One-Loop Radiative Correction to the Triple Higgs Coupling in the Higgs   Singlet Model
  Though the 125 GeV Higgs boson is consistent with the standard model (SM) prediction until now, the triple Higgs coupling can deviate from the SM value in the physics beyond the SM (BSM). In this paper, the radiative correction to the triple Higgs coupling is investigated in the minimal extension of the SM by adding a real gauge singlet scalar. In this model there are two scalars $h$ and $H$, and both of them are mixing states of the doublet and singlet. Provided that the mixing angle is set to be zero, namely the SM limit, $h$ is the pure left-over of the doublet and its behaviour is the same as that of the SM at the tree level. However the loop corrections can alter $h$-related couplings. In this SM limit case, the effect of the singlet $H$ may show up in the $h$-related couplings, especially the triple $h$ coupling. Our numerical results show that the deviation is sizable. For $\lambda_{\Phi{S}}=1$ (see the text for definition), the deviation $\delta_{hhh}^{(1)}$ around threshold can be more than $20\%$ if mass of the new scalar is light. For $\lambda_{\Phi{S}}=1.5,3$, the deviation $\delta_{hhh}^{(1)}$ can reach above $30\%$ in the vicinity of threshold. For $\lambda_{\Phi{S}}=-1$, $m_H$ can be light. The deviation $\delta_{hhh}^{(1)}$ is negative in this case and can be even $-50\%$ in the threshold enhanced region. The radiative correction for the $hZZ$ coupling is from the counter-term, which is universal in this model and always with negative sign. $\delta_{hZZ}^{(1)}$ is independent of the sign of $\lambda_{\Phi{S}}$ and its typical size is $-0.2\%\sim-2\%$. When combining $hhh$ and $hZZ$ precision measurements together, parameter space of this model can be probed well including the sign and size of $\lambda_{\Phi{S}}$. 
Shi-Ping He, Shou-hua Zhu
hep-ph