arXiv 0705.45692007-05-31hep-ph

味对称破缺的规范-希格斯统一

Gauge-Higgs unification with broken flavor symmetry

Michael Olschewsky

摘要：

在扩展的SM规范群$G_{SM}^{ex}=SU(2)_{L} \times U(1)_{Y} \times SO(3)_{F}$的基础上，研究了轨道折叠$S^{1}/Z_{2}$上的规范-Higgs统一模型.群$SO(3)_{F}$被视为手征规范味对称。电弱相互作用、味相互作用和希格斯相互作用统一在一个单一规范群SU（7）中，通过轨道折叠和附加边界条件，SU（7）又分解为$G_{SM}^{ex}$。紧化尺度为O（1）TeV。将轨道折叠$S^{1}/Z_{2}$置于晶格上。此设置为RG变换提供了一个起始点。结果，整体被积分出来，额外的维度只由两个点组成：轨道不动点。额外维度中的平行输运子（PT）由于块自旋变换而变得非幺正。此外，希格斯势自然出现。PT可以写为酉因子$e^{A_{y}}$和自伴因子$e^η$的乘积$e^{A_{y}} e^η e^{A_{y}}$。SU（7）的伴随代表相对于$SU(6) \supset G_{SM}^{ex}$的约化$48 \to 35 + 6 + \bar{6} + 1$导致三个$SU(2)_{L}$希格斯二重态：每种味道一个。它们的零模是SM希格斯粒子的替代物。当$G_{SM}^{ex}$自发分解为$U(1)_{em}$时，自然会发生指数规范玻色子质量分裂。这种破缺导致$SO(3)_{F}$味规范玻色子的质量远高于紧化标度。因此，树级FCNC自然被抑制。在作了一些简化的假设后，我们还计算了费米子质量和CKM混合角。对于规范玻色子，费米子的质量自然会发生指数分裂。该模型预测了一个由30个希格斯粒子组成的大希格斯扇区，其最简单的形式是弱混合角$θ=0.125$。

英文摘要：

We study Gauge-Higgs unification model on the orbifold $S^{1}/Z_{2}$ based on the extended SM gauge group $G_{SM}^{ex}=SU(2)_{L} \times U(1)_{Y} \times SO(3)_{F}$. The group $SO(3)_{F}$ is treated as a chiral gauged flavour symmetry. Electroweak-, flavour- and Higgs interactions are unified in one single gauge group SU(7) which is broken again down to $G_{SM}^{ex}$ by orbifolding and imposing additional boundary conditions. The compactification scale is O(1) TeV. The orbifold $S^{1}/Z_{2}$ is put on a lattice. This setting gives a staring point for RG-transformations. As a result the bulk is integrated out and the extra dimension consist of only two points: the orbifold fixed points. Parallel transporters (PT) in the extra dimension become nonunitary as a result of the blockspin transformations. In addition, a Higgs potential emerges naturally. The PTs can be written as a product $e^{A_{y}} e^η e^{A_{y}}$ of unitary factors $e^{A_{y}}$ and a selfadjoint factor $e^η$. The reduction $48 \to 35 + 6 + \bar{6} + 1$ of the adjoint reps of SU(7) with respect to $SU(6) \supset G_{SM}^{ex}$ leads to three $SU(2)_{L}$ Higgs doublets: one for each flavour. Their zero modes serve as a substitute for the SM Higgs. When $G_{SM}^{ex}$ is spontaneously broken down to $U(1)_{em}$, an exponential gauge boson mass splitting occurs naturally. This breaking leads to $SO(3)_{F}$ flavour gauge boson masses much above the compactification scale. Thus tree-level FCNC are naturally suppressed. Making some simplifying assumptions we also calculate fermion masses and CKM mixing angles. As for the gauge bosons an exponential fermion mass splitting occurs naturally. The model predicts a large Higgs sector consisting of 30 Higgs particles and in its simplest form the weak mixing angle $θ=0.125$.

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英文摘要：

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