Polarized bosons

The Higgs boson discovery at the Large Hadron Collider (LHC) completed the Standard Model of Particle Physics (SM), and it confirmed the Higgs mechanism as a suitable description of the Electroweak-Symmetry-Breaking (EWSB). Nevertheless, the dynamics of the EWSB are one of the most consequential questions in particle physics and a fascinating topic due to its connection to other open questions about the structure of the early universe, matter-anti-matter asymmetry and fermionic mass hierarchies. Scrutinising the EWSB mechanism and the Higgs potential is a high-priority target of the current and future LHC physics programme. Exploring the EWSB at LHC requires global scalar and electroweak sector analyses through precision measurements of the SM's massive bosons (Higgs, W- and Z-boson).

A pathway to study the EWSB mechanism is to investigate the longitudinal polarisation state of the massive electroweak bosons linked through the Equivalence-theorem to the Nambu-Goldstone states of the Higgs field and, therefore, to the Higgs potential and dynamics. Specifically, at the LHC, it is possible to study the production of polarised bosons and to probe their interactions. Through the measurement of differential cross-sections of (multi-)boson final states such as boson pair production (WW, WZ, ZZ, WH and ZH), vector-boson fusion (VBF) and vector-boson scattering (VBS) processes, these interactions become trackable.

Due to the short lifespan of the bosons, a direct measurement of individual boson's polarisation is impossible. However, the kinematics of their decay products are tightly linked to the boson's polarisation and allow the reconstruction of the polarisation states. So, extracting the polarisation fractions, i.e. the (differential) fraction of produced bosons with a given polarisation, is possible by comparing polarised cross-section predictions to measurements on the level of differential distributions of the decay products. The SM predicts these fractions, and any deviation from the expectations in a measurement is a direct hint of new physics. This approach of testing the scalar sector and the EWSB requires high precision and accuracy experimentally and theoretically.

The VBS processes are 'golden' channels to measure the quartic vector-boson vertices and the restoration of unitarity through the Higgs mechanism in longitudinal vector-boson scattering. Unfortunately, the cross-sections for these processes are small. They are just at the cusp of observation with Run II data. Even with Run III and the high-luminosity phase, the experimental uncertainties will remain significant, allowing a 3-sigma observation of the longitudinal polarisation fraction at the LHC optimistically.

Direct production processes with one or two bosons in the final state, e.g. W/Z/H and WW/ZZ/WZ production, can, however, be measured with high statistics and low systematic experimental uncertainties (for example) and are therefore ideal for extracting the longitudinal polarisation fractions. At the High Luminosity LHC, measurements will reach a few per cent relative uncertainties. They would allow correspondingly precise extraction of polarised fractions. This task requires theory inputs at the same level of accuracy and precision. The research community has identified that improvements in theory predictions for the corresponding polarised final states are needed to diminish the dominant theoretical uncertainties, which originate from unphysical scales arising in the computations.

Specifically, the computation of corrections in Quantum Chromodynamics (QCD) is essential at hadron colliders, such as the LHC, due to the hadronic environment. The high energy scale in the collisions allows predictions to be calculated in the collinear factorisation framework and perturbative quantum field theory. Dependencies on factorisation and renormalisation scales give rise to theoretical uncertainties. They can be systematically improved through the inclusion of higher-order corrections. Therefore, the availability of higher-order QCD corrections for polarised boson production processes is a limiting factor in extracting corresponding polarised cross-sections at the LHC.

This project aims to push the precision of theory predictions for polarised cross-sections to the percent-level - the project targets specifically vector-boson pair production processes, the most precisely measured channels at the LHC. The aim is to provide dedicated phenomenological studies of the impact of higher-order corrections on the relevant process-specific observables and, finally, to deliver the results in a publicly available and reusable format to facilitate the usage of these predictions by experimental collaborations.

Related to this effort is the COST action COMETA and the activities of WG 1.

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