Anti- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>k</mml:mi><mml:mi>T</mml:mi></mml:msub></mml:math> jet function at next-to-next-to-leading order

Jets constructed via clustering algorithms (e.g., anti-${k}_{T}$, soft-drop) have been proposed for many precision measurements, such as the strong coupling ${\ensuremath{\alpha}}_{s}$ and nucleon intrinsic dynamics. However, theoretical accuracy is affected by missing QCD corrections at higher orders jet functions in associated factorization theorems. Their calculation complicated procedure. In this work, we propose a method to evaluate QCD. The involves phase space sector decomposition with suitable soft subtractions. As concrete example, present quark-jet function using anti-${k}_{T}$ algorithm $E$-scheme recombination next-to-next-to-leading order.