The influence of Wilson lines on heavy quark anti-quark potential and mass

Abstract

The holographic heavy quark potential is investigated via holographic Wilson loops in the AdS soliton with gauge potential. We analyze two types of holographic Wilson loops. {In the first type, holographic heavy quark potential shows the area law behavior. In the second type, the potential becomes zero at a critical length and physics analogous to the dissociation occurs. The mass of heavy quarkonia and the binding energy are examined.} Lastly, the mass of $0^{++}$ glueball-like operators dual to massless dilaton is calculated. The mass of $0^{++}$ glueball-like operator decreases with increase of the gauge potential as expected in arXiv:2309.03491 [hep-th]. The results are comparable with lattice QCD.

Figures (6)

• Figure 1: (a) The normalized quark anti-quark potential $V=\alpha'E/R^2$ is plotted as as a function of $M_0L$ ($M_0=0.4$). The gauge potential is changed. The area law behavior is observed in any case. The QCD string tension (represented by the slope) is suppressed when the gauge potential is large. (b) The quark anti-quark potential $V$ is shown as a function of $|a_{\phi}|L$ ($M_0=0$). Note that $a_{\phi}$ must be imaginary. The area law is observed except when $a_{\phi}=0$. The QCD string tension increases when $|a_{\phi}|$ increases.
• Figure 2: The normalized quark anti-quark potential is plotted as a function of $|a_{\phi}|L$ for $a_{\phi}=0.1$. The area law behavior is evident in any case. The QCD string tension (represented by the slope) increases with the Kaluza-Klein mass $M_0$ increase.
• Figure 3: (a) The normalized mass of the excitation of QCD strings is plotted as a function of $a_{\phi}$ ($M_0=0.4$). The mass decreases as $a_{\phi}$ increases. More excited modes contribute to DOF at large $a_{\phi}$. (b) The normalized mass is plotted as a function of $| a_{\phi}|$ in the extremal limit ($M_0=0$). Note that $a_{\phi}$ is purely imaginary. For $a_{\phi}=0$, both $M_0$ and $M_{st}$ are zero, while $M_{st}$ increases as $|a_{\phi}|$ increases. It implies that the mass of the excitation decouples others in a slightly low energy limit when $|a_{\phi}|$ increases.
• Figure 4: (a) The normalized quark anti-quark potential $V=\alpha'E/R^2$ is plotted as a function of $M_0L$ ($M_0=0.4$) with varying $a_{\phi}$. Because the point of the zero potential shifts to large $L$ for large values of $a_{\phi}$, phenomena analogous to the dissociation are harder to occur. (b) The quark anti-quark potential $V$ is shown as a function of $|a_{\phi}|L$ ($M_0=0$). Note that $a_{\phi}$ must be imaginary.
• Figure 5: $M_0$ dependence of the normalized quark anti-quark potential is illustrated as a function of $M_0L$ ($a_{\phi}=0.1$). Because the zero-potential point shifts to large $L$ for small $M_0$, phenomena analogous to the dissociation are harder to occur.