N-jettiness beam functions at N3LO
Markus A. Ebert, Bernhard Mistlberger, Gherardo Vita
Abstract
A bstract We present the first complete calculation for the quark and gluon N -jettiness ( $$ {\mathcal{T}}_N $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:math> ) beam functions at next-to-next-to-next-to-leading order (N 3 LO) in perturbative QCD. Our calculation is based on an expansion of the differential Higgs boson and Drell-Yan production cross sections about their collinear limit. This method allows us to employ cutting edge techniques for the computation of cross sections to extract the universal building blocks in question. The class of functions appearing in the matching coefficents for all channels includes iterated integrals with non-rational kernels, thus going beyond the one of harmonic polylogarithms. Our results are a key step in extending the $$ {\mathcal{T}}_N $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:math> subtraction methods to N 3 LO, and to resum $$ {\mathcal{T}}_N $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:math> distributions at N 3 LL′ accuracy both for quark as well as for gluon initiated processes.