Quarkiton: a one-quark state near a boundary of confinement phase of QCD

TL;DR

The paper investigates whether one-quark states can exist in the confinement phase near a reflective boundary by introducing a neutral chromometallic mirror in lattice SU(3) Yang–Mills theory. The authors extract the quark–mirror free energy from Polyakov-loop correlators and renormalize ultraviolet contributions, finding a Cornell-type potential $F^{\rm ren}_{Q|}(T,d) = -\frac{\alpha_{Q|}(T)}{d} + \sigma_{Q|}(T) d + F_0(T)$ that binds the quark to the wall with a boundary string tension $\sigma_{Q|}(T)$. They observe that $\sigma_{Q|}$ decreases with temperature and, upon extrapolation to $T\to 0$, obtain $\mathcal{R}_{Q|} = \lim_{T\to 0} \sigma_{Q|}(T)/\sigma_{Q\bar{Q}}(T) = 0.699(4)$, indicating a robust yet reduced confinement to the boundary. The results imply the existence of non-Abelian boundary states, or quarkitons, with possible relevance to confining–deconfining interfaces in rotating quark–gluon plasmas and to related edge-state phenomena in non-Abelian gauge theories.

Abstract

We discuss a one-quark state in the confinement phase near a reflective chromometallic boundary both at finite and zero temperature. Using numerical simulations of lattice Yang-Mills theory, we show that the test quark is confined to the neutral mirror by an attractive potential of the Cornell type, suggesting the existence of a mirror-bound one-quark state, a "quarkiton". Surprisingly, the tension of the string spanned between the quark and the mirror is lower than the fundamental string tension. The quarkiton state exhibits a partial confinement: while the quark is localized in the vicinity of the mirror, it can still travel freely along it. Such quarkiton states share similarity with the surface excitons in metals and semiconductors that are bound to their negatively charged images at a boundary. The quarkitons can exist at the hadronic side of the phase interfaces in QCD that arise, for example, in the thermodynamic equilibrium of vortical quark-gluon plasma.

Figures (6)

• Figure 1: (a) A schematic visualization of the quarkiton state between a single quark $Q$ (right) and a neutral mirror (a vertical solid line). The quark is bound by a chromoelectric flux tube to the mirror by inducing an image antiquark $\bar{Q}$ (left). The quarkiton state (a) is a non-Abelian analog of the surface exciton (b) in which the electrons $(e^-)$ and holes $(e^+)$ form photon-mediated Coulomb-bound states with their images at the boundary.
• Figure 2: Unrenormalized free energy of a static heavy quark as a function of distance to the mirror $d$ at temperature $T=0.629T_c$ for several values of the temporal extension $N_t$ of the lattice, which correspond, via Eq. \ref{['eq_temp_phys']}, to different ultraviolet cutoffs (lattice spacings) $a$. The linear slopes of potentials are marked by the straight lines. The physical scale is given by the zero-temperature fundamental string tension $\sigma_0$. The calculation is performed at $N_t \times 254 \times 254 \times 30$ lattices.
• Figure 3: The renormalized free energy of a single heavy quark at the distance $d$ to the chromoelectric mirror at the temperatures (a) $T = 0.629 T_c$ and (b) $T = 0.996 T_c$ for various lattice spacings controlled by the temporal extension of the lattice $N_t$. The solid lines show the best fits by the Cornell potential \ref{['eq_cornell_fit']}. We use the $N_t \times 254 \times 254 \times 30$ lattices.
• Figure 4: The quarkiton string tension $\sigma_{Q|}$, which determines the long-distance linear attraction \ref{['eq_cornell_fit']} between a single heavy quark $Q$ and a neutral chromometallic mirror, as a function of temperature $T$. The solid line represents the best fit of the data by function \ref{['eq_sigmaQ_fit']}.
• Figure 5: The ratio of the quarkitonic string tension to the fundamental string tension, $\sigma_{Q|}(T)/\sigma_{Q\bar{Q}}(T)$, for different temperatures. The average of the plateau in the range of temperatures $T \leqslant 0.75 T_c$ is shown by the solid line, with the uncertainty shown by the shaded region.