Proposed measurement of longitudinally polarised vector bosons in $WH$ and $ZH$ production at Hadron colliders

Abstract

The longitudinal polarisation states of the $W$ and $Z$ bosons arise during electroweak (EW) symmetry breaking as the vector bosons absorb the Higgs boson's massless degrees of freedom. Consequently, these states are intrinsically linked to the EW symmetry breaking mechanism. Measuring the production of longitudinally polarised vector bosons in association with the Higgs boson thus offers a unique probe of EW symmetry breaking and provides potential sensitivity to physics beyond the Standard Model. This work studies vector boson polarisation in associated $WH$ and $ZH$ production at the LHC and proposes targeted analysis strategies for their measurement. We explore kinematic and angular observables and employ machine learning techniques to optimise the separation between longitudinal and transverse polarisation states. Furthermore, we perform a statistical analysis to project the measurement precision and discovery significance for longitudinally polarised $W^\pm$ and $Z$ bosons ($W^\pm_\mathrm{L}H$ and $Z_\mathrm{L}H$) in the $H \rightarrow γγ$ and $H \rightarrow b\bar{b}$ decay channels. Our studies project that 5.0 standard deviation discovery significances can be achieved at the High-Luminosity LHC with integrated luminosities of 210\,fb$^{-1}$ for $Z_\mathrm{L}H$ (in $H \rightarrow b\bar{b}$) and 340\,fb$^{-1}$ (425\,fb$^{-1}$) for $W^\pm_\mathrm{L}H$ in the $H\rightarrow b\bar{b}$ ($H\rightarrowγγ$) decay modes. With the full High-Luminosity LHC dataset of 3000\,fb$^{-1}$, inclusive cross-section measurement precisions are expected to reach up to $13\%$ ($10\%$) for $W^\pm_\mathrm{L}H$ and $8\%$ ($35\%$) for $Z_\mathrm{L}H$ in the $H \rightarrow b\bar{b}$ ($H \rightarrow γγ$) channels, demonstrating the feasibility of isolating longitudinally polarised vector bosons produced in association with a Higgs boson in future LHC analyses.