Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1999-10-05
Phys.Rev.Lett.84:4545-4548,2000
Physics
High Energy Physics
High Energy Physics - Phenomenology
4 pages,2 figures, Latex
Scientific paper
10.1103/PhysRevLett.84.4545
We show that it is possible to extract the weak mixing angle alpha via a measurement of the rate for B^+(-) -> \pi^+(-) e^+e^-. The sensitivity to cos(alpha) results from the interference between the long and short distance contributions. The short distance contribution can be computed, using heavy quark symmetry, in terms of semi-leptonic form factors. More importantly, we show that, using Ward identities and a short distance operator product expansion, the long distance contribution can be calculated without recourse to light cone wave functions when the invariant mass of the lepton pair, q^2, is much larger than LQCDs. We find that for q^2 > 2 GeV^2 the branching fraction is approximately 1 * 10^{-8}|V_{td}/0.008|^2. The shape of the differential rate is very sensitive to the value of cos(alpha) at small values of q^2 with dGamma /dq^2 varying up to 50% in the interval -1< cos(alpha)< 1 at q^2= 2 GeV^2. The size of the variation depends upon the ratio V_{ub}/V_{td}.
Grinstein Benjamin
Nolte Detlef R.
Rothstein Ira Z.
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