Thermodynamics of lattice QCD with 3 flavors of color-sextet quarks. II. $N_t=6$ and $N_t=8$

We have been studying QCD with two flavors of color-sextet quarks as a candidate walking-technicolor theory using lattice-QCD simulations. The evolution of the coupling constant with lattice spacing is measured at the finite-temperature chiral transition to determine if this theory is asymptotically free and hence QCD-like. The lattice spacing is varied by changing the number of lattice sites, $N_t$, in the Euclidean time direction. QCD with three flavors is studied for comparison. Since this theory is expected to be conformal, with an infrared fixed point, the coupling constant at the chiral transition should approach a nonzero value as $N_t$ becomes large. Our earlier simulations on lattices with $N_t=4$ and $N_t=6$ exhibited a significant decrease in coupling at the chiral transition as $N_t$ was increased. We have now extended these simulations to $N_t=8$, and performed additional simulations at $N_t=6$ to measure the coupling constant at the chiral transition more precisely. These indicate that while there is an appreciable decrease in coupling between $N_t=6$ and $N_t=8$, this is much smaller than that between $N_t=4$ and $N_t=6$. Thus we are hopeful that we are approaching the large-$N_t$ limit. However, further simulations at larger $N_t(\mathrm{s})$ are needed.

Figure 1

$⟨\overline{\psi }\psi ⟩$ as functions of $\beta =6/g^2$ on a ${12}^3\times 6$ lattice, in the state with a real positive Wilson line, for $m=0.02$, 0.01, 0.005.

Figure 2

Chiral susceptibilities as functions of $\beta =6/g^2$ on a ${12}^3\times 6$ lattice, in the state with a real positive Wilson line, for $m=0.02$, 0.01, 0.005.

Figure 3

Chiral susceptibility for $m=0.005$ as a function of $\beta$ on a ${12}^3\times 6$ lattice, showing the fit to a parabola mentioned in the text.

Figure 4

(a) $⟨\overline{\psi }\psi ⟩$ as functions of $\beta =6/g^2$ on a ${16}^3\times 8$ lattice, in the state with a real positive Wilson line, for $m=0.01$, 0.005. (b) $⟨\overline{\psi }\psi ⟩$ on a ${16}^3\times 8$ lattice, subtracted using the valence subtraction used by the Lattice Higgs Collaboration.

Figure 5

Chiral susceptibilities as functions of $\beta =6/g^2$ on a ${16}^3\times 8$ lattice, in the state with a real positive Wilson line, for $m=0.01$, 0.005.

Figure 6

Chiral susceptibility as a function of $\beta =6/g^2$ on a ${16}^3\times 8$ lattice, in the state with a real positive Wilson line, for 0.005, showing the parabolic fit mentioned in the text.