Investigations of charmless decays of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3872</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> via intermediate meson loops

The charmless decay processes of $X(3872)$ provide us a good platform to study the nature and mechanism $X(3872)$. Based on molecular as $\overline{D}{D}^{*}$ bound state, we have investigated decays $X(3872)\ensuremath{\rightarrow}VV$ $VP$ via intermediate ${D}^{*}\overline{D}+\mathrm{c}.\mathrm{c}.$ meson loops, where $V$ $P$ stand for light vector pseudoscalar mesons, respectively. We discuss three cases, i.e., pure neutral components ($\ensuremath{\theta}=0$), isospin singlet ($\ensuremath{\theta}=\ensuremath{\pi}/4$) dominant ($\ensuremath{\theta}=\ensuremath{\pi}/6$), $\ensuremath{\theta}$ is phase angle describing proportion charged constituents. constituent has an influence widths $VP$. With coupling constant channel obtained under molecule ansatz resonance, predicted are about tens keVs, while width can reach few hundreds keVs $X(3872)\ensuremath{\rightarrow}VP$. dependence these ratios between different modes $X(3872)\ensuremath{\rightarrow}VP$ mixing also investigated. It expected that theoretical calculations here be tested by future experiments.