We study the hadronic effects on the $X\left(3872\right)$ meson abundance in heavy ion collisions. We evaluate the absorption cross sections of the $X\left(3872\right)$ meson by pions and rho mesons in the hadronic stage of heavy ion collisions, and further investigate the variation in the $X\left(3872\right)$ meson abundance during the expansion of the hadronic matter for its two possible quantum number states; $J^P=1^{+}$ and $2^{-}$. We show that the absorption cross sections and the time evolution of the $X\left(3872\right)$ meson abundance are strongly dependent on the structure and quantum number of the $X\left(3872\right)$ meson. We thus suggest that studying the abundance of the $X\left(3872\right)$ meson in relativistic heavy ion collisions provides a chance to infer its quantum number as well as its structure.

• Received 14 April 2013

DOI:https://doi.org/10.1103/PhysRevC.88.054901