Radiative Corrections for ZH Production at Electron-Positron Collider

Current experimental measurements on Higgs boson properties are consistent with the Standard Model(SM) predictions, but large experimental uncertainties still leave room for the possibility of new physics. To reduce experimental uncertainties, a so-called "Higgs factory" including the International Linear Collider (ILC) \cite{ilc1,ilc2}, Future Circular Collider (FCC-ee)\cite{fccee}, and Circular Electron-Positron Collider (CEPC) \cite{cepc}, has been proposed. The main production channel of Higgs boson in these $e^+e^-$ colliders is the Higgsstrahlung process, $e^+e^-\to ZH$, which is projected to be measured with sub-percent level precision at these facilities (1.2$\%$ at ILC, 0.4$\%$ at FCC-ee, and 0.5$\%$ at CEPC). Reducing the theoretical uncertainty to the same level as the experimental one is crucial to prevent theoretical errors from dominating when extracting Higgs couplings, and this constitutes a significant part of this thesis, in which the largest missing contribution, the next-to-next-to-leading order(NNLO) electroweak corrections, will be presented. Moreover, the increasing experimental accuracy will impose stringent bounds on new physics. The thesis also investigates one specific class of new physics, fermionic dark matter, as a possible explanation for potential deviations on the cross section of the Higgsstrahlung process, and explores the parameter space that may be probed at future Large Hadron Collider(LHC)