Analysis of exclusive \(k_T\) jet algorithms in electron-positron annihilation

We study the factorization of the dijet cross section in \(e^+ e^-\) annihilation using the generalized exclusive jet algorithm which includes the cone-type, the JADE, the \(k_T\), the anti-\(k_T\) and the Cambridge/Aachen jet algorithms as special cases. In order to probe the characteristics of the jet algorithms in a unified way, we consider the generalized \(k_T\) jet algorithm with an arbitrary weight of the energies, in which various types of the \(k_T\)-type algorithms are included for specific values of the parameter. We show that the jet algorithm respects the factorization property for the parameter \(\alpha