Statistical Behavior of Lepton Pair Spectrum in the Drell-Yan Process and Signal from Quark-Gluon Plasma in High-Energy Collisions

Abstract

We analyze the transverse momentum ( $p_T$ ) spectra of lepton pairs ( $\ell \overline{\ell }$ ) generated in the Drell-Yan process, as detected in proton-nucleus (pion-nucleus) and proton-(anti)proton collisions by ten collaborations over a center-of-mass energy $\left(\sqrt{s_{NN}}\right.$ or $\sqrt{s}$ if in a simplified form) range from $~20$  GeV to above 10 TeV. Three types of probability density functions (the convolution of two Lévy-Tsallis functions, the two-component Erlang distribution, and the convolution of two Hagedorn functions) are utilized to fit and analyze the $p_T$ spectra. The fit results are approximately in agreement with the collected experimental data. Consecutively, we obtained the variation law of related parameters as a function of $\sqrt{s}$ and invariant mass $\left(Q\right)$ . In the fit procedure, a given Lévy-Tsallis (or Hagedorn) function can be regarded as the probability density function of transverse momenta contributed by a single quark ( $q$ ) or anti-quark ( $\overline{q}$ ). The Drell-Yan process is then described by the statistical method.