[Paper Review] Spectroscopy of SU(4) lattice gauge theory with fermions in the two index anti-symmetric representation

Thomas DeGrand, Yuzhi Liu+3 more|arXiv (Cornell University)|Dec 16, 2014

Particle physics theoretical and experimental studies11 references3 citations

TL;DR

This study presents the first lattice spectroscopy of SU(4) gauge theory with two flavors of Dirac fermions in the two-index antisymmetric (AS2) representation, using Wilson-clover fermions and the Wilson plaquette gauge action at β=9.6. The results show good agreement with large-Nc scaling predictions, including meson and baryon spectra that follow expected patterns such as the rotor formula for baryons and rescaled decay constants consistent with large-Nc expectations, with deviations below 20%.

ABSTRACT

We present a study of spectroscopy of SU(4) lattice gauge theory coupled to two flavors of Dirac fermions in the anti-symmetric two index representation. The fermion representation is real, and the pattern of chiral symmetry breaking is SU(2Nf) -> SO(2Nf) with Nf flavors of Dirac fermions. It is an interesting generalization of QCD, for several reasons: it allows direct exploration of an alternate large Nc expansion, it can be simulated at non-zero chemical potential with no sign problem, and several UV completions of composite Higgs systems are built on it. We present preliminary results on the baryon and meson spectra of the theory and compare them with SU(3) results and with expectations for large Nc scaling.

Motivation & Objective

• To investigate the spectroscopy of SU(4) lattice gauge theory with two flavors of Dirac fermions in the two-index antisymmetric representation.
• To test large-Nc scaling behavior in a theory with a different chiral symmetry breaking pattern than QCD.
• To compare meson and baryon masses and decay constants with SU(3) QCD and quenched SU(Nc) results.
• To assess the validity of large-Nc expansions in a non-fundamental representation with real fermion representations.
• To explore the implications for UV completions of composite Higgs models based on SU(4) gauge theories.

Proposed method

• Lattice simulations are performed using the Wilson plaquette gauge action and Wilson-clover fermions with nHYP-smeared gauge links at β=9.6 and four κ values.
• The quark mass is defined via the axial Ward identity (AWI), and decay constants are computed using matrix elements of axial and vector currents.
• The lattice spacing is fixed using the r1 parameter, defined by r1²F(r1) = -1.0, ensuring comparability across theories.
• Pseudoscalar and vector meson decay constants are renormalized using Z factors close to unity, with rescaling applied for large-Nc comparisons.
• Baryon masses are fitted to the rotor formula M_B(J) ≈ N_b m_0 + B J(J+1)/N_b to extract mass splitting parameters.
• Partially quenched data are used to improve spectral resolution, and results are compared across SU(3), SU(5), SU(7), and SU(4) with AS2 fermions.

Experimental results

Research questions

• RQ1 Does the SU(4) gauge theory with two flavors of AS2 fermions exhibit large-Nc scaling in its meson and baryon spectra?
• RQ2 How do the pseudoscalar and vector meson decay constants in the AS2 representation compare to those in fundamental representations at large Nc?
• RQ3 To what extent does the baryon spectrum follow the rotor model prediction M_B(J) ≈ N_b m_0 + B J(J+1)/N_b?
• RQ4 Is the observed scaling of the baryon mass parameter B with m_0 consistent with the rotor model’s prediction of B ∝ 1/m_0?
• RQ5 Can the AS2 fermion representation in SU(4) gauge theory serve as a viable UV completion for composite Higgs models?

Key findings

• The pseudoscalar and vector meson masses in the SU(4) AS2 theory show weak dependence on Nc and representation, consistent with large-Nc scaling expectations.
• The rescaled pseudoscalar and vector decay constants in SU(4) AS2 lie within 20% of those in SU(3) with fundamental fermions, supporting large-Nc universality.
• The baryon mass spectrum at κ=0.1285 fits well to the rotor formula M_B(J) ≈ N_b m_0 + B J(J+1)/N_b, with m_0 and B as free parameters.
• A log-log plot of r1B vs. 1/(r1m_0) shows a slope near one, indicating B ∝ 1/m_0, consistent with the rotor model’s prediction for the moment of inertia.
• Partially quenched data and dynamical SU(3) results show good agreement with quenched SU(Nc) data, supporting the reliability of the large-Nc extrapolation.
• The phase diagram shows a bulk transition that may terminate the chiral limit at strong coupling, suggesting a critical β beyond which the zero-quark-mass point is inaccessible.