Using Higgs Boson Production in Association with Three Jets via Gluon Fusion at the LHC to Investigate the CP Properties of the Higgs Boson

A neutral Higgs boson $Φ$ with general scalar and pseudoscalar couplings and accompanying jets can be efficiently produced via gluon fusion through heavy-quark loops in high-energy hadronic collisions. We present integrated cross sections and kinematic distributions for the production of a generic Higgs boson $Φ$ in association with three jets, $pp \to Φjjj$, at order $α_{s}^{5}$. We include the full mass dependence of the top- and bottom-quark loop contributions, combined coherently so that their interference is retained. Earlier finite-mass calculations of $Φ+3$ jets with bottom-quark loops and $CP$-odd or $CP$-mixed couplings were restricted to $gg \to gggΦ$; we include the complete set of partonic subprocesses, and find that the quark-containing channels supply close to one half of the pseudoscalar three-jet cross section at $\tanβ=1$. In a Type-II two-Higgs-doublet model the bottom-quark loop comes to dominate the rate as $\tanβ$ is increased, so that the cross section is non-monotonic in $\tanβ$. Comparing against the heavy-top effective theory and its form-factor-improved version, we show that the effective description fails in the hard tails of the transverse-momentum and dijet-mass distributions, while the third-jet centrality $z^\star$ and the rapidity separation of the two leading jets are largely insensitive to the heavy-quark treatment. We further study the multi-jet azimuthal correlation $Φ_{2}$, built from the jet momenta on the two sides of the Higgs boson in rapidity, and find that the bottom-quark contribution modifies its shape even for a state of definite $CP$. For a $CP$-mixed state the interference of the two couplings adds a $\sin2Φ_2$ term, which a simple counting asymmetry isolates and which no $CP$ eigenstate can produce. Numerical results are presented for the LHC at $\sqrt{s}=13.6~$TeV and $m_Φ=125.2~$GeV.