We develop the perturbative QCD formalism for semileptonic $B$ meson decays, which includes Sudakov suppression on the spatial extent of a heavy meson containing a light valence quark. We show that the perturbative calculation for the spectrum of the decay $B\to \pi l\nu$ is reliable for the energy fraction of the pion above 0.3. Combining predictions from soft pion theorems, we obtain an upper limit of the matrix element $|V_{\mathrm{ub}}|$ of roughly $3.5\times {10}^{-3\mathrm{}}$.

• Received 26 July 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.4388