The Collins-Soper (CS) kernel may be obtained through the TMD soft function by formulating
the Wilson line in terms of 1-dimensional auxiliary fermion fields on the lattice. Our computation
takes place in the region of the lattice that corresponds to the “spacelike” region in Minkowski
space, i.e., Collins’ scheme. We explore two methods for obtaining the CS kernel. The “ratio
method”; which would allow us to obtain the soft function as well as the CS kernel. And the
“double ratio”; which allows us to achieve a high degree of statistical precision, but only produces
the CS kernel. The matching of our result to Minkowski space is achieved through the mapping of
the complex auxiliary field directional vector to the Wilson line rapidity. We present a preliminary
extraction of the CS kernel using the “double ratio”, and discuss the methodology employed.