Baryonic flux in quenched and two-flavor dynamical QCD after Abelian projection

We study the distribution of color electric flux of the three-quark system in quenched and full QCD (with $N_f=2$ flavors of dynamical quarks) at zero and finite temperature. To reduce ultraviolet fluctuations, the calculations are done in the Abelian projected theory fixed to the maximally Abelian gauge. In the confined phase we find clear evidence for a $\mathrm{Y}$-shape flux tube surrounded and formed by the solenoidal monopole current, in accordance with the dual superconductor picture of confinement. In the deconfined, high temperature phase monopoles cease to condense, and the distribution of the color electric field becomes Coulomb-like.

Figure 1

Three-quark Wilson loop.

Figure 2

The Abelian baryon potential in full and quenched QCD.

Figure 3

Comparison of the Abelian and SU(3) baryon potential in the quenched approximation on the ${16}^{3}32$ lattice at $\beta =6.0$. The SU(3) potential is taken from [4].

Figure 4

The Abelian baryon potential in full QCD, together with its monopole and photon part, as a function of $L_{\mathsf{Y}}$ (top) and $L_{\Delta }$ (bottom), respectively. The curves show fits (25) (top) and (23) (bottom) to the data with equal distances between the static sources.

Figure 5

The Abelian three-quark potential and $\Delta$ and $Y$-Ansätze in full QCD for quarks in equilateral triangles as function of quark separation $d=L_Y/\sqrt{3}=L_{\Delta }/3$. The solid line is a fit to the data, the dotted line is the $\Delta$-Ansatz prediction Eq. (23) and the dashed line is the $Y$-Ansatz prediction Eq. (25). For both Ansätze Eq. (24) was used.

Figure 6

Same as Fig. 5 for quenched QCD.

Figure 7

Distribution of the color electric field ${\overrightarrow{E}}^{3Q}$ in the $(x,y)$ plane on the ${24}^{3}48$ lattice (center bottom figure), together with the monopole currents $k^{3Q}$ in the $(x,z)$ and $(y,z)$ planes (adjacent figures), respectively, at the position marked by the respective solid lines. The magnitude of $E^{3Q}$ and $k^{3Q}$ is indicated by the length of the arrows.

Figure 8

Schematic view of the color electric field.

Figure 9

Distribution of the Abelian color electric field ${\overrightarrow{E}}^{3Q}$ (top) broken into monopole (middle) and photon parts (bottom) on the ${24}^{3}48$ lattice in full QCD. The color index of the electric field operators corresponds to that of the quark in the bottom-right corner. Only part of the lattice is shown here.

Figure 10

The Abelian action density of the $3Q$ system in full QCD, together with the monopole and photon part.

Figure 11

The action density ${\rho }_A^{3Q}{r}_0^4$ of Fig. 10 plotted across the flux tube at the distance $3a$ from the quark and $2a$ from the junction.

Figure 12

The Abelian action density of the $3Q$ system as predicted by the $\Delta$-Ansatz in full QCD.

Figure 13

The monopole part of the baryon potential at finite temperature in full QCD as a function of $L_{\mathsf{Y}}$ ($T\le T_c$) and $L_{\Delta }$ ($T>T_c$), respectively.

Figure 14

The Abelian action density in the deconfined phase at $\kappa =0.1360$.

Figure 15

The color electric field (top) and monopole currents (bottom) on the ${16}^{3}8$ lattice at $\kappa =0.1335$ (left), 0.1344 (middle) and 0.1360 (right). The three quarks lie in (what we call) the $(x,y)$ plane. The bottom figures show the monopole currents in the $(x,z)$ plane at the position marked by the solid lines in the top figures.