[Paper Review] Bootstrap Dynamical Symmetry Breaking with New Heavy Chiral Quarks

Yukihiro Mimura, W.-S. Hou+1 more|arXiv (Cornell University)|Jun 26, 2012

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper proposes a bootstrap dynamical symmetry breaking mechanism driven by strong Yukawa coupling of a new heavy chiral quark doublet (Q), which generates its own mass while simultaneously justifying the Goldstone boson (G) as massless in loops. Numerical solutions of the gap equation yield a heavy quark mass in the 2–3 TeV range, consistent with a dilaton interpretation of the 126 GeV boson if the true Higgs is heavy or absent.

ABSTRACT

A Higgs-like new boson with mass around 126 GeV is now established, but its true nature probably cannot be settled with 2011--2012 LHC data. We assume it is a dilaton with couplings weaker than the Higgs boson (except to $γγ$ and $gg$), and explore dynamical symmetry breaking (DSB) by strong Yukawa coupling of a yet unseen heavy chiral quark doublet $Q$. Assuming the actual Higgs boson to be heavy, the Goldstone boson $G$ of electroweak symmetry breaking still couples to $Q$ with Yukawa coupling $λ_Q$. A ``bootstrap" gap equation without a Higgs particle is constructed. Electroweak symmetry breaking via strong $λ_Q$ generates both heavy mass for $Q$, while self-consistently justifying $G$ as a massless Goldstone particle in the loop. The spontaneous breaking of scale invariance in principle \emph{allows} for a dilaton. We numerically solve such a gap equation and find the mass of the heavy quark to be a couple of TeV. We offer a short critique on the results of the scale-invariant model of Hung and Xiong, where a similar gap equation is built with a massless scalar doublet. Through this we show that a light SM Higgs at 126 GeV cannot be viable within our approach to DSB, while a dilaton with weaker couplings is consistent with our main result.

Motivation & Objective

• To explore dynamical electroweak symmetry breaking (DSB) without a fundamental Higgs boson, assuming the 126 GeV state is a dilaton with suppressed couplings.
• To construct a self-consistent gap equation that generates the mass of a new heavy chiral quark doublet Q via strong Yukawa coupling to the Goldstone boson G.
• To demonstrate that the Goldstone boson G remains massless in the loop despite the heavy quark mass generation, preserving the Nambu-Goldstone nature.
• To show that a light SM Higgs at 126 GeV is inconsistent with this DSB mechanism, while a dilaton with weaker couplings is viable.
• To provide a framework where scale invariance is spontaneously broken via dynamical dynamics, allowing for a dilaton as a physical state.

Proposed method

• Construct a 'bootstrap' gap equation that self-consistently generates the mass of a heavy chiral quark doublet Q via strong Yukawa coupling λQ to the Goldstone boson G.
• Treat the Goldstone boson G as massless within the loop, based on the experimental fact that electroweak symmetry is spontaneously broken.
• Use the empirical fact that no new states are observed below 1–2 TeV to truncate the momentum integral at 2mQ, with mQ to be solved for.
• Solve the coupled integral equation numerically, drawing analogy to strongly coupled, scale-invariant QED with massless fermions.
• Apply the Landau gauge-like simplification in the context of the gap equation, though the system remains a coupled integral equation.
• Extend the model to include possible Q̄Q mesons (color octets π8, ω8 and singlet ω1), suggesting novel production channels at the LHC.

Experimental results

Research questions

• RQ1 Can electroweak symmetry breaking be dynamically generated via strong Yukawa coupling of a new heavy chiral quark doublet without a fundamental Higgs boson?
• RQ2 Is it possible to construct a self-consistent gap equation where the Goldstone boson remains massless while the heavy quark acquires mass?
• RQ3 What is the resulting mass scale of the heavy chiral quark doublet Q in such a bootstrap DSB scenario?
• RQ4 How does the presence of a 126 GeV dilaton with suppressed couplings compare to the SM Higgs in this framework?
• RQ5 Can this model accommodate a dilaton as a physical state while breaking scale invariance dynamically?

Key findings

• The numerical solution of the bootstrap gap equation yields a heavy chiral quark doublet mass in the 2–3 TeV range.
• The Yukawa coupling λQ required to generate this mass is found to be near the critical value of approximately 4π, analogous to the π–N system.
• The model is inconsistent with a light SM Higgs boson at 126 GeV, as such a state would conflict with the strong-coupling DSB mechanism.
• A dilaton interpretation of the 126 GeV state is consistent with the model, provided its couplings to fermions and vector bosons are suppressed by v/f.
• The model predicts the existence of new Q̄Q mesons, including color octets (π8, ω8) and a color singlet (ω1), which could be observable at the LHC.
• The LHC could test the dilaton nature of the 126 GeV state by measuring suppressed vector boson fusion (VBF) and Higgsstrahlung (VH) production rates, which would reveal the dilaton decay constant f.