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We present the first complete calculation for the quark and gluon $N$-jettiness ($Tau_N$) 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 $Tau_N$ subtraction methods to N$^3$LO, and to resum $Tau_N$ distributions at N$^3$LL$^prime$ accuracy both for quark as well as for gluon initiated processes.
$N$-jettiness subtractions provide a general approach for performing fully-differential next-to-next-to-leading order (NNLO) calculations. Since they are based on the physical resolution variable $N$-jettiness, $mathcal{T}_N$, subleading power correc
We compute the unpolarized quark and gluon transverse-momentum dependent fragmentation functions (TMDFFs) at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD. The calculation is based on a relation between the TMDFF and the limit o
We present the Higgs boson production cross section at Hadron colliders in the gluon fusion production mode through N3LO in perturbative QCD. Specifically, we work in an effective theory where the top quark is assumed to be infinitely heavy and all o
We derive the leading-power singular terms at three loops for both $q_T$ and 0-jettiness, $cal{T}_0$, for generic color-singlet processes. Our results provide the complete set of differential subtraction terms for $q_T$ and $cal{T}_0$ subtractions at
We present several key steps towards the computation of differential Higgs boson cross sections at N$^3$LO in perturbative QCD. Specifically, we work in the framework of Higgs-differential cross sections that allows to compute precise predictions for