B1a : N$^3$LO QCD predictions for production cross sections of colourless systems in association with a resolved jet

The goal of this project is to study the production of two colourless final state particles, in particular gauge-boson pairs, or the production of a vector gauge boson or a Higgs boson in association with a jet at next-to-next-to-next-to-leading order in QCD. A good understanding of these processes is of paramount importance for Standard Model physics, precision Higgs physics, and searches for new phenomena. The predictions will be obtained with slicing methods and the required 1-jettiness soft function will be evaluated.

1. NNLO QCD computations for $V+j$ processes at NNLO QCD: fast and reliable calculations in nearly-singular kinematic regions (small $p_\perp$ or jettiness) for $V^*+j$ and $H+j$.
2. Beam functions at N$^3$LO QCD: computation of the jettiness beam function at N$^3$LO QCD; computation of the $p_\perp$ beam function at N$^3$LO QCD.
3. Soft function at N$^3$LO QCD: computation of the jettiness soft function at N$^3$LO QCD.
4. Phenomenology: Color-singlet phenomenology at N$^3$LO QCD (fiducial cross sections, Higgs couplings, charge asymmetry, lepton $p_\perp$ distribution, parton distribution functions, $W$-boson mass.