Heavy quark potential in the instanton liquid model

Abstract

We study the heavy quark potential in the instanton liquid model by carefully measuring Wilson loops out to a distance of order 3$fm$. A random instanton ensemble with a fixed radius $\rho$ = 1/3$fm$ generates a potential $V(R)$ growing very slowly at large $R$. In contrast, a more realistic size distribution growing as $\rho^6$ at small $\rho$ and decaying as $\rho^{-5}$ at large $\rho$, leads to a potential which grows linearly with $R$. The string tension, however, is only about 1/10 of the phenomenological value.Comment: LATTICE98(confine

Instanton contributions to the low-lying hadron mass spectrum

“…[25] where the string tension was reduced to only 27% of its original value after 25 sweeps of the unimproved cooling algorithm. This also differs from the theoretical prediction of the instanton liquid model, which was shown to generate a string tension [36], but with a value much smaller than the physical value. The over-improved stout-link smearing algorithm tuned specifically to preserve instanton-like structure in the gauge field configurations retains the long-distance string tension remarkably well.…”

Instantons, the QCD vacuum, and hadronic physics

“…These and related issues are addressed by high statistics calculations [44] of the potentials in an instanton liquid with fixed instanton size and with the size distribution ρ 6 (ρ 3.5 0 + ρ 3.5 ) − 11 3.5 , corresponding to a frozen coupling constant . The potentials are linear at small distance and approach a constant at large distance as expected analytically [45].…”

Center vortex model for the infrared sector of Yang–Mills theory — topological susceptibility

“…In this manner, instanton models are very successful at also describing the spontaneous breaking of chiral symmetry and the associated low-energy hadronic phenomena. On the other hand, instanton models have hitherto failed to provide for confinement [6]. Presumably, a strongly interacting dynamics with intricate instanton correlations would be necessary to achieve the latter.…”