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Register a new userReal-time quantum dynamics of heavy quark systems at high temperature
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Authors
Yukinao Akamatsu
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On the basis of the closed-time path formalism of non-equilibrium quantum field theory, we derive the real-time quantum dynamics of heavy quark systems. Even though our primary goal is the description of heavy quarkonia, our method allows a unified description of the propagation of single heavy quarks as well as their bound states. To make calculations tractable, we deploy leading-order perturbation theory and consider the non-relativistic limit. Various dynamical equations, such as the master equation for quantum Brownian motion and time-evolution equation for heavy quark and quarkonium forward correlators, are obtained from a single operator, the renormalized effective Hamiltonian. We are thus able to reproduce previous results of perturbative calculations of the drag force and the complex potential simultaneously. In addition, we present stochastic time-evolution equations for heavy quark and quarkonium wave function, which are equivalent to the dynamical equations.
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We review important ideas on nuclear and quark matter description on the basis of high- temperature field theory concepts, like resummation, dimensional reduction, interaction scale separation and spectral function modification in media. Statistical and thermodynamical concepts are spotted in the light of these methods concentrating on the - partially still open - problems of the hadronization process.
We derive equations for the time evolution of the reduced density matrix of a collection of heavy quarks and antiquarks immersed in a quark gluon plasma. These equations, in their original form, rely on two approximations: the weak coupling between the heavy quarks and the plasma, the fast response of the plasma to the perturbation caused by the heavy quarks. An additional semi-classical approximation is performed. This allows us to recover results previously obtained for the abelian plasma using the influence functional formalism. In the case of QCD, specific features of the color dynamics make the implementation of the semi-classical approximation more involved. We explore two approximate strategies to solve numerically the resulting equations in the case of a quark-antiquark pair. One involves Langevin equations with additional random color forces, the other treats the transition between the singlet and octet color configurations as collisions in a Boltzmann equation which can be solved with Monte Carlo techniques.
We present a calculation of the heavy quark transport coefficients in a quark-gluon plasma under the presence of a strong external magnetic field, within the Lowest Landau Level (LLL) approximation. In particular, we apply the Hard Thermal Loop (HTL) technique for the resummed effective gluon propagator, generalized for a hot and magnetized medium. Using the derived effective HTL gluon propagator and the LLL quark propagator we analytically derive the full results for the longitudinal and transverse momentum diffusion coefficients as well as the energy losses for charm and bottom quarks beyond the static limit. We also show numerical results for these coefficients in two special cases where the heavy quark is moving either parallel or perpendicular to the external magnetic field.
We present an extension of the Arnold-Moore-Yaffe kinetic equations for jet energy loss to NLO in the strong coupling constant. A novel aspect of the NLO analysis is a consistent description of wider-angle bremsstrahlung (semi-collinear emissions), which smoothly interpolates between 2<->2 scattering and collinear bremsstrahlung. We describe how many of the ingredients of the NLO transport equations (such as the drag coefficient) can be expressed in terms of Wilson line operators and can be computed using a Euclidean formalism or sum rules, both motivated by the analytic properties of amplitudes at light-like separations. We conclude with an outlook on the computation of the shear viscosity at NLO.
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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