Landau gauge gluon and ghost propagators at finite temperature from quenched lattice QCD

The behavior of the Landau gauge gluon and ghost propagators is studied in pure $SU(3)$ gauge theory at nonzero temperature on the lattice. We concentrate on the momentum range (0.6, 2.0) GeV. For the longitudinal as well as for the transverse component of the gluon propagator we extract the continuum limit. We demonstrate the smallness of finite-size and Gribov-copy effects at temperatures close to the deconfinement phase transition at $T=T_c$ and within the restricted range of momenta. Since the longitudinal component $D_L(q)$ turns out to be most sensitive with respect to the phase transition, we propose some combinations of $D_L(q)$ signaling the transition much like “order parameters.”

Figure 1

Temperature dependence of the longitudinal (l.h.s.) and the transverse (r.h.s.) gluon propagator for $\beta =6.337$ and a spatial lattice size $N_{\sigma }=48$.

Figure 2

The longitudinal propagator, $D_L$, (l.h.s.) and the transverse one, $D_T$, (r.h.s.) vs temperature for a few low momenta, the latter represented as ($k_1$, $k_2$, $k_3$, $k_4$). $\beta =6.337$ and $N_{\sigma }=48$.

Figure 3

Temperature behavior of the ratios $\chi$ (Eq. (19), left panel) and $\alpha$ (Eq. (21), right panel) at low momenta, as given in the legend, for a spatial lattice size $N_{\sigma }=48$ and $\beta =6.337$.

Figure 4

The renormalized ghost dressing function $J(q,T)$ for various temperature values (l.h.s.) and its dependence on the temperature shown for the fixed diagonal 3-momenta ($(k,k,k,0)$, $k=1,2,3$), and normalized with $J(q,T_{\min })$ for $T_{\min }=0.65T_c$ (r.h.s.). The lowest panel shows the lowest momentum. All data are obtained at $\beta =6.337$ on a lattice with spatial size $N_{\sigma }=48$.

Figure 5

Finite-size effect study for $D_L$ at $\beta =6.337$. l.h.s.: $T=0.86T_c$, r.h.s.: $T=1.20T_c$.

Figure 6

Same as in Fig. 5 but for $D_T$.

Figure 7

Comparison of the bc with the fc Gribov-copy result for the longitudinal propagator $D_L$ (unrenormalized) (l.h.s.: $T=0.86T_c$, r.h.s.: $T=1.20T_c$).

Figure 8

Same as in Fig. 7 but for the transverse propagator $D_T$ (l.h.s.: $T=0.86T_c$, r.h.s.: $T=1.20T_c$).

Figure 9

The longitudinal propagator $D_L$ renormalized at $\mu =5\mathrm{GeV}$ and obtained for fixed physical volume and temperature but varying $a=a(\beta )$ (l.h.s.: $T=0.86T_c$, r.h.s.: $T=1.20T_c$).

Figure 10

Same as in Fig. 9 but for the transverse propagator $D_T$ (l.h.s.: $T=0.86T_c$, r.h.s.: $T=1.20T_c$).

Figure 11

$D_L$ vs lattice spacing $a$ for a set of different preselected momenta $p$ (l.h.s. $T=0.86T_c$; r.h.s. $T=1.20T_c$).

Figure 12

Same as in Fig. 11 but for $D_T$ (l.h.s. $T=0.86T_c$; r.h.s. $T=1.20T_c$).

Figure 13

Comparison of the renormalized propagators $D_L(q)$ (l.h.s.) and $D_T(q)$ (r.h.s.) obtained from the Monte Carlo simulation at $\beta =6.337$ with some continuum limit extrapolated values.

Figure 14

Continuum extrapolated values of $D_L(q)$ (l.h.s.) and $D_T(q)$ (r.h.s.) together with their respective interpolation curves for two temperature values.