Charged charmonium-like Z+(4430) from rescattering in conventional B decays

Abstract

In a previous paper we suggested an explanation for the peak designated as $Z(4430{)}^{+}$ in the ${\psi }^{\prime }{\pi }^{+}$ mass spectrum, observed by Belle in $\bar{B}\to {\psi }^{\prime }{\pi }^{+}K$ decays, as an effect of $\bar{D}{}^{\ast 0}{D}^{+}\to {\psi }^{\prime }{\pi }^{+}$ rescattering in the decays $\bar{B}\to D_s^{\prime -}D$, where the $D_s^{\prime -}$ is an as-yet unobserved radial excitation of the pseudoscalar ground state $D_s^{-}$-meson. In this paper, we demonstrate that this hypothesis provides an explanation of the double $Z^{+}$-like peaking structures, which were studied by LHCb with much higher statistics. While according to our hypothesis, the origin of the peaking structures is purely kinematical, reflecting the presence of a conventional resonance in the hidden intermediate state, the amplitude of the $Z(4430{)}^{+}$ peak carries a Breit-Wigner-like complex phase, arising from the intermediate $D_s^{\prime -}$ resonance. Thus, our hypothesis is entirely consistent with the recent LHCb measurement of the resonant-like amplitude behaviour of the $Z(4430{)}^{+}$. We perform a toy fit to the LHCb data, which illustrates that our approach is also consistent with all the observed structure in the LHCb $M({\psi }^{\prime }{\pi }^{+})$ spectrum. We suggest a critical test of our hypothesis that can be performed experimentally.

arXiv comment6 pages, 5 figures

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