  In soft-collinear effective theory, we analyze the structure of rapidity
divergence due to the collinear and soft modes residing in disparate phase
spaces. The idea of an effective theory is applied to a system of collinear
modes with large rapidity and soft modes with small rapidity. The
large-rapidity (collinear) modes are integrated out to obtain the effective
theory for the small-rapidity (soft) modes. The full SCET with the collinear
and soft modes should be matched onto the soft theory at the rapidity boundary,
and the matching procedure becomes exactly the zero-bin subtraction. The
large-rapidity region is out of reach for the soft mode, which results in the
rapidity divergence. The rapidity divergence in the collinear sector comes from
the zero-bin subtraction, which ensures the cancellation of the rapidity
divergences from the soft and collinear sectors. In order to treat the rapidity
divergence, we construct the rapidity regulators consistently for all the
modes. They are generalized by assigning independent rapidity scales for
different collinear directions. The soft regulator incorporates the correct
directional dependence when the innate collinear directions are not
back-to-back, which is discussed in the $N$-jet operator. As an application, we
consider the Sudakov form factor for the back-to-back collinear current and the
soft-collinear current, where the soft rapidity regulator for a soft quark is
developed. We extend the analysis to the boosted heavy quark sector and exploit
the delicacy with the presence of the heavy quark mass. We present the resummed
results of large logarithms in the form factors for various currents with the
light and the heavy quarks, employing the renormalization group evolution on
the renormalization and the rapidity scales.
