Meson screening masses in ($2+1$)-flavor QCD

We present lattice QCD results for mesonic screening masses in the temperature range $140\mathrm{MeV}\lesssim T\lesssim 2500\mathrm{MeV}$. Our calculations were carried out using ($2+1$) flavors of the highly improved staggered quark action, with a physical value for the strange quark mass and two values of the light quark mass corresponding to pion masses of 160 and 140 MeV. Continuum-extrapolated results were obtained using calculations with a variety of lattice spacings corresponding to temporal lattice extents $N_{\tau }=6–16$. We discuss the implications of these results for the effective restoration of various symmetries in the high temperature phase of QCD, as well as the approach toward the perturbative limit.

Figure 1

Screening masses for in the vector channel with a different number of states varying the fit interval for $48^3\times 12$ lattice for $\beta =8.710$, which corresponds to $T=866\mathrm{MeV}$. Fit results selected by the Akaike information criterion (AICc) criterion (shown in black) for different values of minimum distance for the fits seem to fall on a nice plateau.

Figure 2

Comparison of point versus corner wall sources for (top) the scalar ($\mathcal{M}1$) channel using a $48^3\times 12$ lattice at $T=769\mathrm{MeV}$ and (bottom) the vector (average of $\mathcal{M}6$ and $\mathcal{M}7$) channel using a $64^3\times 16$ lattice at $T=146\mathrm{MeV}$. Numbers appearing in parenthesis correspond to the number of states taken in the fit for the nonoscillating and oscillating part of the correlator. The method of using AICc selection criterion to find a plateau among various fits has been described in the main text.

Figure 3

$T=0$ masses of the four kinds of mesons studied in this work for the $\overline{u}d$, $\overline{u}s$, and $\overline{s}s$ flavor channels, respectively. Horizontal lines correspond to the physical values of the masses [52]. The scalar meson mass is $2m_{\pi }$ instead of $m_{a0}$ (or $m_{\pi }+m_{\eta }$) due to a staggered artifact at finite lattice spacing. This discrepancy vanishes when the continuum limit of the correlator would be taken before calculating the screening mass [53, 54] (see Sec. 4c).

Figure 4

Masses of the different taste partners of the pseudoscalar mesons, labeled by different ${\mathrm{\Gamma }}_T$, for light-light ($\overline{u}d$), light-strange ($\overline{u}s$), and strange-strange ($\overline{s}s$) sectors, normalized to the corresponding Goldstone $\pi$, $K$, and ${\eta }_{\overline{s}s}$ masses, respectively. The lattice spacings considered here range from approximately 0.085–0.072 fm. Also plotted are the RMS masses defined in Eq. (4).

Figure 5

Examples for the continuum extrapolations for the pseudoscalar (top), scalar (bottom) screening masses in a reduced temperature range. The data for different $N_{\tau }$ were fitted to an $N_{\tau }$-dependent fit function. Also shown in each figure are the bands for each $N_{\tau }$, obtained using the same fit function.

Figure 6

(Left to right) Results for all four screening masses for the $\overline{u}d$, $\overline{u}s$, and $\overline{s}s$ flavor combinations. The gray vertical band in all the figures represents the pseudocritical temperature, $T_{pc}=156.5(1.5)\mathrm{MeV}$ [6]. The dashed lines corresponds to the free theory limit of $m=2\pi T$.

Figure 7

Continuum bands for screening masses of all four types of mesons for $\overline{u}d$, $\overline{u}s$, and $\overline{s}s$ (left to right).

Figure 8

Difference between the pseudoscalar and scalar susceptibilities as a function of the temperature. The difference is multiplied by $m_s^2$ to renormalize and normalized to $1/T_{pc}^4$. The continuum extrapolation is also shown in the figure as a superimposed band.

Figure 9

Screening masses divided by the temperature, for temperatures $T\gtrsim 200\mathrm{MeV}$ and for $N_{\tau }=6$, 8, 10, and 12 for all four channels in different flavor sectors. The gray curve in the top right part of each figure is the resummed perturbation theory prediction [67, 68]. The horizontal dashed line in each plot is the infinite-temperature limit $m_{\mathrm{scr}}^{\mathrm{free}}/T=2\pi$. Both the infinite-temperature limit as well as the perturbative result are the same for all screening masses irrespective of their spin. Beyond $T\gtrsim 1\mathrm{GeV}$, only $N_{\tau }=8$ data exist as a result of which a continuum extrapolation is not possible. The lattice results are obtained with corner wall source for $V$ and $AV$ channels for $T\lesssim 300\mathrm{MeV}$ and with point source elsewhere.

Figure 10

Comparison of updated $f_{K}a(\beta )$ parametrization and the older one from Ref. [40].