Production of true para-muonium in linearly polarized photon fusions

True muonium (TM) -- the bound state of $\mu^+\mu^-$ -- has not been discovered yet. It was demonstrated that searching for TM via $\gamma\gamma$ fusions in heavy ion collisions is feasible due to the enhancement of the atom number. We study the production of the true para-muonium (pTM) in the collisions of linearly polarized photons in the experiments of heavy-ion collisions, calculate the production rate as well as the transverse spectrum of pTM, and explore the discovery potential in nuclear experiments. Our results show that there is a significant correlation between the linearly polarized photon distribution and the transverse momentum distribution of pTM. The optimal kinematic region of the generated pTM is identified, which can provide a theoretical guide to the detection of pTM in experiments.