Scaling and adiabaticity in a rapidly expanding gluon plasma
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13130_2022_Article_18433.pdf
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Author(s)
Brewer, Jasmine
Scheihing-Hitschfeld, Bruno
Yin, Yi
Date Issued
May 23, 2022
Publisher
Springer Berlin Heidelberg
Citation
Journal of High Energy Physics. 2022 May 23;2022(5):145
Version
Final published version
Abstract
Abstract
In this work we aim to gain qualitative insight on the far-from-equilibrium behavior of the gluon plasma produced in the early stages of a heavy-ion collision. It was recently discovered [1] that the distribution functions of quarks and gluons in QCD effective kinetic theory (EKT) exhibit self-similar “scaling” evolution with time-dependent scaling exponents long before those exponents reach their pre-hydrodynamic fixed-point values. In this work we shed light on the origin of this time-dependent scaling phenomenon in the small-angle approximation to the Boltzmann equation. We first solve the Boltzmann equation numerically and find that time-dependent scaling is a feature of this kinetic theory, and that it captures key qualitative features of the scaling of hard gluons in QCD EKT. We then proceed to study scaling analytically and semi-analytically in this equation. We find that an appropriate momentum rescaling allows the scaling distribution to be identified as the instantaneous ground state of the operator describing the evolution of the distribution function, and the approach to the scaling function is described by the decay of the excited states. That is to say, there is a frame in which the system evolves adiabatically. Furthermore, from the conditions for adiabaticity we can derive evolution equations for the time-dependent scaling exponents. In addition to the known free-streaming and BMSS fixed points, we identify a new “dilute” fixed point when the number density becomes small before hydrodynamization. Corrections to the fixed point exponents in the small-angle approximation agree quantitatively with those found previously in QCD EKT and arise from the evolution of the ratio between hard and soft scales.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP05(2022)145
