  We construct the Lagrangian for an effective theory of highly energetic
quarks with energy Q, interacting with collinear and soft gluons. This theory
has two low energy scales, the transverse momentum of the collinear particles,
p_perp, and the scale p_perp^2/Q. The heavy to light currents are matched onto
operators in the effective theory at one-loop and the renormalization group
equations for the corresponding Wilson coefficients are solved. This running is
used to sum Sudakov logarithms in inclusive B -> X_s gamma and B -> X_u \ell nu
decays. We also show that the interactions with collinear gluons preserve the
relations for the soft part of the form factor for heavy to light decays found
by Charles et al., establishing these relations in the large energy limit of
QCD.
