Higgs单重态模型中三重Higgs耦合的单圈辐射修正
One-Loop Radiative Correction to the Triple Higgs Coupling in the Higgs Singlet Model
摘要：
125GeV的Higgs玻色子与标准模型（SM）的预言是一致的，但在超越SM（BSM）的物理中，三重Higgs耦合可能偏离SM值。本文研究了在SM的最小扩张中通过加一个实规范单重标量对三重Higgs耦合的辐射修正。在这个模型中有两个标量$h$和$H$，它们都是双重态和单重态的混合态。假设混合角被设置为零，即SM极限，$h$是双重的纯剩余，其行为与树级的SM相同。然而，环路校正可以改变$h$相关的耦合。在这种SM极限情况下，单线态$H$的影响可能会在$h$相关的耦合中出现，特别是三重$h$耦合。我们的数值结果表明，偏差是相当大的。对于$λ_{Φ{S}}=1$（定义见正文），如果新标量的质量较轻，则阈值附近的偏差$δ_{hhh}^{(1)}$可能大于$20\%$。对于$λ_{Φ{S}}=1.5,3$，在阈值附近，偏差$δ_{hhh}^{(1)}$可以达到$30\%$以上。对于$λ_{Φ{S}}=-1$，$m_H$可以很轻。偏差$δ_{hhh}^{(1)}$在这种情况下是负的，并且在阈值增强区域中可以是偶数$-50\%$。对$hZZ$耦合的辐射修正来自反项，反项在该模型中是通用的，并且总是带负号。$δ_{hZZ}^{(1)}$与$λ_{Φ{S}}$的符号无关，其典型大小为$-0.2\%\sim-2\%$。将$hhh$和$hZZ$精度测量结合起来，可以很好地探索该模型的参数空间，包括$λ_{Φ{S}}$的符号和大小。
英文摘要：
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 $λ_{Φ{S}}=1$ (see the text for definition), the deviation $δ_{hhh}^{(1)}$ around threshold can be more than $20\%$ if mass of the new scalar is light. For $λ_{Φ{S}}=1.5,3$, the deviation $δ_{hhh}^{(1)}$ can reach above $30\%$ in the vicinity of threshold. For $λ_{Φ{S}}=-1$, $m_H$ can be light. The deviation $δ_{hhh}^{(1)}$ 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. $δ_{hZZ}^{(1)}$ is independent of the sign of $λ_{Φ{S}}$ 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 $λ_{Φ{S}}$.
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