arXiv 1009.54822010-09hep-phhep-lathep-th

保形边技术

Techni-dilaton at Conformal Edge

Michio Hashimoto, Koichi Yamawaki

备注：: 17 pages, 14 figures; discussions clarified, references added, to appear in Phys.Rev.D
发表信息：: Phys.Rev.D83:015008,2011
DOI：: 10.1103/PhysRevD.83.015008

摘要：

Technicolor（TD）是很早以前在Technicolor（TC）近临界性/保形性中提出的。为了揭示TD的临界行为，我们明确地计算了非微扰贡献的尺度异常$<θ^μ_μ>$和技术胶子凝聚$<G_{μν}^2>$，这是由动力学质量m的技术费米子。我们的计算是基于（改进的）阶梯Schwinger-Dyson方程，与规范耦合$α$取代的双循环运行一个$α(μ)$具有卡斯韦尔-班克斯-扎克斯IR固定点$α_*$：$α(μ) \simeq α= α_*$的IR区域$m < μ< Λ_{TC}$，其中$Λ_{TC}$是与微扰标度异常相关的本征标度（类似于QCD的$Λ_{QCD}$）。我们发现$-<θ^μ_μ>/m^4\to const \ne 0$和$<G_{μν}^2>/m^4\to (α/α_{cr}-1)^{-3/2}\to\infty$处于临界极限$m/Λ_{TC}\sim\exp(-π/(α/α_{cr}-1)^{1/2})\to 0$（$α=α_* \to α_{cr}$）（“共形边”）.我们的结果精确地再现了形式恒等式$<θ^μ_μ>=(β(α)/4 α) <G_{μν}^2>$，其中$β(α)=-(2α_{cr}/π) (α/α_{cr}-1)^{3/2}$是对应于$m/Λ_{TC}$的上述本质奇异标度的非微扰beta函数。因此，PCDC意味着临界极限下的$(M_{TD}/m)^2 (F_{TD}/m)^2=-4<θ_μ^μ>/m^4 \to const \ne 0$，其中$M_{TD}$是TD的质量，$F_{TD}$是TD的衰变常数。因此，我们得出结论，在临界极限的TD可以成为一个“真正的（无质量）南武-戈德斯通玻色子”$M_{TD}/m\to 0$，只有当$m/F_{TD}\to 0$，即得到解耦，是“全息TD”的哈巴松崎山胁的情况下。退耦的TD可能是暗物质的候选者。

英文摘要：

Techni-dilaton (TD) was proposed long ago in the technicolor (TC) near criticality/conformality. To reveal the critical behavior of TD, we explicitly compute the nonperturbative contributions to the scale anomaly $<θ^μ_μ>$ and to the techni-gluon condensate $<G_{μν}^2>$, which are generated by the dynamical mass m of the techni-fermions. Our computation is based on the (improved) ladder Schwinger-Dyson equation, with the gauge coupling $α$ replaced by the two-loop running one $α(μ)$ having the Caswell-Banks-Zaks IR fixed point $α_*$: $α(μ) \simeq α= α_*$ for the IR region $m < μ< Λ_{TC}$, where $Λ_{TC}$ is the intrinsic scale (analogue of $Λ_{QCD}$ of QCD) relevant to the perturbative scale anomaly. We find that $-<θ^μ_μ>/m^4\to const \ne 0$ and $<G_{μν}^2>/m^4\to (α/α_{cr}-1)^{-3/2}\to\infty$ in the criticality limit $m/Λ_{TC}\sim\exp(-π/(α/α_{cr}-1)^{1/2})\to 0$ ($α=α_* \to α_{cr}$) ("conformal edge"). Our result precisely reproduces the formal identity $<θ^μ_μ>=(β(α)/4 α) <G_{μν}^2>$, where $β(α)=-(2α_{cr}/π) (α/α_{cr}-1)^{3/2}$ is the nonperturbative beta function corresponding to the above essential singularity scaling of $m/Λ_{TC}$. Accordingly, the PCDC implies $(M_{TD}/m)^2 (F_{TD}/m)^2=-4<θ_μ^μ>/m^4 \to const \ne 0$ at criticality limit, where $M_{TD}$ is the mass of TD and $F_{TD}$ the decay constant of TD. We thus conclude that at criticality limit the TD could become a "true (massless) Nambu-Goldstone boson" $M_{TD}/m\to 0$, only when $m/F_{TD}\to 0$, namely getting decoupled, as was the case of "holographic TD" of Haba-Matsuzaki-Yamawaki. The decoupled TD can be a candidate of dark matter.

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摘要：

英文摘要：

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