Large momenta fluctuations of charm quarks in the Quark-Gluon Plasma⋆

We show that large fluctuations of D-mesons kinetic-energy (or momentum) distributions might be a signature of a phase transition to the Quark-Gluon Plasma (QGP). In particular, a jump in the variance of the momenta or kinetic energy, as a function of a control parameter (temperature or Fermi energy at finite baryon densities) might be a signature for a first-order phase transition to the QGP. This behavior is completely consistent with the order parameter defined for a system of interacting quarks both at zero temperature (and finite baryon densities) or at finite temperatures which shows a jump in correspondence with a first-order phase transition to the QGP. The J/Ψ displays exactly the same behavior of the order parameter and of the variance of the D-mesons. We discuss implications for relativistic heavy-ion collisions within the framework of a transport model and possible hints for experimental search.