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Register a new userThe chiral transition and U(1)_A symmetry restoration from lattice QCD using Domain Wall Fermions
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We present results on both the restoration of the spontaneously broken chiral symmetry and the effective restoration of the anomalously broken U(1)_A symmetry in finite temperature QCD at zero chemical potential using lattice QCD. We employ domain wall fermions on lattices with fixed temporal extent N_tau = 8 and spatial extent N_sigma = 16 in a temperature range of T = 139 - 195 MeV, corresponding to lattice spacings of a approx 0.12 - 0.18 fm. In these calculations, we include two degenerate light quarks and a strange quark at fixed pion mass m_pi = 200 MeV. The strange quark mass is set near its physical value. We also present results from a second set of finite temperature gauge configurations at the same volume and temporal extent with slightly heavier pion mass. To study chiral symmetry restoration, we calculate the chiral condensate, the disconnected chiral susceptibility, and susceptibilities in several meson channels of different quantum numbers. To study U(1)_A restoration, we calculate spatial correlators in the scalar and pseudo-scalar channels, as well as the corresponding susceptibilities. Furthermore, we also show results for the eigenvalue spectrum of the Dirac operator as a function of temperature, which can be connected to both U(1)_A and chiral symmetry restoration via Banks-Casher relations.
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We report on a study of the finite-temperature QCD transition region for temperatures between 139 and 196 MeV, with a pion mass of 200 MeV and two space-time volumes: $24^3times8$ and $32^3times8$, where the larger volume varies in linear size between 5.6 fm (at T=139 MeV) and 4.0 fm (at T=195 MeV). These results are compared with the results of an earlier calculation using the same action and quark masses but a smaller, $16^3times8$ volume. The chiral domain wall fermion formulation with a combined Iwasaki and dislocation suppressing determinant ratio gauge action are used. This lattice action accurately reproduces the $sua$ and $ua$ symmetries of the continuum. Results are reported for the chiral condensates, connected and disconnected susceptibilities and the Dirac eigenvalue spectrum. We find a pseudo-critical temperature, $T_c$, of approximately 165 MeV consistent with previous results and strong finite volume dependence below $T_c$. Clear evidence is seen for $ua$ symmetry breaking above $T_c$ which is quantitatively explained by the measured density of near-zero modes in accordance with the dilute instanton gas approximation.
We study the thermal transition of QCD with two degenerate light flavours by lattice simulations using $mathcal{O}(a)$-improved Wilson quarks. Particular emphasis lies on the pattern of chiral symmetry restoration, which we probe via the static screening correlators. On $32^3$ volumes we observe that the screening masses in transverse iso-vector vector and axial-vector channels become degenerate at the transition temperature. The splitting between the screening masses in iso-vector scalar and pseudoscalar channels is strongly reduced compared to the splitting at zero temperature and is actually consistent with zero within uncertainties. In this proceedings article we extend our studies to matrix elements and iso-singlet correlation functions. Furthermore, we present results on larger volumes, including first results at the physical pion mass.
We present results for the nucleon axial charge g_A at a fixed lattice spacing of 1/a=1.73(3) GeV using 2+1 flavors of domain wall fermions on size 16^3x32 and 24^3x64lattices (L=1.8 and 2.7 fm) with length 16 in the fifth dimension. The length of the Monte Carlo trajectory at the lightest m_pi is 7360 units, including 900 for thermalization. We find finite volume effects are larger than the pion mass dependence at m_pi= 330 MeV. We also find that g_A exhibits a scaling with the single variable m_pi L which can also be seen in previous two-flavor domain wall and Wilson fermion calculati ons. Using this scaling to eliminate the finite-volume effect, we obtain g_A = 1.20(6)(4) at the physical pion mass, m_pi = 135 MeV, where the first and second errors are statistical and systematic. The observed finite-volume scaling also appears in similar quenched simulations, but disappear when Vge (2.4 fm)^3. We argue this is a dynamical quark effect.
We present a lattice calculation of the neutron and proton electric dipole moments (EDMs) with $N_f=2+1$ flavors of domain-wall fermions. The neutron and proton EDM form factors are extracted from three-point functions at the next-to-leading order in the $theta$ vacuum of QCD. In this computation, we use pion masses 0.33 and 0.42 GeV and 2.7 fm$^3$ lattices with Iwasaki gauge action and a 0.17 GeV pion and 4.6 fm$^3$ lattice with I-DSDR gauge action, all generated by the RBC and UKQCD collaborations. The all-mode-averaging technique enables an efficient and high statistics calculation. Chiral behavior of lattice EDMs is discussed in the context of baryon chiral perturbation theory. In addition, we also show numerical evidence on relationship of three- and two-point correlation function with local topological distribution.
Quenched QCD simulations on three volumes, $8^3 times$, $12^3 times$ and $16^3 times 32$ and three couplings, $beta=5.7$, 5.85 and 6.0 using domain wall fermions provide a consistent picture of quenched QCD. We demonstrate that the small induced effects of chiral symmetry breaking inherent in this formulation can be described by a residual mass ($mres$) whose size decreases as the separation between the domain walls ($L_s$) is increased. However, at stronger couplings much larger values of $L_s$ are required to achieve a given physical value of $mres$. For $beta=6.0$ and $L_s=16$, we find $mres/m_s=0.033(3)$, while for $beta=5.7$, and $L_s=48$, $mres/m_s=0.074(5)$, where $m_s$ is the strange quark mass. These values are significantly smaller than those obtained from a more naive determination in our earlier studies. Important effects of topological near zero modes which should afflict an accurate quenched calculation are easily visible in both the chiral condensate and the pion propagator. These effects can be controlled by working at an appropriately large volume. A non-linear behavior of $m_pi^2$ in the limit of small quark mass suggests the presence of additional infrared subtlety in the quenched approximation. Good scaling is seen both in masses and in $f_pi$ over our entire range, with inverse lattice spacing varying between 1 and 2 GeV.
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