Symmetry and geometry in a generalized Higgs effective field theory: Finiteness of oblique corrections versus perturbative unitarity
Symmetry and geometry in a generalized Higgs effective field theory: Finiteness of oblique corrections versus perturbative unitarity
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DOI：
10.1103/physrevd.100.075020
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发表时间：
2019-04
影响因子：
5
通讯作者：
R. Nagai;M. Tanabashi;K. Tsumura;Yoshiki Uchida
中科院分区：
文献类型：
--
作者：
R. Nagai;M. Tanabashi;K. Tsumura;Yoshiki Uchida
我们制定了希格斯有效场论 (HEFT) 的推广，包括任意数量的额外中性和带电希格斯玻色子——广义 HEFT (GHEFT)——来描述非最小电弱对称性破缺模型。利用可被视为标量流形上的非线性 sigma 模型的 GHEFT 拉格朗日几何形式，表明标量玻色子散射振幅是用标量流形的黎曼曲率张量（几何）和势的协变导数来描述的。倾斜校正参数 $S$ 和 $U$ 中的单环发散项的系数也可以用 Killing 矢量（对称性）和黎曼曲率张量（几何）来表示。研究发现，涉及希格斯玻色子和纵向规范玻色子的散射振幅的微扰幺正性要求标量流形是平坦的。这种语言也阐明了电弱倾斜校正的有限性与散射振幅的微扰幺正性之间的关系：我们验证了一旦保证了树级幺正性，倾斜校正参数$S$和$U$的单循环有限性就自动得到保证。
We formulate a generalization of Higgs effective field theory (HEFT) including an arbitrary number of extra neutral and charged Higgs bosons---a generalized HEFT (GHEFT)---to describe nonminimal electroweak symmetry breaking models. Using the geometrical form of the GHEFT Lagrangian, which can be regarded as a nonlinear sigma model on a scalar manifold, it is shown that the scalar boson scattering amplitudes are described in terms of the Riemann curvature tensor (geometry) of the scalar manifold and the covariant derivatives of the potential. The coefficients of the one-loop divergent terms in the oblique correction parameters $S$ and $U$ can also be written in terms of the Killing vectors (symmetry) and the Riemann curvature tensor (geometry). It is found that the perturbative unitarity of the scattering amplitudes involving the Higgs bosons and the longitudinal gauge bosons demands that the scalar manifold be flat. The relationship between the finiteness of the electroweak oblique corrections and the perturbative unitarity of the scattering amplitudes is also clarified in this language: we verify that once the tree-level unitarity is ensured, the one-loop finiteness of the oblique correction parameters $S$ and $U$ is automatically guaranteed.