[Paper Review] Nonperturbative investigation of the diquark potential

Z. Fodor, Christian Hoelbling+2 more|ArXiv.org|Nov 16, 2005

Quantum Chromodynamics and Particle Interactions10 references3 citations

TL;DR

This paper presents a nonperturbative lattice QCD study of the diquark potential using Polyakov loop correlations in full QCD with dynamical fermions. It finds an attractive quark-quark interaction, with the diquark free energy showing a similar shape to the quark-antiquark potential but weaker, and observes a flattening above the critical temperature, indicating deconfinement effects.

ABSTRACT

We perform an investigation of the static quark-quark-potential both in the confined and the deconfined phase. We discuss conceptual and technical problems and present first results of an exploratory numerical investigation.

Motivation & Objective

• To investigate the static quark-quark potential in both confined and deconfined phases of QCD using Polyakov loop correlations.
• To determine whether diquarks form bound states by measuring the free energy of two quarks via Polyakov loop correlators.
• To address technical challenges in computing the Polyakov loop and its correlators in full QCD, especially at low temperatures.
• To compare the diquark free energy with the quark-antiquark potential to assess the strength of quark-quark attraction.
• To explore the behavior of the diquark potential near and above the deconfinement transition temperature.

Proposed method

• Use the Polyakov loop correlation function $\left< P(x)P(y) \right> $ as a proxy for the diquark free energy via the relation $ \widehat{F_{qq}} = -\frac{1}{aN_t} \log \left( \frac{\left< P(x)P(y) \right>}{\left< P(x) \right>^2} \right) $.
• Perform lattice simulations with 2+1 flavor dynamical staggered fermions and the Symanzik tree-level improved gauge action on $18^3 \times 6$ lattices.
• Utilize finite-temperature configurations from previous simulations to access the deconfined phase at $T/T_c = 1.14$ and the confined phase at $T/T_c = 0.96$.
• Apply box-averaging for large distances ($r > 0.5$ fm) to reduce statistical errors in the diquark free energy.
• Use a modified version of the MILC code with a next-nearest-neighbor communication architecture for efficient computation.
• Avoid gauge fixing by relying solely on Polyakov loop operators, which are gauge-invariant and sensitive to center symmetry.

Experimental results

Research questions

• RQ1 Does the correlation between two Polyakov loops signal an attractive interaction between two quarks in full QCD?
• RQ2 How does the diquark free energy compare quantitatively to the quark-antiquark potential in both confined and deconfined phases?
• RQ3 What is the behavior of the diquark potential at large distances, particularly above the critical temperature?
• RQ4 Can the diquark potential be reliably computed at zero temperature, given the exponential decay of the Polyakov loop?
• RQ5 Does the diquark free energy exhibit a flattening at large distances, indicating deconfinement, similar to the quark-antiquark system?

Key findings

• The diquark free energy shows a clear attractive interaction between two quarks, as evidenced by a decreasing free energy at short distances.
• The diquark free energy has a similar functional form to the quark-antiquark potential but is weaker in magnitude.
• At $T/T_c = 0.96$, the diquark free energy decreases at short distances and begins to flatten at $r \gtrsim 0.8$ fm, indicating a long-range attractive component.
• At $T/T_c = 1.14$, the diquark free energy flattens above $r \approx 0.8$ fm and becomes compatible with zero, consistent with deconfinement.
• The diquark free energy does not approach a constant value below $T_c$ in the same way as in quenched QCD, suggesting a more complex behavior in full QCD.
• The signal for diquark attraction remains detectable even at large distances, though with increasing statistical uncertainty, and is compatible with zero at $r > 0.8$ fm in both phases.