自然性变得简单：最小SM扩展上的双循环自然性界限
Naturalness made easy: two-loop naturalness bounds on minimal SM extensions
摘要：
本文的主要结果是收集保守的自然界的标准模型的最小扩展（类矢量）费米或标量规范多重态。在内部，我们倡导建立在重正化群方程基础上的直观和物理的自然概念。在标准模型加质量为$M$的规范多重态的有效场论中，低尺度Higgs质量参数是定义在某个高尺度$Λ_h > M$上的$\overline{\rm MS}$输入参数的可计算函数。如果希格斯质量对这些输入参数非常敏感，那么这意味着自然性问题。为了合理地捕捉的灵敏度，它示出了如何可以严格推导出的灵敏度测量作为贝叶斯模型的比较，这减少了在相关的限制Barbieri-Giudice的微调措施。这个措施是完全推广到任何微扰EFT。我们的双圈重正化组研究的有趣结果如下：对于$Λ_h=Λ_{Pl}$，我们发现在$M<\mathcal{O}(1$ -- $10)$ TeV的各种规范多重态的质量上存在“$10\%$微调”边界，而在费米子规范多重态上的边界明显弱于纯量，这些边界在极限$Λ_h\to M^+$中保持有限，减弱到$M<\mathcal{O}(10$ -- $100)$ TeV;而有色多重态的边界并不比电弱多重态更严格，因为它们只直接修正了三圈处的希格斯质量。
英文摘要：
The main result of this paper is a collection of conservative naturalness bounds on minimal extensions of the standard model by (vector-like) fermionic or scalar gauge multiplets. Within, we advocate for an intuitive and physical concept of naturalness built upon the renormalisation group equations. In the effective field theory of the standard model plus a gauge multiplet with mass $M$, the low scale Higgs mass parameter is a calculable function of $\overline{\rm MS}$ input parameters defined at some high scale $Λ_h > M$. If the Higgs mass is very sensitive to these input parameters, then this signifies a naturalness problem. To sensibly capture the sensitivity, it is shown how a sensitivity measure can be rigorously derived as a Bayesian model comparison, which reduces in a relevant limit to a Barbieri--Giudice-like fine-tuning measure. This measure is fully generalisable to any perturbative EFT. The interesting results of our two-loop renormalisation group study are as follows: for $Λ_h=Λ_{Pl}$ we find "$10\%$ fine-tuning" bounds on the masses of various gauge multiplets of $M<\mathcal{O}(1$--$10)$ TeV, with bounds on fermionic gauge multiplets significantly weaker than for scalars; these bounds remain finite in the limit $Λ_h\to M^+$, weakening to $M<\mathcal{O}(10$--$100)$ TeV; and bounds on coloured multiplets are no more severe than for electroweak multiplets, since they only directly correct the Higgs mass at three-loop.
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