[Paper Review] Analytic continuation of the critical line in 2-color QCD at nonzero temperature and density

Paolo Cea, Leonardo Cosmai+2 more|ArXiv.org|Oct 10, 2007

High-Energy Particle Collisions Research3 citations

TL;DR

This study tests the analytic continuation of the pseudo-critical line in 2-color QCD from imaginary to real chemical potential using Monte Carlo simulations and polynomial interpolation. It finds that a quadratic polynomial in μ² provides the best fit to critical β values at imaginary μ, and the extrapolated line agrees well with direct simulations at real μ, validating the method’s reliability for this observable.

ABSTRACT

We determine the pseudo-critical line in the temperature - chemical potential plane of 2-color QCD by direct Monte Carlo simulations and by analytic continuation from imaginary chemical potential.

Motivation & Objective

• To test the feasibility and accuracy of analytic continuation for the pseudo-critical line in 2-color QCD from imaginary to real chemical potential.
• To compare analytic continuation results with direct Monte Carlo simulations at real chemical potential.
• To optimize the choice of interpolating function for critical β values across varying μ.
• To assess systematic uncertainties in analytic continuation by using multiple observables (chiral condensate, Polyakov loop, plaquette).

Proposed method

• Perform lattice Monte Carlo simulations at fixed temperature and varying imaginary chemical potential (μ = iμ_I) to determine critical β values via peak detection in susceptibility.
• Interpolate the critical β(μ_I²) data using polynomial functions, specifically testing quadratic forms (A + Bμ²), to model the pseudo-critical line.
• Extrapolate the fitted function to real chemical potential (μ_R) to predict critical β values.
• Compare the extrapolated critical β values with direct Monte Carlo determinations at real μ = 0.20 and 0.30.
• Use the bootstrap method to estimate uncertainties in peak positions and fit parameters.
• Validate results by comparing extrapolated endpoints with known Roberge-Weiss transition points at μ_I = π/8.

Experimental results

Research questions

• RQ1 Can the pseudo-critical line in 2-color QCD be reliably analytically continued from imaginary to real chemical potential?
• RQ2 Which functional form (e.g., polynomial, rational function) best interpolates the critical β values at imaginary μ?
• RQ3 How well does the analytic continuation agree with direct Monte Carlo simulations at real chemical potential?
• RQ4 What is the impact of observable choice (chiral condensate, Polyakov loop, plaquette) on the accuracy of the extrapolation?
• RQ5 To what extent do systematic errors from the interpolation method affect the reliability of the critical line extrapolation?

Key findings

• The critical β values at imaginary chemical potential are best described by a quadratic polynomial in μ², with coefficients showing minimal dependence across different observables.
• The extrapolated critical line at real μ shows good agreement with direct Monte Carlo determinations at μ = 0.20 and 0.30, supporting the validity of the analytic continuation method.
• The extrapolated critical β at μ_I = π/8 (the first Roberge-Weiss transition line) is consistent with independent determinations of β_E, confirming the phase diagram structure.
• A small deviation is observed at μ = 0.30 for the chiral condensate, suggesting potential need for refined analysis or higher-order interpolation.
• The use of simple polynomials outperforms higher-order or rational functions, which reduce to the same quadratic form, indicating robustness of the μ² dependence.
• The bootstrap method confirms that peak position uncertainties are small and consistent across all observables and μ values.