[Paper Review] Contribution to understanding the phase structure of strong interaction matter: Lee-Yang edge singularities from lattice QCD

P. Dimopoulos, Lorenzo Dini+7 more|arXiv (Cornell University)|Oct 29, 2021

High-Energy Particle Collisions Research71 references69 citations

TL;DR

This paper investigates Lee-Yang edge singularities in the complex baryon chemical potential plane using lattice QCD with highly improved staggered quarks at Nτ = 4 and 6. By constructing rational function approximations of net baryon number density data at imaginary chemical potentials, the authors identify singularities that scale with temperature according to expected critical behavior near the Roberge-Weiss and chiral phase transitions, providing strong evidence for the universality of these critical points.

ABSTRACT

We present a calculation of the net baryon number density as a function of imaginary baryon number chemical potential, obtained with highly improved staggered quarks (HISQ) at temporal lattice extent of $N_ au=4,6$. We construct various rational function approximations of the lattice data and discuss how poles in the complex plane can be determined from them. We compare our results of the singularities in the chemical potential plane to the theoretically expected positions of the Lee-Yang edge singularity in the vicinity of the Roberge-Weiss and chiral phase transitions. We find a temperature scaling that is in accordance with the expected power law behavior.

Motivation & Objective

• To understand the phase structure of strong interaction matter by probing critical singularities in the complex chemical potential plane.
• To test the theoretical prediction of Lee-Yang edge singularities near the Roberge-Weiss and chiral phase transitions using lattice QCD simulations.
• To validate the critical scaling behavior of these singularities and assess their consistency with universal scaling laws.
• To demonstrate that rational approximations of lattice data at imaginary μB can extract non-universal parameters and estimate the radius of convergence of analytic expansions.
• To provide evidence that the position of singularities can map to the QCD critical end point, as shown in model studies.

Proposed method

• Lattice QCD simulations with highly improved staggered quarks at Nτ = 4 and 6, using purely imaginary baryon chemical potential (μB).
• Calculation of net baryon number density and its cumulants (up to fourth order) from Monte Carlo data.
• Construction of rational function approximations (via multipoint Padé method) that reproduce the cumulants and encode analytic structure in the complex μB plane.
• Identification of poles in the rational approximants as proxies for Lee-Yang edge singularities in the complex μB plane.
• Comparison of extracted singularity positions with theoretical expectations from Z(2) and O(2) universality classes near Roberge-Weiss and chiral transitions.
• Use of scaling theory to test critical behavior, including power-law scaling with temperature and functional dependence on nonuniversal parameters.

Experimental results

Research questions

• RQ1 Do Lee-Yang edge singularities in the complex μB plane exhibit the expected critical scaling behavior near the Roberge-Weiss transition in (2+1)-flavor QCD?
• RQ2 Is the temperature dependence of the singularities consistent with the predicted power-law scaling of the universal scaling function?
• RQ3 Can rational approximations of lattice data at imaginary μB accurately locate singularities and estimate the radius of convergence of Taylor expansions?
• RQ4 Do the extracted singularities align with the expected critical scaling near a hypothetical QCD critical end point?
• RQ5 To what extent are the results robust against artifacts from the rooting procedure in staggered fermion formulations?

Key findings

• The positions of the Lee-Yang edge singularities extracted from rational approximations show temperature scaling consistent with the expected power-law behavior of the universal scaling function near the Roberge-Weiss transition.
• The singularities exhibit scaling behavior compatible with the Z(2) universality class, supporting the second-order nature of the Roberge-Weiss transition in (2+1)-flavor QCD with physical quark masses.
• Near the chiral transition, the singularities align with O(2) universality class predictions, indicating consistency with the expected critical scaling despite the O(2) symmetry breaking in staggered fermions.
• The method successfully identifies singularities that scale with temperature as T ∼ (T − Tc)βδ, confirming the validity of the analytic continuation approach.
• The extracted singularities are consistent with the expected critical scaling even when nonuniversal parameters are varied, indicating robustness of the method.
• The results suggest that the position of the singularities can be used to estimate the radius of convergence of Taylor expansions and to map QCD to universal scaling functions, including potential localization of the QCD critical end point.