Measuring the Higgs-Vector boson Couplings at Linear $e^{+} e^{-}$ Collider

TL;DR

The work assesses how well linear colliders can constrain CP-even dimension-6 HVV operators by combining five Higgs production channels with the optimal observables approach. It formulates an eight-operator HVV basis, maps to the standard operator set, and derives observable-dependent weight functions and covariance matrices across $\sqrt{s}=250$–$1000$ GeV with/without $e^-$ polarization. The study demonstrates energy- and polarization-driven improvements, achieving percent-level constraints for several combinations and clarifying correlations among $HWW$, $HZZ$, $HZ\gamma$, and $H\gamma\gamma$ couplings, including the no-tag and single-tag photon-fusion channels. The results provide a comprehensive, model-independent projection for HVV precision at the ILC, and offer direct mappings to dimension-6 operator coefficients to compare with precision EW tests and other collider studies.

Abstract

We estimate the accuracy with which the coefficient of the CP even dimension six operators involving Higgs and two vector bosons (HVV) can be measured at linear $e^+ e^-$ colliders. Using the optimal observables method for the kinematic distributions, our analysis is based on the five different processes. First is the WW fusion process in the t-channel ($e^+e^- \to \barν_e ν_e H$), where we use the rapidity y and the transverse momentum $\pT$ of the Higgs boson as observables. Second is the ZH pair production process in the s-channel, where we use the scattering angle of the Z and the Z decay angular distributions, reproducing the results of the previous studies. Third is the t-channel ZZ, fusion processes ($e^+e^- \to e^+e^ -H$), where we use the energy and angular distributions of the tagged $e^+$ and $e^-$. In the fourth, we consider the rapidity distribution of the untagged $e^+e^-H$ events, which can be approximated well as the $γγ$ fusion of the bremsstrahlung photons from $e^+$ and $e^-$ beams. As the last process,we consider the single tagged $e^+e^- H$ events, which probe the $γe^{\pm} \to H e^{\pm}$ process. All the results are presented in such a way that statistical errors of the constraints on the effective couplings and their correlations are read off when all of them are allowed to vary simultaneously, for each of the above processes, for $m_H=120 $ GeV, at $\sqrt{s}=250\GEV$, $350\GEV$ $500\GEV$ and $1\TEV$, with and without $e^-$ beam polarization of 80%.

Figures (11)

• Figure 1: The $HVV$ Vertex.
• Figure 2: Feynman diagrams for $e^{-} e^{+} \rightarrow f \bar{f} H$.
• Figure 3: Total cross sections versus $e^+e^-$ collision energy $\sqrt{s}$ for the five processes that are sensitive to the $HVV$ couplings at ILC. All the curves are for $m_{H}^{}=120 ~{\rm GeV}$. The $ZH$ production cross section is the sum over all $Z\to f\bar{f}$ decay modes with $\vert m_{\nu\bar{\nu}}-m_Z\vert <5\,\Gamma_Z$, while the solid thin curves shows the $\Gamma_Z=0$ limit. The $\nu\bar{\nu}\,H$ and the double tag $e^+e^-\, H$ events satisfy $\vert m_{f\bar{f}}-m_{Z}^{}\vert >5\,\Gamma_Z$, and the tagged $e^{\pm}$ has $\vert \cos\theta_{e^{\pm}}\vert<0.995$ and ${p_{\rm T}}_{e^{\pm}}>1 ~{\rm GeV}$, while ${p_{\rm T}}_{H} >10 ~{\rm GeV}$ is imposed on $\nu\bar{\nu}H$ process. The solid thin curves for $e^+e^-\to \nu_e\bar{\nu}_e \,H$ and $e^+e^-\to e^+e^- \, H$ give the cross sections calculated from the $t$-channel $W$ and $Z$ boson exchange amplitudes only without imposing the invariant mass cut.
• Figure 4: Total cross sections versus $m_{H}^{}$ for the five processes which are sensitive to the $HVV$ couplings at ILC, at (a) $\sqrt{s}=250 ~{\rm GeV}$, (b) $500 ~{\rm GeV}$ and (c) $1 ~{\rm TeV}$. The tagged $e^{\pm}$ has $|\cos\theta_{e^{\pm}}|<0.995$ and ${p_{\rm T}}_{e^{\pm}}>1 ~{\rm GeV}$ in the laboratory frame. $\vert m_{f\bar{f}} -m_Z\vert <5\,\,\Gamma_Z$ for $ZH$ production and $\vert m_{f\bar{f}} -m_Z\vert >5\,\,\Gamma_Z$ for $\nu_e\bar{\nu}_e\,H$ and double tag $e^+e^-\,H$. The thin curves in (a) for $\nu\bar{\nu}\, H$ and $e^+e^-\,H$ show the cross sections when the $Z\to f\bar{f}$ exclusion cut is removed, and that for $ZH$ shows the $\Gamma_Z=0$ limit. ${p_{\rm T}}_{H} >10 ~{\rm GeV}$ is imposed on $\nu\bar{\nu}H$ process.
• Figure 5: Histogram showing the $p_{\rm T}$ distributions of the Higgs boson, where the differential cross section is integrated over $y_{H}$ in each ${p_{\rm T}}_{H}$ bin of $10 ~{\rm GeV}$ width at $\sqrt{s}=500 ~{\rm GeV}$ for $m_{H}^{}=120 ~{\rm GeV}$. $\Sigma_{\rm SM}$ gives the SM distribution, and $\Sigma_{c_i}$ shows the coefficients of the non-standard $HWW$ couplings $c_i=(c_{1WW}^{}, c_{2WW}^{}, c_{3WW}^{})$