B1a : Production of color-singlet states through N$^3$LO QCD

Processes with colour-singlet single-particle final states play an important role in high-energy physics. Indeed, measurements of rates and kinematic distributions of virtual photons, $Z$ and $W$ bosons produced in proton collisions are essential for the determination of parton distribution functions and very precise measurements of the $W$-boson mass and the weak mixing angle. Moreover, the gluon fusion process $gg \to H$ is the main production mechanism of the Higgs boson at the LHC and, as such, plays a very important role in the determination of the different properties of this particle. Studies of the associated production of the Higgs boson $pp \to V^* \to HV$, $V=Z,W$ are crucial for measuring the anomalous couplings of the Higgs boson, including Yukawa couplings of $b$-quarks and $\tau$-leptons.

The goal of this project is to study the production of colour-neutral single-particle final states $X$ in the processes $pp \to X$, $X \in (H,Z/\gamma^*,W) $ at N$^3$LO in perturbative QCD, keeping full information about accompanying QCD radiation and the kinematics of the decay products of the particle $X$. To achieve this goal, we will combine the fully-differential computations of NNLO QCD corrections to $pp \to X+{\rm jet}$ processes with three-loop computations of soft and beam functions that describe physics of $X$-production at small transverse momentum. The computation of the required soft and beam functions at three loops in perturbative QCD is the essential part of the project. We will also study the phenomenology of $pp \to X$ production at N$^3$LO focusing on a large number of interesting observables that go beyond total cross sections.

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.