Probing the electroweak symmetry breaking with Higgs production at the LHC

The electroweak symmetry breaking (EWSB) mechanism is still an undecided question in particle physics. We propose to utilize the single top quark and Higgs associated production ($th$), $Zh$ production via gluon fusion at the LHC to probe the couplings between the Higgs and the gauge bosons and further to test the EWSB. We demonstrate that the $th$ and $gg\to Zh$ productions are sensitive to the relative sign of couplings ($ht\bar{t}$, $hWW$) and ($ht\bar{t}$, $hZZ$), respectively. We find that the relative sign between $hWW$ and $hZZ$ couplings could be fully determined after combining the present measurements from $gg\to h$, $t\bar{t}h$ and the $th$, $Zh$ channels, as well as $tZj$ and $Zt\bar{t}$ production at the 13 TeV LHC, and this conclusion is not sensitive to the possible new physics contribution induced by $Zt\bar{t}$ couplings in the $gg\to Zh$ production.