Free $μ^{+}μ^{-}$ and bound-free $e^{+}e^{-}$ pair production in relativistic heavy-ion collisions
In our previous studies, we calculated the cross-section for the production of free $μ^{+}μ^{-}$ pairs using a probability function dependent on the impact parameter, and also, we computed bound-free $e^{+}e^{-}$ pair production cross section. In this study, unlike the others, we obtained the cross section for the production of bound-free $e^{+}e^{-}$ pairs using the probability function dependent on the impact parameter. Here also, we simultaneously calculated the cross sections for producing free $μ^{+}μ^{-}$ with bound-free $e^{+}e^{-}$ pairs in relativistic $Pb+Pb$ collisions at the LHC with Lorentz factors at $γ=1500$ and $γ=3000$ reported in the literature. Our calculation is based on second-order perturbation theory, implemented by using Monte Carlo integration techniques. We present impact parameter dependent pair production probabilities for free $μ^{+}μ^{-}$ and bound-free $e^{+}e^{-}$ pair production processes. Notably, the bound-free $e^{+}e^{-}$ pair production was evaluated by using a formalism adapted from that of free $μ^{+}μ^{-}$ pair production. Our results obtained here for the free $μ^{+}μ^{-}$ with bound-free $e^{+}e^{-}$ pair production cross sections are compared with those from other theoretical methods available in the literature. This study aims to provide predictions that can be tested against future experimental data, thereby offering a valuable check for quantum electrodynamics (QED) in strong electromagnetic fields.