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We calculate the radiative corrections to the unpolarized and the fourpolarized spectrum and rate functions in the leptonic decay of a polarized $\mu $ into a polarized electron. The new feature of our calculation is that wekeep the mass of the final state electron finite which is mandatory if onewants to investigate the threshold region of the decay. Analytical results aregiven for the energy spectrum and the polar angle distribution of the finalstate electron whose longitudinal and transverse polarization is calculated. Wealso provide analytical results on the integrated spectrum functions. Weanalyze the $ m_e \to 0 $ limit of our general results and investigate thequality of the $ m_e \to 0 $ approximation. In the $ m_e \to 0 $ case wediscuss in some detail the role of the $ O(\alpha) $ anomalous helicity flipcontribution of the final electron which survives the $ m_e \to 0 $ limit. Theresults presented in this 0203048 also apply to the leptonic decays ofpolarized $ \tau $-leptons for which we provide numerical results.Comment: 39 pages, 11 postscript figures added. Updated version. Four  references added. A few text improvements. Final version to appear in  Phys.Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Leptonic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>μ</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math>decays: Mass effects, polarization effects, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>α</mml:mi><mml:mo>)</mml:mo></mml:math>radiative corrections

Leptonicμandτdecays: Mass effects, polarization effects, andO(α)radiative corrections