We rst study the rate and cross section for electron-positron pair creation by rela-rntivistic muon impact on intense laser beams through the process +r! À€€! 0 +e+ +eð€€€.rnWe then study the rate and cross section for electron-positron pair creation by protonrnimpact on intense laser beam through the process p + r! ð€€€! p0 + e+ + eð€€€ in the protonrnrest frame. The Feynman diagrams the pair creation by relativistic muon and protonrnimpact on a circularly polarized high frequency laser beam is evaluated with in the frame-rnwork of laser-dressed quantum electrodynamics employing relativistic Volkov states