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

Abstract

The $a_1(1420)$ with $I^G(J^{PC})=1^{-}(1^{++})$ observed in the ${\pi }^{+}{f}_0(980)$ final state in the ${\pi }^{-}p\to {\pi }^{+}{\pi }^{-}{\pi }^{-}p$ 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 $D^0\to a_1^{-}{\ell }^{+}\nu$ and $D^0\to {\pi }^{\pm }{a}_1^{\mp }$, and in the bottom sector ${\overline{B}}^0\to a_1^{+}{\ell }^{-}\bar{\nu }$, $B\to D{a}_1,{\pi }^{\pm }{a}_1^{\mp }$, $B_c\to J/\psi a_1$ and ${\Lambda }_b\to {\Lambda }_c{a}_1$. 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 $a_1(1420)$.

arXiv comment11 pages, 4 figures

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Cited by in corpus (14)

• Light isovector resonances in ${\pi }^{-}p\to {\pi }^{-}{\pi }^{-}{\pi }^{+}p$ at 190 GeV/$c$
• The "$a_1(1420)$" peak as the $\pi f_0(980)$ decay mode of the $a_1(1260)$
• Semileptonic $D_{(s)}\to A{\ell }^{+}\nu$ and nonleptonic $D\to K_1(1270,1400)\pi$ decays in LCSR
• Tetraquarks in holographic QCD
• Test of the multiquark structure of $a_1(1420)$ in strong two-body decays
• Effects of the fermionic vacuum polarization in QED
• $a_1(1260)$-meson longitudinal twist-2 distribution amplitude and the $D\to a_1(1260){\ell }^{+}{\nu }_{\ell }$ decay processes
• Helicity form factors for $D_{(s)}\to A\ell \nu$ process in the light-cone QCD sum rules approach
• The role of $a_1(1260)$ in ${\pi }^{-}p\to a_1^{-}(1260)p$ and ${\pi }^{-}p\to {\pi }^{-}{\rho }^{0}p$ reactions near threshold
• The new $a_1(1420)$ state: structure, mass and width
• Up-down Asymmetries and Angular Distributions in $D\to K_1(\to K\pi \pi ){\ell }^{+}{\nu }_{\ell }$
• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• Spectroscopy of $a_1$ mesons from lattice QCD with the truncated overlap fermions
• The spectrum of light isovector mesons with $C=+1$ from the COMPASS experiment