Color screening masses from string models

We use gauge or string duality to estimate the Debye screening mass at nonzero temperature and baryon chemical potential. We interpret this mass as the smallest one in the open string channel. Comparisons are made with the results from holography and lattice QCD.

Figure 1

String configurations contributing to $C_{1,\overline{1}}$. The arrows show the string orientation chosen to go from positive to negative charges. The horizontal line at $r=r_{\mathrm{h}}$ represents the horizon.

Figure 2

String configurations contributing to $C_{2,0}$ at $N=3$. $V$ is a baryon vertex.

Figure 3

$l$ as a function of $\nu$ at $\kappa =-0.083$ and $h=\frac{1}{9}$. It has a maximum at ${\nu }_{*}\approx 0.917$. Here ${\nu }_{\max }\approx 0.996$.

Figure 4

Two limiting cases [22]. Left: The long-strip limit. Right: Closed string states propagating between two boundary states in the long-cylinder limit.

Figure 5

Screening mass vs temperature. The solid curve is defined by (4.3) and (4.7). Left: The results of numerical holography [25]. Here $\mathfrak{w}=0.70$ and $c_4=0.1$ which is the smallest value among all possible ones. Right: The lattice data from [17]. The dashed curve corresponds to (4.5). Here we set $\mathfrak{w}=-2.05$.

Figure 6

A comparison of different $M(T)$ curves for a pure $SU(3)$ gauge theory. Left: The solid curve is that of Fig. 5, while the dotted curve corresponds to the power law (4.9). Right: The power law at $\mathfrak{w}=-2.13$ and $a=0.107$.

Figure 7

Screening mass vs temperature at zero chemical potential and different quark masses [29]. The solid curve is defined parametrically by (4.3) and (4.7). We set $\mathfrak{w}=-1.04$. Left: Results at $\frac{m_{\mathrm{PS}}}{m_{\mathrm{V}}}=0.80$ and $T_{pc}=357\mathrm{MeV}$. Right: Results at $\frac{m_{\mathrm{PS}}}{m_{\mathrm{V}}}=0.65$ and $T_{pc}=262\mathrm{MeV}$.

Figure 8

Left: Ratio $\frac{9m_2}{m_0}$ versus temperature. The lattice data are taken from [21]. The curve is defined parametrically by (4.7) and (d4). We set $\mathfrak{w}=-1.04$, $\mathfrak{r}=6.00$, and $T_c=0.26\sqrt{\mathfrak{s}}$. Right: The screening mass versus baryon chemical potential. The solid curve is defined by (4.3) and (4.8), while the dashed curve by (4.12). We set $\mathfrak{r}=2.00$ and ${\mu }_{pc}=2\sqrt{\mathfrak{s}}$.

Figure 9

$M$ as a function of $T$ and $\mu$. We set $\mathfrak{r}=3.00$, $T_{pc}=0.30\sqrt{\mathfrak{s}}$, and ${\mu }_{pc}=3\sqrt{\mathfrak{s}}$.

Figure 10

Left: Binding free energies of two-quark states at $T=0.345\sqrt{\mathfrak{s}}$ and $\mu =0$. The solid curve corresponds to $\mathrm{\Delta }{F}_{\mathrm{QQ}}^{\overline{3}}$ and the dashed one to $\frac{1}{2}\mathrm{\Delta }{F}_{\mathrm{Q}\overline{\mathrm{Q}}}^1$. We set $\mathfrak{g}=0.176$, $\mathfrak{w}=-2.05$, and $\kappa =-0.102$. Right: A baryon configuration. $V$ is a baryon vertex. The quarks are placed at ${\mathbf{x}}_i$. For negative values of $\kappa$, gravity pulls the vertex toward the boundary that blunts the tip of the configuration.

Figure 11

Left: $\frac{1}{2}{\alpha }_{\mathrm{Q}\overline{\mathrm{Q}}}$, ${\alpha }_{\mathrm{QQ}}$, and ${\alpha }_{3\mathrm{Q}}$ in units of $\mathfrak{g}$. The intersection points are at $\kappa \approx -0.111$, $-0.102$, $-0.089$. Right: Closed string states propagating between three boundary states placed at the vertices of an equalateral triangle.

Figure 12

A string stretched between a quark placed at $P$ and an antiquark placed at $B$. ${\alpha }_{\pm }$ denote the tangent angles, which are both assumed to be positive. The horizon is at $r=r_{\mathrm{h}}$, while the boundary is at $r=0$.

Figure 13

Three strings meeting at a string junction (vertex) placed at $V$. The black hole horizon is at $r=r_{\mathrm{h}}$.