The Nontrivial Vacuum Structure of an Extended $t\bar{t}$ BEH (Higgs) Bound State

TL;DR

The paper develops a Lorentz-invariant, bilocal description of a BEH bound state formed from ar{t}t, introducing a vacuum state Φ(r) built as a Lorentz-invariant sum over frame-specific internal wave-functions φ_ω(r). By treating the relative-time degree of freedom as a gauge variable and integrating over all ω^μ, the authors construct a vacuum that supports a Schrödinger–Klein–Gordon-like bound-state dynamics with a sombrero potential, yielding a Higgs-like excitation h(X) as a collective mode. The formalism leads to an effective action with a predicted high-scale binding interaction around M_0 ~ 6 TeV and a color-octet of colorons, while diluting the internal wave-function at r=0 to naturally suppress Yukawa and quartic couplings to match observed values. This approach aims to reconcile naturalness with experimental BEH properties, offering testable predictions for new resonances and higher-dimension operators arising from the internal structure. Overall, the work presents a self-consistent, Lorentz-invariant mechanism for top-condensation-based electroweak symmetry breaking with distinctive phenomenological signatures.

Abstract

In a recent reformulation of top-quark condensation for the Brout-Englert-Higgs boson, we introduced an extended internal wave-function, $φ(r)$. We show how this leads to a manifestly Lorentz invariant formalism, where the absence of ``relative time'' is a gauge invariance of the bilocal field theory. This dictates a novel and nontrivial Lorentz invariant vacuum structure for the BEH boson, the relativistic generalization of a condensed matter state such as a BCS or Bose-Einstein condensate.

Figures (1)

• Figure 1: Vacuum wave-function, $\Phi(r)$, spanning the timelike hyperboloid in 4-vectors $\omega_\mu$ by integrating over "internal wave-functions," $\phi_\omega(r)$, to form the Lorentz invariant $\Phi(r)={\cal{N}}\int d^4\omega \;\delta(\omega^2-1) \;\phi_\omega(r^\mu)$.