Higgs form factors in Associated Production

TL;DR

The paper develops a general form-factor formalism for Higgs-like couplings to vector bosons and fermion currents, enabling a unified study of $h V \mathcal{F}$ interactions across both $h \to V \mathcal{F}$ decays and $pp \to \mathcal{F} \to Vh$ associated production. By decomposing the amplitude into $q^2$-dependent form factors and performing EFT power counting, it shows how linear and nonlinear realizations of the electroweak gauge symmetry map onto these form factors and how non-SM momentum dependence enhances sensitivity in differential spectra. The authors demonstrate that measuring the $Vh$ invariant-mass distribution and, crucially, the differential $d\sigma/dq^2$ in associated production provides a more robust and model-independent probe of BSM Higgs interactions than total rates alone, with the potential to distinguish between EFT realizations. They discuss current constraints from LHC data, outline the expected gains from future spectra, and emphasize the need for experimental reporting of differential spectra and effective $\bar{q}^2$ to fully exploit the EFT framework for Higgs couplings.

Abstract

We further develop a form factor formalism characterizing anomalous interactions of the Higgs-like boson (h) to massive electroweak vector bosons (V) and generic bilinear fermion states (F). Employing this approach, we examine the sensitivity of pp -> F ->Vh associated production to physics beyond the Standard Model, and compare it to the corresponding sensitivity of h -> V F decays. We discuss how determining the Vh invariant-mass distribution in associated production at LHC is a key ingredient for model-independent determinations of h V F interactions. We also provide a general discussion about the power counting of the form factor's momentum dependence in a generic effective field theory approach, analyzing in particular how effective theories based on a linear and non-linear realization of the SU(2)_L x U(1)_Y gauge symmetry map into the form factor formalism. We point out how measurements of the differential spectra characterizing h -> V F decays and pp -> F -> Vh associated production could be the leading indication of the presence of a nonlinear realization of the SU(2)_L x U(1)_Y gauge symmetry.

Figures (3)

• Figure 1: Left:${\rm d} \Gamma(h\to Z\ell^+\ell^-)/{\rm d} {\hat{q}}^2$ spectra ($\hat{q}^2=m_{\ell\ell}^2/m_h^2$), in arbitrary units, for different values of the EFT parameters chosen to leave the total $h \rightarrow Z \ell^+ \ell^-$ rate unchanged. The values were not chosen so that the total integrated associated production cross section is the same. The black (full) curve corresponds to the SM, $c_i=(1,0,0)$, the red (dotted) curve is for $c_i=(0.82,-0.8,0.8)$, the green (dashed) curve for $c_i=(0.06,0,1.4)$. Right: the partonic $d\sigma(q\bar{q} \to Zh)/d \hat{q}^2$ for the same EFT parameter choices (again arbitrary units). For the sake of presentation, in the right curve the {black, red, green} curves have been multiplied by a factor $\{ 5,1,2.7\}$.
• Figure 2: Left: Convolution of the partonic $q^2$ spectrum with a Breit-Wigner distribution for the reconstructed on-shell $V$ with an effective $\Gamma_V =10 \, {\rm GeV}$. Middle: Convolution of the partonic $q^2$ spectrum with a Breit-Wigner distribution for the reconstructed $h$ with an effective $\Gamma_h = 10 \, {\rm GeV}$. Right: Convolution with a Breit-Wigner for both $V$ and $h$ invariant masses. In all plots the color codes of the curves (and the corresponding normalization and parameter choice) is as in Fig. \ref{['fig:spectra1']}.
• Figure 3: Differential $pp$ crossection normalized to the SM value: $R(\hat{q}^2) = [\sigma^{\rm SM}(pp\to Zh]^{-1} \times \times {\rm d} \sigma^{\rm EFT}(pp \to Zh)/{\rm d} {\hat{q}}^2$. Top Left: $pp$ cross section for the same $c_i$ used in Fig. \ref{['fig:spectra1']} ($\sqrt{s} = 8 \, {\rm TeV}$) using Eq. (\ref{['eq:trunc']}) . Top Middle: Varying the parameter $c_2$ over values $0.01$ (dashed), $0.05$ (dot-dashed) and $0.2$ (dotted) using Eq. (\ref{['eq:trunc']}). The parameters $c_1,c_3$ are fixed to $1,0$ in this case. Top Right: Varying the parameter $c_3$ over values $0.01$ (dashed), $0.05$ (dot-dashed) and $0.2$ (dotted) using Eq. (\ref{['eq:trunc']}). The parameters $c_1,c_2$ are fixed to $1,0$ in this case. Middle row: Same as the top row except the un-truncated expression for Eq. (\ref{['eq:Rcross']}) is used. Bottom Left: EFT parameters leading to a suppressed leading-order couplings of $h$ to the $Z$: $c_i=(0.5, 1, 0.01)$ for the dashed curve and $c_i=(0.5, 0.01, 1)$ for the dotted curve. Bottom middle and right plot: Same parameter choices as in the corresponding plots in the top row, for $\sqrt{s} = 13 \, {\rm TeV}$.