ISR effects for resonant Higgs production at future lepton colliders

We study the effects of the initial state radiation on the $s$-channel Higgs boson resonant production at ${\mu }^{+}{\mu }^{-}$ and $e^{+}{e}^{-}$ colliders by convoluting with the beam energy spread profile of the collider and the Breit-Wigner resonance profile of the signal. We assess their impact on both the Higgs signal and SM backgrounds for the leading decay channels $h\rightarrow b\bar b,\ WW^*$. Our study improves the existing analyses of the proposed future resonant Higgs factories and provides further guidance for the accelerator designs with respect to the physical goals.