A detailed proof of hard-scattering factorization is given with the inclusion of heavy quark masses. Although the proof is explicitly given for deep-inelastic scattering, the methods apply more generally. The power-suppressed corrections to the factorization formula are uniformly suppressed by a power of $\Lambda /Q,$ independently of the size of heavy quark masses, $M,$ relative to $Q.\mathrm{}$

• Received 9 June 1998

DOI:https://doi.org/10.1103/PhysRevD.58.094002