“…Moreover, the TSP electron (positron) beam can be directly produced via nonlinear Compton scattering (nonlinear Breit-Wheeler pair production) in a standingwave [42][43][44], elliptically polarized [45,46], or bichromatic laser pulses [47][48][49][50] due to the quantum radiative spin effects, and the LSP ones can be produced via the helicity transfer from circularly polarized γ photons in linear [51] or nonlinear Breit-Wheeler processes [52,53], which are generally preproduced via Compton scattering [54,55] or bremsstrahlung [56]. Very recently, an all-optical spin rotation method has been proposed to generate arbitrarily spin polarized (ASP) lepton and ion beams [57]. Thus, such a strong laser pulse could be used to drive the direct production of muon pairs through the quantum electrodynamics (QED) processes [29], such as the Bethe-Heitler (BH) and trident muon pair productions via the beam-target interaction: γ + Z → µ − + µ + + Z and e − + Z → µ − + µ + + e − + Z, and the triplet and e − e + annihilation muon pair productions via the beam-beam interaction: e − + γ → µ − + µ + + e − and e − + e + → µ − + µ + [58][59][60][61][62].…”