Factorization of the dijet cross section in electron-positron annihilation with jet algorithms

We analyze the effects of jet algorithms on each factorized part of the dijet cross sections in $e^{+}{e}^{-}$ scattering using the soft-collinear effective theory. The jet function and the soft function with a cone-type jet algorithm and the Sterman-Weinberg jet algorithm are computed to next-to-leading order in ${\alpha }_s$, and are shown to be infrared finite using the dimensional regularization. The integrated and unintegrated jet functions are presented, and compared with other types of jet functions.