We introduce a method to compute one-loop soft functions for exclusive N - jet processes at hadron colliders, allowing for different definitions of the algorithm that determines the jet regions and of the measurements in those regions. In particular, we generalize the N -jettiness hemisphere decomposition of ref. [1] in a manner that separates the dependence on the jet boundary from the observables measured inside the jet and beam regions. Results are given for several factorizable jet definitions, including anti-k[subscript T], XCone, and other geometric partitionings. We calculate explicitly the soft functions for angularity measurements, including jet mass and jet broadening, in pp → L + 1 jet and explore the differences for various jet vetoes and algorithms. This includes a consistent treatment of rapidity divergences when applicable. We also compute analytic results for these soft functions in an expansion for a small jet radius R. We find that the small-R results, including corrections up to O(R[superscript 2]), accurately capture the full behavior over a large range of R.
United States. Dept. of Energy. Office of Nuclear Physics (Grant DE-SC0011090)
United States. Dept. of Energy. Office of Nuclear Physics (Grant DE-AC02-05CH11231)
United States. Dept. of Energy. Office of Nuclear Physics (Grant DEAC52-06NA25396)
Los Alamos National Laboratory. Laboratory Directed Research and Development Program
Simons Foundation (Investigator Grant 327942)
Massachusetts Institute of Technology (Global MISTI Collaboration Grant)