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Register a new userThermal imaginary part of a real-time static potential from classical lattice gauge theory simulations
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Recently, a finite-temperature real-time static potential has been introduced via a Schrodinger-type equation satisfied by a certain heavy quarkonium Greens function. Furthermore, it has been pointed out that it possesses an imaginary part, which induces a finite width for the tip of the quarkonium peak in the thermal dilepton production rate. The imaginary part originates from Landau-damping of low-frequency gauge fields, which are essentially classical due to their high occupation number. Here we show how the imaginary part can be measured with classical lattice gauge theory simulations, accounting non-perturbatively for the infrared sector of finite-temperature field theory. We demonstrate that a non-vanishing imaginary part indeed exists non-perturbatively; and that its value agrees semi-quantitatively with that predicted by Hard Loop resummed perturbation theory.
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We investigate simulations for gauge theories on a Minkowskian space-time lattice. We employ stochastic quantization with optimized updating using stochastic reweighting or gauge fixing, respectively. These procedures do not affect the underlying theory but strongly improve the stability properties of the stochastic dynamics, such that simulations on larger real-time lattices can be performed.
We compute chromoelectric and chromomagnetic flux densities for hybrid static potentials in SU(2) and SU(3) lattice gauge theory. In addition to the ordinary static potential with quantum numbers $Lambda_eta^epsilon = Sigma_g^+$, we present numerical results for seven hybrid static potentials corresponding to $Lambda_eta^{(epsilon)} = Sigma_u^+, Sigma_g^-, Sigma_u^-, Pi_g, Pi_u, Delta_g, Delta_u$, where the flux densities of five of them are studied for the first time in this work. We observe hybrid static potential flux tubes, which are significantly different from that of the ordinary static potential. They are reminiscent of vibrating strings, with localized peaks in the flux densities that can be interpreted as valence gluons.
We explore a novel approach to compute the force between a static quark and a static antiquark with lattice gauge theory directly. The approach is based on expectation values of Wilson loops or Polyakov loops with chromoelectric field insertions. We discuss theoretical and technical aspects in detail, in particular, how to compensate large discretization errors with a multiplicative renormalization factor and the evaluation using a multilevel algorithm. We also compare numerical results for the static force to corresponding results obtained in the traditional way, i.e., by computing first the static potential and then taking the derivative.
We extract the imaginary part of the heavy-quark potential using classical-statistical simulations of real-time Yang-Mills dynamics in classical thermal equilibrium. The $r$-dependence of the imaginary part of the potential is extracted by measuring the temporal decay of Wilson loops of spatial length $r$. We compare our results to continuum expressions obtained using hard thermal loop theory and to semi-analytic lattice perturbation theory calculations using the hard classical loop formalism. We find that, when plotted as a function of $m_D r$, where $m_D$ is the hard classical loop Debye mass, the imaginary part of the heavy-quark potential is independent of the lattice spacing at small $r$ and agrees well with the semi-analytic hard classical loop result. For large quark-antiquark separations, we quantify the magnitude of the non-perturbative long-range corrections to the imaginary part of the heavy-quark potential. We present our results for a wide range of temperatures, lattice spacings, and lattice volumes. Based on our results, we extract an estimate of the heavy-quark transport coefficient $kappa$ from the short-distance behavior of the classical potential and compare our result with $kappa$ obtained using hard thermal loops and hard classical loops. This work sets the stage for extracting the imaginary part of the heavy-quark potential in an expanding non-equilibrium Yang Mills plasma.
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