Two-loop scale-invariant scalar potential and quantum effective operators
Two-loop scale-invariant scalar potential and quantum effective operators
复制标题
二环尺度不变标量势和量子有效算子
DOI：
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发表时间：
2016
期刊：
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通讯作者：
P. Olszewski
中科院分区：
文献类型：
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作者：
D. Ghilencea;Z. Lalak;P. Olszewski
自发打破量子标度不变性可能为解决层级结构和宇宙常数问题提供一种解决方案。在标度不变正则化中，我们计算了类希格斯标量$$Phi$$ϕ的双圈势，在该理论中，标度对称性只被伸缩子自发破坏($$sigma$$σ)。其VEV$$LANGE西格玛
角度$$⟨σ⟩生成DR减去刻度($$MU SIM LANGE西格玛
角度$$μ∼⟨σ⟩)，避免了传统正则化(其中$$MU$$μ$$=$$=固定比例)破坏显式比例对称性。双环电势包含非多项式性质的有效运算符以及新的校正，而不是通过显式中断($$MU$$μ$$=$$=固定标度)获得的校正。这些算子具有$$Phi^6/Sigma^2$$ϕ6/σ2，$$Phi^8/Sigma^4$$ϕ8/σ4等形式，它们在展开约$$LangelSigma时生成一系列高维多项式算子
角度gg朗格Phi
角度$$⟨σ⟩≫⟨ϕ⟩，其中这样的层次结构通过一个初始的、经典的调优来排列。这些算符出现在量子水平上，来自$$sigma$$∝ϵ和$$Phi$$σ之间的相互作用($$Popto epsilon$$ϕ)，这些相互作用在$$d=4$$d=4中消失，但在$$d=4-2epsilon$$d=4-2ϵ中是经典标度不变性所必需的。我们尊重双圈势的Callan-Symanzik方程，并且耦合的双圈β函数不同于用$$Mu=$$μ=固定标度正则化的相同理论的双圈β函数。因此，耦合的运行使人们能够区分自发的和显式的标度对称破缺。
Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems. In a scale-invariant regularization, we compute the two-loop potential of a Higgs-like scalar $$phi $$ϕ in theories in which scale symmetry is broken only spontaneously by the dilaton ($$sigma $$σ). Its VEV $$langle sigma
angle $$⟨σ⟩ generates the DR subtraction scale ($$mu sim langle sigma
angle $$μ∼⟨σ⟩), which avoids the explicit scale symmetry breaking by traditional regularizations (where $$mu $$μ$$=$$= fixed scale). The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking ($$mu $$μ$$=$$= fixed scale). These operators have the form $$phi ^6/sigma ^2$$ϕ6/σ2, $$phi ^8/sigma ^4$$ϕ8/σ4, etc., which generate an infinite series of higher dimensional polynomial operators upon expansion about $$langle sigma
angle gg langle phi
angle $$⟨σ⟩≫⟨ϕ⟩, where such hierarchy is arranged by one initial, classical tuning. These operators emerge at the quantum level from evanescent interactions ($$propto epsilon $$∝ϵ) between $$sigma $$σ and $$phi $$ϕ that vanish in $$d=4$$d=4 but are required by classical scale invariance in $$d=4-2epsilon $$d=4-2ϵ. The Callan–Symanzik equation of the two-loop potential is respected and the two-loop beta functions of the couplings differ from those of the same theory regularized with $$mu =$$μ= fixed scale. Therefore the running of the couplings enables one to distinguish between spontaneous and explicit scale symmetry breaking.