arXiv 2008.070512020-08hep-ph

动力学混合、保管对称性和暗$Z^{\prime}$质量的下限

Kinetic mixing, custodial symmetry and a lower bound on the dark $Z^{\prime}$ mass

M. Napsuciale, S. Rodríguez, H. Hernández-Arellano

备注：: 9 pages, notation changed to harmonize it with the PDG one, radiative corrections by SM particles explicitly included

摘要：

在这项工作中，我们考虑的标准模型的扩展暗领域的阿贝尔$U(1)_{d}$自发破缺规范对称性在一个隐藏的暗物质的情况下。考虑到所有的四维规范不变项，我们表明，树级关系$M^{2}_{W}=M^{2}_{\tilde Z} \cos^{2} \tilde θ_{w}$持有，并允许写在中性质量规范玻色子扇区，$θ_ζ$，在$M_{Z}$，弱混合角和物理暗规范$Z^{\prime}$玻色子的质量的值的动力学混合诱导的混合角。在环路级，在$\overline{MS}$方案中获得类似的关系。使用从全局拟合到比率$ρ_{0}=M^{2}_{W}/\hat{c}^{2}_{Z} M^{2}_{Z}\hatρ$的弱电精度数据中提取的结果，我们获得了在$94\%$置信水平下的暗$Z^{\prime}$质量的下限$M_{Z^{\prime}}> M_{Z}$。我们认为，这个下限持有的物理理论的一般情况下，超出了标准模型与额外的$U(1)$规范因子子群，只要扩展希格斯势尊重保管对称性。

英文摘要：

In this work we consider the extension of the standard model by dark fields with an Abelian $U(1)_{d}$ spontaneously broken gauge symmetry in a hidden dark matter scenario. Considering all the dimension four gauge invariant terms we show that the tree-level relation $M^{2}_{W}=M^{2}_{\tilde Z} \cos^{2} \tilde θ_{w}$ holds and permits to write the mixing angle induced by the kinetic mixing in the neutral massive gauge boson sector, $θ_ζ$, in terms of the values of $M_{Z}$, the weak mixing angle and of the mass of the physical dark gauge $Z^{\prime}$ boson. At the loop level, a similar relation is obtained in the $\overline{MS}$ scheme. Using the result extracted from the global fit to electroweak precision data for the ratio $ρ_{0}=M^{2}_{W}/\hat{c}^{2}_{Z} M^{2}_{Z}\hatρ$, we obtain a lower bound $M_{Z^{\prime}}> M_{Z}$ for the dark $Z^{\prime}$ mass at the $94\%$ confidence level. We argue that this lower bound holds in the general case of theories for physics beyond the standard model with an extra $U(1)$ gauge factor subgroup, whenever the extended Higgs potential respects custodial symmetry.

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