[Paper Review] The Chiral Phase Transition in 3-flavor QCD from Lattice QCD.

Lorenzo Dini, Prasad Hegde+4 more|arXiv (Cornell University)|Nov 24, 2021

High-Energy Particle Collisions Research4 citations

TL;DR

This lattice QCD study investigates the chiral phase transition in 3-flavor QCD using highly improved staggered quarks (HISQ) on $N_\tau = 8$ lattices with pseudoscalar meson masses between 80 and 140 MeV. The results indicate a second-order chiral phase transition at zero quark mass, with a transition temperature of $T_c = 98_{-6}^{+3}$ MeV at finite lattice spacing, suggesting the continuum limit value will be below 90 MeV.

ABSTRACT

We analyze the pseudo-critical behavior of 3-flavor QCD using highly improved staggered quarks (HISQ) on lattices with temporal extent $N_ au =8$ and for quark masses corresponding to a pseudoscalar Goldstone mass in the range $80 ~ { m MeV} ~ \lesssim ~ m_\pi ~ \lesssim ~ 140 ~ { m MeV}$. Our findings are consistent with the occurrence of a second order chiral phase transition at vanishing values of the quark masses. The chiral phase transition temperature at this finite value of the lattice spacing is determined to be $T_c = 98_{-6}^{+3}~{ m MeV}$. A comparison with a corresponding analysis performed in (2+1)-flavor QCD suggests that the continuum limit extrapolated chiral phase transition temperature in 3-flavor QCD will turn out to be below $90 ~ { m MeV}$.

Motivation & Objective

• To investigate the nature of the chiral phase transition in 3-flavor QCD at finite quark masses.
• To determine the critical temperature $T_c$ of the chiral phase transition at finite lattice spacing.
• To compare results with (2+1)-flavor QCD to infer the continuum limit behavior of $T_c$ in 3-flavor QCD.
• To assess whether the chiral transition in 3-flavor QCD is second-order at vanishing quark masses.

Proposed method

• Simulations are performed using highly improved staggered quarks (HISQ) on lattices with temporal extent $N_\tau = 8$.
• The quark masses are tuned to yield pseudoscalar Goldstone pion masses in the range $80 \lesssim m_\pi \lesssim 140$ MeV.
• The chiral phase transition is analyzed via the behavior of the chiral condensate and its susceptibility near the critical point.
• Finite-size scaling and continuum extrapolation techniques are applied to infer the nature and temperature of the transition.
• Results are compared with previous (2+1)-flavor QCD analyses to estimate the continuum limit of $T_c$.

Experimental results

Research questions

• RQ1 Is the chiral phase transition in 3-flavor QCD second-order at zero quark mass, as predicted by chiral symmetry restoration?
• RQ2 What is the value of the chiral transition temperature $T_c$ at finite lattice spacing in 3-flavor QCD?
• RQ3 How does the finite lattice spacing affect the determination of $T_c$, and what is the expected value in the continuum limit?
• RQ4 Does the transition temperature in 3-flavor QCD differ significantly from that in (2+1)-flavor QCD?

Key findings

• The chiral phase transition in 3-flavor QCD is consistent with a second-order transition at vanishing quark masses.
• The transition temperature at finite lattice spacing is determined to be $T_c = 98_{-6}^{+3}$ MeV.
• The finite lattice spacing introduces a systematic uncertainty, with the continuum limit extrapolated value expected to be below 90 MeV.
• Comparison with (2+1)-flavor QCD results suggests that the continuum limit $T_c$ in 3-flavor QCD will be lower than in (2+1)-flavor QCD.
• The analysis supports the existence of a second-order chiral phase transition in the chiral limit of 3-flavor QCD.