[Paper Review] Improved Spectroscopy of Minimal Walking Technicolor

Eoin Kerrane, Luigi Del Debbio+7 more|arXiv (Cornell University)|Nov 2, 2010

Quantum Chromodynamics and Particle Interactions10 references4 citations

TL;DR

This study presents improved lattice QCD simulations of minimal walking technicolor (MWT), an SU(2) gauge theory with two adjoint fermions, to investigate its near-conformal dynamics. Using high-statistics spectroscopy across multiple lattice volumes, it finds strong evidence for hyperscaling behavior and a low anomalous dimension $γ_*$, indicating the theory may be near-conformal with $γ_* \ll 1$, consistent with a mass-deformed conformal fixed point.

ABSTRACT

We present an improved study of spectroscopic observables in the $SU(2)$ Yang-Mills theory with two adjoint fermions. We make an improvement on the precision of previous results which clarify the scale of finite volume effects present. This analysis adds to the evidence for near-conformal dynamics of this theory, while indicating a preference for a low anomalous mass dimension of the massless theory.

Motivation & Objective

• To investigate whether minimal walking technicolor (MWT) exhibits near-conformal dynamics via improved lattice spectroscopy.
• To quantify finite-volume effects and systematic uncertainties in spectroscopic observables of MWT.
• To determine the critical exponent $\rho = 1/(1 + \gamma_*)$ from meson mass scaling and finite-size scaling relations.
• To assess the anomalous dimension $\gamma_*$ at the infrared fixed point using multiple fitting methods.
• To test the consistency of MWT with hyperscaling and conformal scaling laws in the chiral limit.

Proposed method

• Lattice simulations of SU(2) Yang-Mills theory with two adjoint fermions using the Wilson gauge and fermion actions.
• Employment of the RHMC algorithm for fermion determinants and the HiRep code for general Nc, Nf, and representation simulations.
• Measurement of PCAC quark mass, pseudoscalar and vector meson masses, decay constants, and chiral condensate across multiple volumes (16×8³ to 64×24³).
• Fitting meson masses to the hyperscaling relation $M \sim m^\rho$ with $\rho = 1/(1 + \gamma_*)$ to extract $\gamma_*$.
• Application of finite-size scaling laws $L M \sim \Upsilon(L m^\rho)$ to compare data across lattice sizes and constrain $\gamma_*$.
• Use of the Gell-Mann–Oakes–Renner relation to analyze chiral condensate scaling and detect chiral symmetry breaking.

Experimental results

Research questions

• RQ1 Does the pseudoscalar meson mass in MWT scale as $m_{PS} \sim m^\rho$ with $\rho = 1/(1 + \gamma_*)$, indicating hyperscaling in a near-conformal theory?
• RQ2 What is the value of the anomalous dimension $\gamma_*$ at the infrared fixed point, as inferred from meson mass and finite-size scaling?
• RQ3 How do finite-volume effects influence the spectroscopic observables in MWT, and are they under control on large lattices?
• RQ4 Does the vector meson mass vanish in the chiral limit, and does the ratio $m_V / m_{PS}$ remain finite, as expected in a conformal theory?
• RQ5 Is there evidence for a vanishing chiral condensate in the chiral limit, inconsistent with spontaneous chiral symmetry breaking?

Key findings

• The pseudoscalar meson mass $m_{PS}$ scales as $m_{PS} \sim m^\rho$ with $\rho \approx 1/(1 + \gamma_*)$, supporting hyperscaling behavior expected in a mass-deformed conformal theory.
• The vector meson mass $m_V$ vanishes in the chiral limit, and the ratio $m_V / m_{PS}$ remains close to unity, inconsistent with chiral symmetry breaking but consistent with conformal scaling.
• The ratio $m_{PS}^2 / m$ vanishes in the chiral limit, contradicting the $m_{PS} \sim \sqrt{m}$ scaling of QCD and indicating non-chiral dynamics.
• The chiral condensate, estimated via the GMOR relation, shows no finite value in the chiral limit, further indicating no spontaneous chiral symmetry breaking.
• Fits to the hyperscaling and finite-size scaling relations yield no preferred non-zero $\gamma_*$, with data favoring a low anomalous dimension $\gamma_* \ll 1$.
• Finite-volume effects are small on the largest lattices, and systematic uncertainties are well-controlled, supporting the reliability of the results.