Naturally Light Composite Higgs as a Protected Collective Eigenmode

Abstract

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 $\text{Psec}$ and a sector gap ratio $\text{Rcoll}$, identify collective lightness, but they cannot distinguish an accidental small determinant from a protected zero mode; the missing discriminator is the microscopic sensitivity ${\Delta }_g=\left|\partial \ln |m_H^2|/\partial \ln g\right|$. A protected collective Higgs is defined by $\text{Rcoll}\gg 1$, $\text{Psec}>1$, and ${\Delta }_g=\mathcal{O}(1)$. 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 ${\partial }_h^2{\sum }_A\text{Tr}{\mathcal{M}}_A^2{|}_0=0$. The aligned scalar is therefore lifted only at joint two-spurion order, $m_{\mathrm{br}}^2=-(d_X/2{\pi }^2)g_T^2{g}_D^2(f_B^4/f_H^2)L_X$, giving ${\Delta }_{g_T}={\Delta }_{g_D}=2$ 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.

Comments: 6 pages, 1 figure