Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isospin breaking, coupled-channel effects, and X(3872)   We re-investigate the possibility of X(3872) as a $D\bar{D}^*$ molecule with
$J^{PC}=1^{++}$ within the framework of both the one-pion-exchange (OPE) model
and the one-boson-exchange (OBE) model. After careful treatment of the S-D wave
mixing, the mass difference between the neutral and charged $D(D^*)$ mesons and
the coupling of the $D(D^*)$ pair to $D^*\bar{D}^*$, a loosely bound molecular
state X(3872) emerges quite naturally with large isospin violation in its
flavor wave function. For example, the isovector component is 26.24% if the
binding energy is 0.30 MeV, where the isospin breaking effect is amplified by
the tiny binding energy. After taking into account the phase space difference
and assuming the $3\pi$ and $2\pi$ come from a virtual omega and rho meson
respectively, we obtain the ratio of these two hidden-charm decay modes:
$\mathcal{B}(X(3872)\rightarrow \pi^+\pi^-\pi^0
J/\psi)/\mathcal{B}(X(3872)\rightarrow \pi^+\pi^- J/\psi)=0.42$ for the binding
energy being 0.3 MeV, which is consistent with the experimental value.

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The categories of this paper are: stat
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
9
The categories of this paper are: nlin