Production of true para-muonium in linearly polarized photon fusions

True muonium (TM)—the bound state of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>μ</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>μ</a:mi><a:mo>−</a:mo></a:msup></a:math>—has not been discovered yet. It was demonstrated that searching for TM via <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>γ</c:mi><c:mi>γ</c:mi></c:math> 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.