NNLO soft function for threshold single inclusive jet production

We present a computation of the global soft function for single-inclusive hadronic jet production at next-to-next-to-leading order (NNLO) in the strong coupling constant involving four light-like Wilson lines. Our soft function belongs to SCET$_{\text I}$ observables obeying the non-Abelian exponentiation theorem. We provide the calculation of the soft function involving four collinear light-cone directions for all $2\rightarrow2$ processes extending the previous result. We perform the threshold resummation for these processes at the next-to-next-to-leading logarithmic accuracy and present the corresponding numerical results.