Generation of arbitrarily spin polarized muon pairs is investigated via polarized $e^{-}{e}^{+}$ collision. We calculate the completely polarized cross section $\mathrm{d}{\sigma }_{e^{-}{e}^{+}\to {\mu }^{-}{\mu }^{+}}$ and construct the fully spin-resolved Monte Carlo simulation method to explicitly describe the production of polarized muon pairs. We find that, due to the flip of mixed helicities along the scattering angle, arbitrarily polarized muon pairs with both of the longitudinal and transverse spin components can be produced. Moreover, we also find that the transverse polarization of the muon pairs depends on the directions of transverse spins of initial electrons and positrons. The collision of tightly collimated electron and positron beams with highly longitudinal polarization and nanocoulomb charge can generate about 40% muon pairs with longitudinal polarization and about 60% muon pairs with transverse polarization. The compact high-flux $e^{-}{e}^{+}\to {\mu }^{-}{\mu }^{+}$ muon source could be implemented through the next-generation laser-plasma linear collider and would be essential to facilitate the investigation of fundamental physics and the measurement technology in broad areas.

• Received 26 January 2022
• Revised 19 May 2022
• Accepted 20 May 2022

DOI:https://doi.org/10.1103/PhysRevD.105.113002

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Published by the American Physical Society