The factorization of soft and ultrasoft gluons from collinear particles is
shown at the level of operators in an effective field theory. Exclusive
hadronic factorization and inclusive partonic factorization follow as special
cases. The leading order Lagrangian is derived using power counting and gauge
invariance in the effective theory. Several species of gluons are required, and
softer gluons appear as background fields to gluons with harder momenta. Two
examples are given: the factorization of soft gluons in B->D pi, and the
soft-collinear convolution for the B->Xs gamma spectrum.Comment: 32 pages, 11 figs, journal versio
