Non-trivial Center Dominance in High Temperature QCD

We investigate the properties of quarks and gluons above the chiral phase transition temperature $T_c,$ using the RG improved gauge action and the Wilson quark action with two degenerate quarks mainly on a $32^3\times 16$ lattice. In the one-loop perturbation theory, the thermal ensemble is dominated by the gauge configurations with effectively $Z(3)$ center twisted boundary conditions, making the thermal expectation value of the spatial Polyakov loop take a non-trivial $Z(3)$ center. This is in agreement with our lattice simulation of high temperature QCD. We further observe that the temporal propagator of massless quarks at extremely high temperature $\beta=100.0 \, (T \simeq10^{58} T_c)$ remarkably agrees with the temporal propagator of free quarks with the $Z(3)$ twisted boundary condition for $t/L_t \geq 0.2$, but differs from that with the $Z(3)$ trivial boundary condition. As we increase the mass of quarks $m_q$, we find that the thermal ensemble continues to be dominated by the $Z(3)$ twisted gauge field configurations as long as $m_q \le 3.0 \, T$ and above that the $Z(3)$ trivial configurations come in. The transition is essentially identical to what we found in the departure from the conformal region in the zero-temperature many-flavor conformal QCD on a finite lattice by increasing the mass of quarks. We argue that the behavior is consistent with the renormalization group analysis at finite temperature.Comment: 16 pages, 9 figures; 4 tables, an appendix adde

IR fixed points in SU(3)SU(3) gauge Theories

We propose a novel RG method to specify the location of the IR fixed point in lattice gauge theories and apply it to the $SU(3)$ gauge theories with $N_f$ fundamental fermions. It is based on the scaling behavior of the propagator through the RG analysis with a finite IR cut-off, which we cannot remove in the conformal field theories in sharp contrast with the confining theories. The method also enables us to estimate the anomalous mass dimension in the continuum limit at the IR fixed point. We perform the program for $N_f=16, 12, 8$ and $N_f=7$ and indeed identify the location of the IR fixed points in all cases.Comment: 7 pages, 7 figures, 1 table: the scale of the y axis in Figs..1-4 change; minor modifications as appear in PL

Conformal theories with an infrared cutoff

We give a new perspective on the dynamics of conformal theories realized in the SU(N) gauge theory, when the number of flavors N_f is within the conformal window. Motivated by the renormalization group argument on conformal theories with a finite IR cutoff Λ_IR, we conjecture that the propagator of a meson GH(t) on a lattice behaves at large t as a power-law corrected Yukawa-type decaying form G_(H)(t)=c˜^~_(H)exp(-m^~_(H)t)/t^(αH) instead of the exponentially decaying form c_(H)exp(-mHt), in the small quark mass region where m_H≤cΛ_IR: m_H is the mass of the ground state hadron in the channel H and c is a constant of order 1. The transition between the “conformal region” and the “confining region” is a first order transition. Our numerical results verify the predictions for the N_f=7 case and the N_f=16 case in the SU(3) gauge theory with the fundamental representation

B_K with the Wilson Quark Action: A Non-Perturbative Resolution of Operator Mixing using Chiral Ward Identities

We propose a non-perturbative method to determine the mixing coefficients of $\Delta s=2$ four-quark operators for the Wilson quark action using chiral Ward identities. The method is applied to calculate B_K in quenched QCD.Comment: 3 pages including 3 figures, Talk presented at LATTICE96(phenomenology) by Y. Kuramash