A measurement of the beam-spin asymmetry in the azimuthal distribution of pions produced in semi-inclusive deep-inelastic scattering off protons is presented. The measurement was performed using the {HERMES} spectrometer with a hydrogen gas target and the longitudinally polarized 27.6 GeV positron beam of HERA. The sinusoidal amplitude of the dependence of the asymmetry on the angle $phi$ of the hadron production plane around the virtual photon direction relative to the lepton scattering plane was measured for $pi^+,pi^-$ and $pi^0$ mesons. The dependence of this amplitude on the Bjorken scaling variable and on the pion fractional energy and transverse momentum is presented. The results are compared to theoretical model calculations.
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