Analytical structure of <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> clustering to any order

We present a general analytical expression for the fixed-order structure of the distribution of a generic nonglobal observable with the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>k</a:mi><a:mi>t</a:mi></a:msub></a:math> jet algorithm at any perturbative order. This novel formulation is obtained within the framework of the eikonal approximation, assuming strong-energy ordering of emitted partons. The proposed formula is applicable to a wide range of processes at both lepton and hadron colliders.