Phase Transition In Two-flavor QCD Research Articles

Exploring the nature of chiral phase transition in two-flavor QCD using extra heavy quarks

Chiral phase transition of two-flavor QCD at finite quark masses is known to be a crossover except near the chiral limit, but it can turn to a first order transition when adding many extra flavors. This property is used to explore the nature of the phase transition of massless two-flavor QCD using lattice numerical simulations. The extra heavy flavors being incorporated in the form of the hopping parameter expansion through the reweighting, the number of the extra flavors and their masses appear only in a single parameter, defined by $h$. We determine the critical value of $h$, at which the first order and the crossover regions are separated, and examine its dependence on the two-flavor mass. The lattice calculations are carried out at ${N}_{t}=4$, and show that the critical value of $h$ does not depend on the two-flavor mass in the range we have studied ($0.46\ensuremath{\le}{m}_{\ensuremath{\pi}}/{m}_{\ensuremath{\rho}}\ensuremath{\le}0.66$) and appears to remain finite and positive in the chiral limit, suggesting that the phase transition of massless two-flavor QCD is of second order.

LinkingU(2)×U(2)toO(4)model via decoupling

The nature of chiral phase transition of massless two flavor QCD depends on the fate of flavor singlet axial symmetry ${U}_{A}(1)$ at the critical temperature (${T}_{c}$). Assuming that a finite ${U}_{A}(1)$ breaking remains at ${T}_{c}$, the corresponding three dimensional effective theory is composed of four massless and four massive scalar fields. We study the renormalization group flow of the effective theory in the $\ensuremath{\epsilon}$-expansion, using a mass dependent renormalization scheme, and determine the region of the attractive basin flowing into the $O(4)$ fixed point with a focus on its dependence on the size of the ${U}_{A}(1)$ breaking. The result is discussed from a perspective of the decoupling of massive fields. It is pointed out that, although the effective theory inside the attractive basin eventually reaches the $O(4)$ fixed point, the approaching rate, one of the universal exponents, is different from that of the standard $O(4)$ model. We present the reason for this peculiarity, and propose a novel possibility for chiral phase transition in two-flavor QCD.

Chiral phase transition in two-flavor QCD from an imaginary chemical potential

We investigate the order of the finite temperature chiral symmetry restoration transition for QCD with two massless fermions, by using a novel method, based on simulating imaginary values of the quark chemical potential $\mu=i\mu_i,\mu_i\in\mathbb{R}$. Our method exploits the fact that, for low enough quark mass $m$ and large enough chemical potential $\mu_i$, the chiral transition is decidedly first order, then turning into crossover at a critical mass $m_c(\mu)$. It is thus possible to determine the critical line in the $m - \mu^2$ plane, which can be safely extrapolated to the chiral limit by taking advantage of the known tricritical indices governing its shape. We test this method with standard staggered fermions and the result of our simulations is that $m_c(\mu=0)$ is positive, so that the phase transition at zero density is definitely first order in the chiral limit, on our coarse $N_t=4$ lattices with $a\simeq 0.3\,\mathrm{fm}$.

Finite temperature study of the axial U(1) symmetry on the lattice with overlap fermion formulation

We examine the axial U(1) symmetry near and above the finite-temperature phase transition in two-flavor QCD using lattice QCD simulations. Although the axial U(1) symmetry is always violated by quantization, i.e., the chiral anomaly, the correlation functions may manifest effective restoration of the symmetry in the high-temperature phase. We explicitly study this possibility by calculating the meson correlators as well as the Dirac operator spectral density near the critical point. Our numerical simulations are performed on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}8$ lattice with two flavors of dynamical quarks represented by the overlap fermion formalism. Chiral symmetry and its violation due to the axial anomaly is manifestly realized with this formulation, which is a prerequisite for the study of the effective restoration of the axial U(1) symmetry. In order to avoid discontinuity in the gauge configuration space, which occurs for the exactly chiral lattice fermions, the simulation is confined in a fixed topological sector. It induces a finite-volume effect, which is well described by a formula based on the Fourier transform from the $\ensuremath{\theta}$ vacua. We confirm this formula at finite temperature by calculating the topological susceptibility in the quenched theory. Our two-flavor simulations show degeneracy of the meson correlators and a gap in the Dirac operator spectral density, which implies that the axial U(1) symmetry is effectively restored in the chirally symmetric phase.

Two-flavor chiral phase transition in lattice QCD with the Kogut-Susskind quark action

A summary is presented of a scaling study of the finite-temperature chiral phase transition of two-flavor QCD with the Kogut-Susskind quark action based on simulations on L 3 × 4 ( L = 8, 12, and 16) lattices at the quark mass of m q = 0.075, 0.0375, 0.02 and 0.01. We find a phase transition to be absent for m q ≥ 0.02, and also quite likely at m q = 0.01. The quark mass dependence of susceptibilities is consistent with a second-order transition at m q = 0. The exponents, however, deviate from the O(2) and O(4) values theoretically expected.

Scaling analysis of chiral phase transition for two flavors of kogut-Susskind quarks

Report is made of a systematic scaling study of the finite-temperature chiral phase transition of two-flavor QCD with the Kogut-Susskind quark action based on simulations on $L^3\times4$ ($L$=8, 12 and 16) lattices at the quark mass of $m_q=0.075, 0.0375, 0.02$ and 0.01. Our finite-size data show that a phase transition is absent for $m_q\geq 0.02$, and quite likely also at $m_q=0.01$. The scaling behavior of susceptibilities as a function of $m_q$ is consistent with a second-order transition at $m_q=0$. However, the exponents deviate from the O(2) or O(4) values theoretically expected.

Finite temperature QCD: Progress and outstanding problems

I review recent progress in numerical simulations of finite temperature quantum chromodynamics and discuss the status of some outstanding problems. Included is (1) a discussion of recent results determining the temperature of the ``phase transition'' in full QCD, (2) a scaling analysis of the Polyakov loop variable, leading to the determination of a constituent quark free energy, (3) studies of critical behavior near the phase transition in two-flavor QCD, (4) a discussion of problems and new results in thermodynamic simulations with Wilson fermions, (5) recent results in pure gauge theory with a mixed fundamental/adjoint action, and (6) the nonperturbative determination of the equation of state with dynamical fermions included. Finally I mention briefly new developments in efforts to construct a phenomenology of deconfinement and chiral symmetry restoration, namely (7) the dual superconducting model and (8) the instanton model.

Further study of the finite-temperature chiral phase transition of two-flavor lattice QCD at a small quark mass

A previous finite-size study for the chiral phase transition of two-flavor QCD is extended to a smaller quark mass of ${m}_{q}=0.0125$ in lattice units. The characteristics of the system for lattice sizes (${6}^{3}$ - ${12}^{3}$) \ifmmode\times\else\texttimes\fi{} 4 are found to be quite similar to those for ${m}_{q}=0.0025$. The increase of susceptibilities over this range of the spatial size is still too mild to discriminate among the order of the transition also at this small quark mass.