[Paper Review] Baryon spectrum in the composite sextet model

Zoltán Fodor, Kieran Holland+4 more|Repository of the Academy's Library (Library of the Hungarian Academy of Sciences)|Jan 26, 2015

Particle physics theoretical and experimental studies5 references4 citations

TL;DR

This paper presents the first lattice QCD study of baryon states in an SU(3) gauge theory with two fermions in the sextet (2-index symmetric) representation, a candidate for a minimal composite Higgs model. Using staggered fermions on lattices with β=3.20 and m=0.003–0.008, the authors compute the nucleon mass and find it to be approximately 3 TeV in the chiral limit, indicating a heavy baryon state with potential implications for dark matter as a fractionally charged massive particle.

ABSTRACT

The strongly coupled near-conformal gauge theory with two fermion flavors in the two-index symmetric (sextet) representation of SU(3) is potentially a minimal realization of the composite Higgs mechanism. We discuss the staggered fermion construction of baryonic states, present our first numerical results and comment on implications for dark matter.

Motivation & Objective

• To investigate the existence and mass of baryonic states in a strongly coupled near-conformal SU(3) gauge theory with two sextet fermions, a minimal candidate for composite Higgs physics.
• To construct and evaluate baryon operators in the staggered fermion formalism, addressing the non-trivial color-singlet contraction required for sextet fermions.
• To determine the chiral extrapolation of the nucleon mass and assess its implications for dark matter, particularly as a fractionally charged massive particle (FCHAMP).
• To evaluate the stability and signal quality of different baryon operators to ensure reliable spectroscopy in the lattice simulation.
• To lay the groundwork for future continuum limit studies by comparing baryon mass ratios with other dimensionful quantities across different lattice β values.

Proposed method

• Constructing the baryon operator via symmetric color contraction using epsilon tensors: ε_abc ε_a'b'c' ψ_aa' ψ_bb' ψ_cc', ensuring a color-singlet state from three sextet fermions.
• Implementing the staggered fermion formalism on lattices with volume 32³×64 and 48³×96, using β=3.20 and fermion masses m=0.003 to 0.008.
• Measuring the nucleon correlation function using multiple operator types (e.g., IV_xy, IV_yz, IV_zx) to assess signal-to-noise ratios and consistency across choices.
• Performing time-range fits (t_min to t_max=20) to extract the nucleon mass M_N, with stability confirmed across different fit ranges and operators.
• Using the pion decay constant F_π as a scale-setting observable, with F=0.0253(4) in lattice units, and extrapolating to physical units assuming F=246 GeV.
• Comparing the nucleon mass with meson states (π, ρ, a₁) in the chiral limit to assess the hierarchy of masses in the spectrum.

Experimental results

Research questions

• RQ1 Does a stable, color-singlet baryon state exist in the sextet composite Higgs model, and what is its mass in the chiral limit?
• RQ2 How do different staggered fermion baryon operators compare in terms of signal-to-noise ratio and fit stability?
• RQ3 What is the mass of the lightest baryon state in the SU(3) sextet model, and how does it compare to other mesonic states?
• RQ4 Can the baryon mass ratio with other dimensionful quantities help assess the approach to the continuum limit?
• RQ5 What are the cosmological and dark matter implications of a 3 TeV baryon state in this model?

Key findings

• The nucleon mass in the chiral limit is estimated at approximately 3 TeV when the scale is set by F_π = 246 GeV, based on a lattice calculation at β=3.20.
• The chiral extrapolation of the nucleon mass shows it is heavier than the low-lying mesons (π, ρ, a₁), as expected in a composite Higgs model.
• All tested baryon operators exhibit stable fits, consistent signal-to-noise ratios (~5%), and agreement within errors, indicating robust spectroscopy.
• The nucleon state is stable under the new gauge force and weak decay due to conserved U(1)_em baryon number symmetry, supporting its potential as a dark matter candidate.
• The model does not support remnant Goldstone bosons as dark matter, but the heavy, fractionally charged baryon may act as a FCHAMP, though its relic abundance is expected to be too low for detection.
• The results provide a crucial first step toward testing the model’s viability and assessing its approach to the continuum limit via mass ratios across β values.