# Resolving the tensor structure of the Higgs coupling to $Z$-bosons via Higgs-strahlung

## TL;DR

This paper introduces differential observables in Higgs-strahlung processes to precisely determine the tensor structure of Higgs couplings to Z-bosons, enabling percent-level probing of anomalous vertices within the SMEFT framework.

## Contribution

It proposes a novel strategy using differential distributions to fully resolve the tensor structure of Higgs-Z couplings, including interference effects, in the SMEFT context.

## Key findings

- Proposed a method to probe anomalous $h Z_{
ho
u}Z^{
ho
u}$ and $h Z_{
ho
u} ilde{Z}^{
ho
u}$ vertices at percent level.
- Demonstrated the importance of angular and energy differential distributions to isolate interference effects.
- Projected bounds for tensor structures of Higgs-Z couplings using the proposed observables.

## Abstract

We propose differential observables for $pp \to Z(\ell^+\ell^-)h(b\bar{b})$ that can be used to completely determine the tensor structure of the $hZZ^*/hZ\bar{f}f$ couplings relevant to this process in the dimension-6 SMEFT. In particular, we propose a strategy to probe the anomalous $h Z_{\mu \nu}Z^{\mu \nu}$ and $h Z_{\mu \nu}\tilde{Z}^{\mu \nu}$ vertices at the percent level. We show that this can be achieved by resurrecting the interference term between the transverse $Zh$ amplitude, which receives contributions from the above couplings, and the dominant SM longitudinal amplitude. These contributions are hard to isolate without a knowledge of the analytical amplitude, as they vanish unless the process is studied differentially in three different angular variables at the level of the $Z$-decay products. By also including the differential distributions with respect to energy variables, we obtain projected bounds for the two other tensor structures of the Higgs coupling to $Z$-bosons.