[Paper Review] New Bound States of several Top-quarks bound by Higgs Exchange

C.D. Froggatt, H. B. Nielsen|ArXiv.org|Oct 2, 2008

Particle physics theoretical and experimental studies7 references13 citations

TL;DR

This paper proposes that the top quark Yukawa coupling is finely tuned to allow a bound state of 12 top-antitop quarks (6+6) to be exactly massless via Higgs exchange, with a predicted coupling value of $ g_t|_{m_{12}=0} = 1.01 \pm 0.15 $, remarkably close to the experimental value of $ 0.935 \pm 0.080 $. The near-degeneracy of a condensed 12-quark state and a non-condensed phase is argued to be explained by the Multiple Point Principle (MPP), offering a solution to the hierarchy problem and predicting a spectrum of heavy bound states.

ABSTRACT

It is suggested that there is a fine tuning principle remarkably arranging the top-quark Yukawa coupling to be just so as to make the mass $m_{12}$ of a bound state of 6 top + 6 anti-top quarks become very small. The value of the top Yukawa needed for Higgs and gluon etc. exchanges just binding the 12 quarks to make this mass zero is $g_t|_{m_{12}=0} =1.01 \pm 0.15$, while the experimental running top Yukawa coupling is $g_t = .94$.

Motivation & Objective

• To investigate whether the top quark Yukawa coupling is fine-tuned to allow a 12-quark bound state (6 top + 6 anti-top) to be exactly massless through Higgs exchange.
• To explore the implications of this near-masslessness for the hierarchy problem in the Standard Model.
• To test whether the observed top Yukawa coupling is consistent with a theoretical prediction derived from the Multiple Point Principle (MPP).
• To predict a spectrum of bound states with Z = 10, 11, 12 constituents and estimate their masses.
• To examine the production and decay signatures of these bound states at the LHC or Tevatron.

Proposed method

• Uses a Bohr model approximation to estimate the binding energy of 12 top-antitop quarks via t- and u-channel Higgs exchange, yielding $ E_{\text{binding}} \propto g_t^4 m_t $.
• Applies the infinite momentum frame approximation to treat the relativistic bound state problem in a non-relativistic-like framework.
• Incorporates corrections from gluon exchange and the replacement of left-handed top quarks by left-handed bottom quarks in the bound state formation.
• Derives the critical Yukawa coupling $ g_t|_{m_{12}=0} $ for which the binding energy exactly cancels the rest mass of the 12-quark system.
• Proposes a mass formula $ m_Z^2 = m_t^2 Z^2 (1 - (Z/12)^2) $ as an interpolation for the mass squared of Z-quark bound states.
• Analyzes production mechanisms at colliders, including pair production of 6t+5\bar{t} color triplet states and subsequent decay into the 12-quark bound state.

Experimental results

Research questions

• RQ1 What value of the top Yukawa coupling would make a 12-quark bound state (6 top + 6 anti-top) exactly massless via Higgs exchange?
• RQ2 How does the observed experimental value of the top Yukawa coupling compare to the theoretical prediction for $ m_{12} = 0 $?
• RQ3 Can the near-degeneracy of a 12-quark condensate phase and a non-condensed phase be explained by a fundamental principle like the Multiple Point Principle (MPP)?
• RQ4 What is the predicted mass spectrum of bound states with Z = 10, 11, 12 top-antitop quarks?
• RQ5 What are the collider signatures for the production and decay of these heavy bound states at the LHC or Tevatron?

Key findings

• The critical top Yukawa coupling for which the 12-quark bound state becomes massless is predicted to be $ g_t|_{m_{12}=0} = 1.01 \pm 0.15 $, based on a detailed calculation including multiple corrections.
• This predicted value is in very good agreement with the experimentally measured running top Yukawa coupling of $ 0.935 \pm 0.080 $, suggesting a remarkable coincidence.
• The mass of the 11-quark bound state is estimated to be $ m_{11} = 760 \, \text{GeV} $, and the 10-quark state to be $ m_{10} = 950 \, \text{GeV} $, based on the proposed mass formula.
• The 12-quark bound state cannot be produced directly via gluon fusion due to its color singlet nature but could be produced as a decay product of heavier 6t+5\bar{t} color triplet states.
• The 12-quark state, if very light, would decay into multiple gluon jets and could appear as a single jet at high energies, potentially detectable in association with top quarks.
• The existence of such a degenerate vacuum with a 12-quark condensate, combined with a Planck-scale degenerate vacuum, provides a solution to the hierarchy problem via the Multiple Point Principle (MPP).