decays

Abstract

The $a_1(1420)$ with $I^G(J^{PC})=1^{-}(1^{++})$ observed in the $\ddot{I}{€}^{+}{f}_0(980)$ final state in the $\ddot{I}{€}^{-}p\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{-}p$ process by the COMPASS collaboration seems unlikely to be an ordinary $\bar{q}q$ mesonic state. Available theoretical explanations include tetraquark or rescattering effects due to $a_1(1260)$ decays. If the $a_1(1420)$ were induced by the rescattering, its production rates are completely determined by those of the $a_1(1260)$. In this work, we propose to explore the ratios of branching fractions of heavy meson weak decays into the $a_1(1420)$ and $a_1(1260)$, and testing the universality of these ratios would be a straightforward way to validate/invalidate the rescattering explanation. The decay modes include in the charm sector the $D^0\to a_1^{-}{\ell }^{+}\hat{I}½$ and $D^0\to \ddot{I}{€}^{\pm }{a}_1^{\mp }$, and in the bottom sector ${\overline{B}}^0\to a_1^{+}{\ell }^{-}\bar{\hat{I}}½$, $B\to D{a}_1,\ddot{I}{€}^{\pm }{a}_1^{\mp }$, $B_c\to J/\ddot{I}ˆa_1$ and $\hat{I}{›}_b\to \hat{I}{›}_c{a}_1$. We calculate the branching ratios for various decay modes into the $a_1(1260)$. The numerical results indicate that there is a promising prospect to study these decays on experiments including BES-III, LHCb, Babar, Belle and CLEO-c, the forthcoming Super-KEKB factory and the under-design Circular Electron-Positron Collider. Experimental analyses in future will lead to a deeper understanding of the nature of the $a_1(1420)$.

11 pages, 4 figures