Abstract

In this work, we revisit the isospin violating decays of $X(3872)$ in a coupled-channel effective field theory. In the molecular scheme, the $X(3872)$ is interpreted as the bound state of ${\overline{D}}^{*0}{D}^{0}/{\overline{D}}^{0}{D}^{*0}$ and ${D}^{*\ensuremath{-}}{D}^{+}/{D}^{\ensuremath{-}}{D}^{*+}$ channels. In a cutoff-independent formalism, we relate the coupling constants of $X(3872)$ with the two channels to the molecular wave function. The isospin violating decays of $X(3872)$ are obtained by two equivalent approaches, which amend some deficiencies about this issue in literature. In the quantum field theory approach, the isospin violating decays arise from the coupling constants of $X(3872)$ to two dimeson channels. In the quantum mechanics approach, the isospin violating is attributed to wave functions at the origin. We illustrate that how to cure the insufficient results in literature. Within the comprehensive analysis, we bridge the isospin violating decays of $X(3872)$ to its inner structure. Our results show that the proportion of the neutral channel in $X(3872)$ is over 80%. As a by-product, we calculate the strong decay width of $X(3872)\ensuremath{\rightarrow}{\overline{D}}^{0}{D}^{0}{\ensuremath{\pi}}^{0}$ and radiative one $X(3872)\ensuremath{\rightarrow}{\overline{D}}^{0}{D}^{0}\ensuremath{\gamma}$. The strong decay width and radiative decay width are about 30 keV and 10 keV, respectively, for the binding energy from $\ensuremath{-}300\text{ }\text{ }\mathrm{keV}$ to $\ensuremath{-}50\text{ }\text{ }\mathrm{keV}$.

Highlights

  • In 2003, the observation of Xð3872Þ [1] launched a new era of hadron spectroscopy

  • The Xð3872Þ is interpreted as the bound state of D Ã0D0=D 0DÃ0 and DÃ−Dþ=D−DÃþ channels

  • In the quantum field theory approach, the isospin violating decays arise from the coupling constants of Xð3872Þ to two dimeson channels

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Summary

INTRODUCTION

In 2003, the observation of Xð3872Þ [1] launched a new era of hadron spectroscopy. Amounts of candidates of exotic hadrons (beyond the qqmesons and qqq baryons) were observed in experiments (see Refs. [2,3,4,5,6,7,8,9] for reviews). [35], the authors stressed that the isospin violating effect arises from the wave function of Xð3872Þ, which is related to the coupling constants [30,33,39,40]. We focus on the molecular scheme of Xð3872Þ and aim to make a comprehensive investigation on the isospin violating decays of Xð3872Þ To this end, we will adopt the coupled-channel effective field theory [30,41] to clarify some conceptional ambiguities about coupling constants, wave function and its value at the origin. More details about calculating sequential decays are presented in the Appendix

COUPLING CONSTANTS
WAVE FUNCTIONS
STRONG AND RADIATIVE DECAYS OF Xð3872Þ
Findings
SUMMARY

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