Response of the QGP medium with large gradients

The quark-gluon plasma is a multi-scale many-body system. Characterizing its dynamical properties at different scales is an important goal of the high-energy nuclear physics community.

We have already known that in the long-wavelength limit, the QGP behaviors as an almost perfect liquid with tiny specific shear and bulk viscosities. In the long-wavelength limit, the asymptotic freedom nature of QCD allows for perturbative treatment of the scattering of energetic partons. However, the medium response in the intermediate domain where the wavelength is comparable to the collisional mean-free-path and screening length scale is still a somewhat mystery. One possible way to probe the medium in this domain is to look at the medium response excited by the passage of energetic partons, which excite medium dynamic over a broad range of wavelength.

In the past, many studies applied various hydrodynamic theories to describe the response in this intermediate domain, which poses the question of whether the hydrodynamic approach is appropriate to describe the jet-medium coupling where the wavelength can be much shorter than the mean-free-path (()(\lambda_{R} )()).

We systematically compared the response function in kinetic theory and various hydrodynamic approximations. We found that the hydrodynamic modes dominate the late-time response up to farily large wave numbers (k\lambda_R > 1). However, the dispersion relation is not well described in either first-order or second-order hydrodynamics. We then developed the MIS({}^{*}) linearized hydrodynamic equations with two additional second-order transport parameters. After matching the second-order terms to the response behavior of the microscopic theory in the intermediate wave-number domain, we found that the MIS({}^{*}) equations nicely capture the kinetic-type of response at large (k).

It suggests an effective hydro-based approach can still be applied to study the jet-induced medium response, and the precise value of the second-order transport coefficient does not have to be those defined in the long-wavelength limit but carries information of the medium response in the large gradient domain.