Measuring the Higgs-vector boson couplings at lineare+e−collider

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 ${e}^{+}{e}^{\ensuremath{-}}$ 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 (${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{\ensuremath{\nu}}}_{e}{\ensuremath{\nu}}_{e}H$), where we use the rapidity $y$ and the transverse momentum ${p}_{\mathrm{T}}$ 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 (${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}H$), where we use the energy and angular distributions of the tagged ${e}^{+}$ and ${e}^{\ensuremath{-}}$. In the fourth, we consider the rapidity distribution of the untagged ${e}^{+}{e}^{\ensuremath{-}}H$ events, which can be approximated well as the $\ensuremath{\gamma}\ensuremath{\gamma}$ fusion of the bremsstrahlung photons from ${e}^{+}$ and ${e}^{\ensuremath{-}}$ beams. As the last process, we consider the single-tagged ${e}^{+}{e}^{\ensuremath{-}}H$ events, which probe the $\ensuremath{\gamma}{e}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}H{e}^{\ifmmode\pm\else\textpm\fi{}}$ 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 ${m}_{H}=120\text{ }\text{ }\mathrm{GeV}$, at $\sqrt{s}=250\text{ }\text{ }\mathrm{GeV}$, 350 GeV, 500 GeV, and 1 TeV, with and without ${e}^{\ensuremath{-}}$ beam polarization of 80%. We find, for instance, that the $HZZ$ and $HWW$ couplings can be measured with 0.6% and 0.9% accuracy, respectively, for the integrated luminosity of $L=100\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ at $\sqrt{s}=250\text{ }\text{ }\mathrm{GeV}$, 350 GeV, and $L=500\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ at $\sqrt{s}=500\text{ }\text{ }\mathrm{GeV}$, 1 TeV, for the luminosity uncertainty of 1% at each energy. We find that the luminosity uncertainty affects only one combination of the nonstandard couplings, which are proportional to the standard $HWW$ and $HZZ$ couplings, while it does not affect the errors of the other independent combinations of the couplings. As a consequence, we observe that a few combinations of the eight dimension-six operators can be constrained as accurately as the two operators, which have been constrained by the precision measurements of the $Z$ and $W$ boson properties.