Method for Extracting the Quark Mixing Parameter cos{alpha} via B{sup {+-}} {yields}{pi}{sup {+-}}e{sup +}e{sup -}

We show that it is possible to extract the weak mixing angle {alpha} via a measurement of the rate for B{sup {+-}}{yields}{pi}{sup {+-}}e{sup +} e{sup -} . The sensitivity to cos {alpha} results from the interference between the long and short distance contributions. The short distance contribution is given in terms of semileptonic form factors. The long distance contribution can be calculated using Ward identities and a short distance operator product expansion if the invariant mass of the lepton pair, q{sup 2} , is larger than {lambda}{sup 2}{sub QCD} . For q{sup 2}{>=}2 GeV {sup 2} the branching fraction is approximately 1x10{sup -8}|V{sub td}/0.008|{sup 2} . The shape of d{gamma}/dq{sup 2} is very sensitive to the value of cos {alpha} at small values of q{sup 2} and varies by 50% when -1