Optimizing Higgs factories by modifying the recoil mass

It is difficult to measure the $WW$-fusion Higgs production process ($e^+e^- \to \nu \bar{\nu} h$) at a lepton collider with a center of mass energy of 240-250 GeV due to its small rate and the large background from the Higgsstrahlung process with an invisible $Z$ ($e^+e^- \to hZ,\,Z\to \nu\bar{\nu}$). We construct a modified recoil mass variable, $m^p_{\rm recoil}$, defined using only the 3-momentum of the reconstructed Higgs particle, and show that it can better separate the $WW$-fusion and Higgsstrahlung events than the original recoil mass variable $m_{\rm recoil}$. Consequently, the $m^p_{\rm recoil}$ variable can be used to improve the overall precisions of the extracted Higgs couplings, in both the conventional framework and the effective-field-theory framework. We also explore the application of the $m^p_{\rm recoil}$ variable in the inclusive cross section measurements of the Higgsstrahlung process, while a quantitive analysis is left for future studies.