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arXiv 1306.0703hep-ph
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规范膨胀对称破缺的标准模型规范耦合

Standard Model gauge couplings from gauge-dilatation symmetry breaking

Kosuke Odagiri

备注：
19 pages, uses axodraw.sty
发表信息：
Foundations of Physics: Volume 44, Issue 9 (2014), Page 932-952
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摘要：

我们认为，有一个自发破缺的时空坐标和规范理论相位之间的旋转对称性。玻希格斯玻色子的真空期望值决定了规范耦合。这种机制要求三个规范-理论耦合的二次发散，或称蝌蚪，在一定尺度上统一起来。我们验证了这一说法，发现这发生在Λ_u ~ 4 × 10^7 GeV。蝌蚪相消条件与量子自能一起确定了统一蝌蚪系数的值为1/[4 ln（Λ_cut/Λ_u）]。在Λ_u处观测到的耦合常数值意味着Λ_cut约为4 × 10^18 GeV，这接近于约化普朗克质量MR_Pl=M_Pl/sqrt（8 pi）=2.4 × 10^18 GeV。换句话说，通过假设在M_Pl或MR_Pl处截止，我们能够获得与真实值在百分之几内一致的规范耦合的预测。事实证明，这种对称性破缺只有在借助诸如电弱对称性破缺等其他手段产生质量时才能发生。假设动力学对称性破缺起源于MR_P1，我们得到M_chi ~ 10^9 GeV，这不是不合理的，但略高于Λ_u。要消除费米子自能中的反常现象，需要费米子代数等于三。

英文摘要：

We argue that there is a spontaneously broken rotational symmetry between space-time coordinates and gauge theoretical phases. The dilatonic mode acts as the massive Higgs boson, whose vacuum expectation value determines the gauge couplings. This mechanism requires that the quadratic divergences, or tadpoles of the three gauge-theory couplings, unify at a certain scale. We verify this statement, and find that this occurs at Λ_u ~ 4x10^7 GeV. The tadpole cancellation condition, together with the dilaton self-energy, fixes the value of the unified tadpole coefficient to be 1/[4 ln(Λ_cut/Λ_u)]. The observed values of the coupling constants at Λ_u then implies Λ_cut ~ 4x10^18 GeV, which is close to the value of the reduced Planck mass MR_Pl=M_Pl/sqrt(8 pi)=2.4 x 10^18 GeV. In other words, by assuming a cutoff at M_Pl or MR_Pl, we are able to obtain predictions for the gauge couplings which agree with the true values to within a few percent. It turns out that this symmetry breaking can only take place if mass is generated with the aid of some other means such as electroweak symmetry breaking. Assuming dynamical symmetry breaking originating at MR_Pl, we obtain M_chi ~ 10^9 GeV, which is not unreasonable but somewhat higher than Λ_u. The cancellation of an anomaly in the dilaton self-energy requires that the number of fermionic generations equals three.

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