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Unformatted text preview: 1 -LEPTON DECAY PARAMETERS Updated July 2007 by A. Stahl (RWTH Aachen). The purpose of the measurements of the decay parameters ( i.e. , Michel parameters) of the is to determine the structure (spin and chirality) of the current mediating its decays. Leptonic Decays: The Michel parameters are extracted from the energy spectrum of the charged daughter lepton = e, in the decays . Ignoring radiative corrections, neglect- ing terms of order ( m /m ) 2 and ( m / s ) 2 , and setting the neutrino masses to zero, the spectrum in the laboratory frame reads d dx = G 2 m 5 192 3 f ( x ) + f 1 ( x ) + m m f 2 ( x ) P [ g 1 ( x ) + g 2 ( x )] , (1) with f ( x ) = 2 6 x 2 + 4 x 3 f 1 ( x ) = 4 9 + 4 x 2 32 9 x 3 g 1 ( x ) = 2 3 + 4 x 6 x 2 + 8 3 x 3 f 2 ( x ) = 12 (1 x ) 2 g 2 ( x ) = 4 9 16 3 x + 12 x 2 64 9 x 3 . The quantity x is the fractional energy of the daughter lepton , i.e. , x = E /E ,max E / ( s/ 2) and P is the polarization of the tau leptons. The integrated decay width is given by = G 2 m 5 192 3 1 + 4 m m . (2) The situation is similar to muon decays e e . The gener- alized matrix element with the couplings g and their relations to the Michel parameters , , , and have been described in the Note on Muon Decay Parameters. The Standard Modelthe Note on Muon Decay Parameters....
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