Factorization and resummation with N-Jettiness

  I will talk about a factorization formula for the double-differential cross-section in the N-jettiness variables $tau_1$ and $tau_0$. The  phase space spanned by these two variables is not well-known in the region  $tau_1 sim tau_0$  due to the absence of a proper factorization formula in this scenario. This region corresponds to two unordered but resolved  emissions. Using the power counting argument in Soft collinear Effective  theory (SCET), I will describe how to separate the soft and collinear modes at the measurement level. The collinear and soft contributions are encoded  inside new double-differential Beam and Soft functions respectively. In addition, I will also comment on the structure of these objects as well as  on their consistencies, and describe the resummation and matching with other regions of phase space, in particular the SCET+ region with strongly ordered emissions. This has immediate application on the improvement of parton shower accuracy in Geneva framework at NNLL' accuracy as well as on the jet substructure observables without hierarchies.