Evolution equation for the heavy quark distribution function in the parton model approach

We explore the perturbative QCD corrections to the inclusive semileptonic decays of $B$ mesons. In inclusive $B$ decay processes the parton picture works well and the scaling feature manifests because the mass of $b$ quark is larger than the QCD scale. Due to this property, the decay rate may be expressed by a single structure function describing the light-cone distribution of $b$ quark apart from the kinematic factor. We derive a $q^2$ evolution equation for the distribution function, which violates the scaling property through the Altarelli-Parisi type approach. The evolution equation is numerically solved and its phenomenological implications are also discussed.