作为受保护集体本征模的自然轻复合希格斯玻色子
Naturally Light Composite Higgs as a Protected Collective Eigenmode
AI总结：
研究提出一种新机制，通过多算子标量核的本征值保护轻复合希格斯玻色子，用两个指标识别集体轻性，证明该机制存在且可通过特定方法检验。
摘要：
标准的轻复合希格斯玻色子途径要么依赖于调整单个接近临界的通道，要么保护陪集的赝南布 - 戈德斯通坐标。我们引入了第三种机制类别，其中受保护的对象是强相互作用扇区重整化多算子标量核的一个本征值。两个基不变诊断量，扇区参与数\(\Psec\)和扇区能隙比\(\Rcoll\)，识别集体轻性，但它们无法区分偶然的小行列式和受保护的零模；缺失的判别器是微观灵敏度\(\Delta_g=\left|\partial\ln|m_H^2|/\partial\ln g\right|\)。一个受保护的集体希格斯玻色子由\(\Rcoll\gg1\)，\(\Psec>1\)和\(\Delta_g=\mathcal{O}(1)\)定义。我们证明这个类别是非空的。一个一阶的TC - DTC锁定不变量禁止树级对齐曲率，而通用的类矢量DQCD桥费米子，在微观拉格朗日量中无质量但获得一个共同的DQCD组成质量，满足\(\partial_h^2\sum_A\Tr\mathcal{M}_A^2\big|_0=0\)。因此，对齐标量仅在联合双spurion阶被提升，\(m^2_{\mathrm{br}}=-(d_X/2\pi^2)g_T^2g_D^2(f_B^4/f_H^2)L_X\)，在领先对数阶给出\(\Delta_{g_T}=\Delta_{g_D}=2\)。相同的DTC拓扑允许集体顶完备化以及减少正色荷对\(S\)贡献的矢量解耦途径。该机制可通过扇区限制的晶格光谱学和耦合响应扫描来证伪。
英文摘要：
Standard routes to a light composite Higgs either rely on tuning a single channel near criticality or protect a pseudo-Nambu--Goldstone coordinate of a coset. We introduce a third mechanism class in which the protected object is an \emph{eigenvalue} of the renormalized multi-operator scalar kernel of the strong sector. Two basis-invariant diagnostics, a sector participation number $\Psec$ and a sector gap ratio $\Rcoll$, identify collective lightness, but they cannot distinguish an accidental small determinant from a protected zero mode; the missing discriminator is the microscopic sensitivity $Δ_g=\left|\partial\ln|m_H^2|/\partial\ln g\right|$. A protected collective Higgs is defined by $\Rcoll\gg1$, $\Psec>1$, and $Δ_g=\mathcal{O}(1)$. We prove that this class is nonempty. A rank-one TC--DTC locking invariant forbids tree-level aligned curvature, while universal vectorlike DQCD bridge fermions, massless in the microscopic Lagrangian but acquiring a common DQCD constituent mass, obey $\partial_h^2\sum_A\Tr\mathcal{M}_A^2\big|_0=0$. The aligned scalar is therefore lifted only at joint two-spurion order, $m^2_{\mathrm{br}}=-(d_X/2π^2)g_T^2g_D^2(f_B^4/f_H^2)L_X$, giving $Δ_{g_T}=Δ_{g_D}=2$ at leading logarithmic order. The same DTC topology admits a collective top completion and a vector-decoupling route to reducing the positive technicolor contribution to $S$. The mechanism is falsifiable by sector-restricted lattice spectroscopy and coupling-response scans.
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