Perturbative QCD study of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>*</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mi>γ</mml:mi></mml:math>decay

Abstract

We apply the perturbative QCD factorization theorem developed recently for nonleptonic heavy meson decays to the radiative decay $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{*}\ensuremath{\gamma}$. In this formalism the evolution of the Wilson coefficients from the W boson mass down to the characteristic scale of the decay process is governed by the effective weak Hamiltonian. The evolution from the characteristic scale to a lower hadronic scale is formulated by the Sudakov resummation. In addition to computing the dominant contribution arising from the magnetic-penguin operator ${O}_{7},$ we also calculate the contributions of four-quark operators. By fitting our prediction for the branching ratio of the $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{*}\ensuremath{\gamma}$ decay to the CLEO data, we determine the B meson wave function that possesses a sharp peak at a low momentum fraction.