Hidden Local Symmetry at Loop -- A New Perspective of Composite Gauge Boson and Chiral Phase Transition --
Hidden Local Symmetry at Loop -- A New Perspective of Composite Gauge Boson and Chiral Phase Transition --
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DOI：
10.1016/s0370-1573(03)00139-x
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发表时间：
2003-02
期刊：
影响因子：
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通讯作者：
M. Harada;K. Yamawaki
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文献类型：
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作者：
M. Harada;K. Yamawaki
我们基于伪标量介子 (π) 作为 Nambu-Goldstone 玻色子和矢量介子 (ρ) 作为规范玻色子的隐藏局域对称性 (HLS) 模型，开发了超出标准模型的 QCD 和类 QCD 理论的有效场论。 HLS 规范对称性的存在对于系统低能展开或具有 ρ 和 π 环的手征微扰理论 (ChPT) 至关重要。我们首先用 HLS 详细制定 ChPT，并进一步包括对手性相变至关重要的二次散度。给出了HLS模型参数的单环重整化群方程的详细计算，并在此基础上给出了全参数空间的相图。 HLS 模型的裸参数（在截止点 Λ 处定义）是通过当前相关器的算子乘积展开与 Λ 处的基础 QCD 进行匹配（“威尔逊匹配”）来确定的。令人惊讶的是，威尔逊匹配为有效场论提供了潜在 QCD 的其他未知信息，例如显式 Nc 依赖性，并预测了三味 QCD 的低能量现象，与实验非常一致。此外，当手性对称性恢复发生在底层的 QCD 中时，威尔逊匹配独特地导致了矢量表现（VM）作为维格纳实现手性对称性的新模式，其中 ρ 因无质量 π 作为手性伙伴而变得简并。在VM中，向量的优势被严重侵犯。 VM实际上是在Nf→Nfcrit−0时在大NfQCD中实现的，手性对称恢复点Nfcrit≃5Nc/3与Nc=3时的晶格模拟大致一致。临界点附近的大NfQCD提供了强耦合规范理论的具体例子，该理论产生了弱耦合轻复合规范玻色子的理论。与 SUSY QCD 中的塞伯格对偶性类似，SU(Nf) HLS 扮演着与 SU(Nc) QCD 对偶的“磁理论”角色，作为“电理论”。 HLS 低能量定理在任何循环阶数下的证明都是完整的，甚至包括二次散度。 VM也可以以热和/或密集QCD来实现。
We develop an effective field theory of QCD and QCD-like theories beyond the Standard Model, based on the hidden local symmetry (HLS) model for the pseudoscalar mesons (π) as Nambu–Goldstone bosons and the vector mesons (ρ) as gauge bosons. The presence of gauge symmetry of HLS is vital to the systematic low energy expansion or the chiral perturbation theory (ChPT) with loops of ρ as well as π. We first formulate the ChPT with HLS in details and further include quadratic divergences which are crucial to the chiral phase transition. Detailed calculations of the one-loop renormalization-group equation of the parameters of the HLS model are given, based on which we show the phase diagram of the full parameter space. The bare parameters (defined at cutoff Λ) of the HLS model are determined by the matching (“Wilsonian matching”) with the underlying QCD at Λ through the operator-product expansion of current correlators. Amazingly, the Wilsonian matching provides the effective field theory with the otherwise unknown information of the underlying QCD such as the explicit Ncdependence and predicts low energy phenomenology for the three-flavored QCD in remarkable agreement with the experiments. Furthermore, when the chiral symmetry restoration takes place in the underlying QCD, the Wilsonian matching uniquely leads to the Vector Manifestation (VM) as a new pattern of Wigner realization of chiral symmetry, with the ρ becoming degenerate with the massless π as the chiral partner. In the VM the vector dominance is badly violated. The VM is in fact realized in the large NfQCD when Nf→Nfcrit−0, with the chiral symmetry restoration point Nfcrit≃5Nc/3 being in rough agreement with the lattice simulation for Nc=3. The large NfQCD near the critical point provides a concrete example of a strong coupling gauge theory that generates a theory of weakly coupled light composite gauge bosons. Similarly to the Seiberg duality in the SUSY QCD, the SU(Nf) HLS plays a role of a “magnetic theory” dual to the SU(Nc) QCD as an “electric theory”. The proof of the low energy theorem of the HLS at any loop order is intact even including quadratic divergences. The VM can be realized also in hot and/or dense QCD.