Studying hard probe dynamics in QGP using effective field theory

TL;DR

This work develops a derivation-based hydrodynamic EFT (phi-EFT) for the quark–gluon plasma and couples heavy quarks to the fluid’s phonon sector to study momentum exchange in a strongly coupled medium. By introducing a UV scale $\Lambda_{ m h}$ that controls the derivative expansion and phonon self-interactions, the authors derive the phonon kinetic term, identify the Mach-like conditions for phonon emission/absorption, and compute the heavy-quark decay width and 2→2 quark–phonon scattering amplitudes in a thermal bath. Key contributions include the explicit construction of the hydrodynamic EFT, the identification of $\Lambda_{ m h}$ with a scale of order a few $T$, and the demonstration of how phonon-mediated processes contribute to heavy-quark transport, with clear formulas for decay widths and matrix elements. The framework provides a path to quantitative predictions once Wilson coefficients are fixed (e.g., via AdS/CFT matching or experimental fits), enabling calculation of the Boltzmann kernel and drag coefficients for heavy-quark dynamics in the QGP.

Abstract

An effective field theory framework is developed to study the interaction of heavy quarks in strongly coupled quark-gluon plasma (QGP). The latter is treated as a relativistic non-dissipative colorless fluid which can be studied using a derivatively coupled effective field theory based on previous work. Coupling this to heavy quarks provides systematic way to obtain the interaction between the heavy quark and phonons, excitations of the fluid. In particular we calculate the decay width of heavy quark to phonon and phonon-heavy quark scattering in a thermal medium.

Figures (8)

• Figure 1: Feynman diagrams for three and four phonon self-interactions. $n$-phonon interactions exist for all $n>2$, but are suppressed by $\Lambda_{\rm h}^{-(2n-4)}$, respectively.
• Figure 2: Feynman diagrams for quark-phonon, quark-gluon, gluon-phonon, and quark-gluon-phonon interactions. Each diagram exists with an arbitrary number of phonon insertions.
• Figure 3: Feynman diagrams for two-to-two fermion-phonon scattering. The point-like interaction is suppressed by a higher power of $\Lambda_{\rm h}$ and is therefore neglected.
• Figure 4: Feynman diagrams for two-body decay width. Left: phonon emission; right: phonon absorption.
• Figure 5: Decay width as function of heavy quark momentum and temperature for different values of the speed of sound for a charm quark. The transition between the different ranges in which the three $\theta$ functions in Eq. (\ref{['eq:Gamma']}) are non-zero can be seen, where the derivative of the decay width is not continuous.