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Event patterns extracted from transverse momentum and rapidity spectra of Z bosons and quarkonium states produced in pp and Pb-Pb collisions at LHC

Transverse momentum ($p_T$) and rapidity ($y$) spectra of $Z$ bosons and quarkonium states (some charmonium $c\bar c$ mesons such as $J/ψ$ and $ψ(2S)$, and some bottomonium $b\bar b$ mesons such as $Υ(1S)$, $Υ(2S)$, and $Υ(3S)$) produced in proton-proton ($pp$) and lead-lead (Pb-Pb) collisions at the large hadron collider (LHC) are uniformly described by a hybrid model of two-component Erlang distribution for $p_T$ spectrum and two-component Gaussian distribution for $y$ spectrum. The former distribution results from a multisource thermal model, and the latter one results from the revised Landau hydrodynamic model. The modelling results are in agreement with the experimental data measured in $pp$ collisions at center-of-mass energies $\sqrt{s}=2.76$ and 7 TeV, and in Pb-Pb collisions at center-of-mass energy per nucleon pair $\sqrt{s_{NN}}=2.76$ TeV. Based on the parameter values extracted from $p_T$ and $y$ spectra, the event patterns (particle scatter plots) in two-dimensional $p_T$-$y$ space and in three-dimensional velocity space are obtained.