Energy and scale dependence of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover accent="true"><mml:mi>q</mml:mi><mml:mo></mml:mo></mml:mover></mml:math> and the “JET puzzle”
Amit Kumar, Abhijit Majumder, Chun Shen
Abstract
We present an attempt to probe the underlying structure of the quark-gluon plasma (QGP) at high resolution, based on the extracted jet transport coefficient $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{q}$. We argue that the exchanged momentum $k$ between the hard parton and the medium varies over a range of scales, and for $k\ensuremath{\ge}1\phantom{\rule{0.28em}{0ex}}\mathrm{GeV},\phantom{\rule{0.28em}{0ex}}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{q}$ can be expressed in terms of a parton distribution function (PDF). Because the mass of a QGP constituent is unknown, we define a scaling variable ${x}_{N}$ to represent the ratio of the parton momentum to the momentum of a self-contained section of the plasma which has a mass of 1 GeV. This scaling variable is used to parametrize the QGP-PDF. Calculations based on this reconstructed $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{q}$ are compared to data sensitive to the hardcore of jets, i.e., the single hadron suppression in terms of the nuclear modification factor ${R}_{AA}$ and the azimuthal anisotropy parameter ${v}_{2}$ as a function of transverse momentum ${p}_{\mathrm{T}}$, centrality, and energy of the collision. It is demonstrated that the scale evolution of the QGP-PDF is responsible for the reduction in the normalization of $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{q}$ between fits to the Relativistic Heavy-Ion Collider and the Large Hadron Collider data; a puzzle, first discovered by the JET Collaboration.