arXiv 1709.035012017-09-11hep-phhep-ex

BSM模型中的扰动约束

Perturbativity Constraints in BSM Models

Manuel E. Krauss, Florian Staub

备注：: 64 pages, 20 figures
发表信息：: Eur. Phys. J. C (2018) 78:185
DOI：: 10.1140/epjc/s10052-018-5676-5

摘要：

对标准模型的非超对称扩展进行的唯象研究通常使用树级参数作为输入来定义模型的标量扇区。这隐含地假设标量扇区的完整壳上计算是可能的-并且是有意义的。然而，这并不一定是我们在Georgi-Machacek模型的例子中明确展示的情况。该模型具有吸引人的保管对称性，以解释$ρ$参数的小。然而，该模型不能在不破坏保管对称性的情况下在壳层上重正化。此外，我们发现，它经常发生的辐射修正是如此之大，任何考虑的基础上微扰膨胀似乎是毫无意义的：反项四次耦合可以变得比$4π$和/或两个环路的质量修正可以变得比一个环路的更大。因此，条件是必要的，挑出来的参数区域，不能处理微扰。我们提出并讨论了不同的设置这样的微扰条件，并显示其对参数空间的Georgi-Machacek模型的影响。此外，所提出的条件是足够的一般性，他们可以适用于其他模型以及。我们还指出，真空稳定性的限制在Georgi-Machacek模型，到目前为止，只适用于在树的水平，收到至关重要的辐射修正。我们表明，大区域的参数空间，其特点是一个稳定的电弱真空在回路水平会被错误地排除了树级条件。

英文摘要：

Phenomenological studies performed for non-supersymmetric extensions of the Standard Model usually use tree-level parameters as input to define the scalar sector of the model. This implicitly assumes that a full on-shell calculation of the scalar sector is possible - and meaningful. However, this doesn't have to be the case as we show explicitly at the example of the Georgi-Machacek model. This model comes with an appealing custodial symmetry to explain the smallness of the $ρ$ parameter. However, the model cannot be renormalised on-shell without breaking the custodial symmetry. Moreover, we find that it can often happen that the radiative corrections are so large that any consideration based on a perturbative expansion appears to be meaningless: counter-terms to quartic couplings can become much larger than $4π$ and/or two-loop mass corrections can become larger than the one-loop ones. Therefore, conditions are necessary to single out parameter regions which cannot be treated perturbatively. We propose and discuss different sets of such perturbativity conditions and show their impact on the parameter space of the Georgi-Machacek model. Moreover, the proposed conditions are general enough that they can be applied to other models as well. We also point out that the vacuum stability constraints in the Georgi-Machacek model, which have so far only been applied at the tree level, receive crucial radiative corrections. We show that large regions of the parameter space which feature a stable electroweak vacuum at the loop level would have been - wrongly - ruled out by the tree-level conditions.

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