Pseudorapidity profile of transverse momentum fluctuations in heavy ion collisions

We investigate pseudorapidity correlations of the average transverse flow of particles emitted in relativistic heavy-ion collisions. We employ $3+1$-dimensional viscous relativistic hydrodynamics with initial conditions from the quark Glauber Monte Carlo model to confront the recent measurements on the pseudorapidity correlations of the average transverse momentum in Pb+Pb collisions at $\sqrt{s_{NN}}=2760$ GeV. We find good agreement between the model predictions and data. Further, we study two other observables build with the covariance of the average transverse momentum in different rapidity bins. These observables have better stability under various systematics, thus allowing for a robust comparison between data and model. The transverse flow-transverse flow correlation coefficient is directly related to correlations of the underlying collective flow at different pseudorapidities. The three-bin measure of $p_T$ factorization breaking in pseudorapidity gives an estimate of possible decorrelation of the average transverse flow in the longitudinal direction.

Figure 1

Preliminary data from ALICE Collaboration [37] on Pearson correlation coefficient $b\left({\left[p_T\right]}_F,{\left[p_T\right]}_B\right)$ in Pbb+Pb collisions at $\sqrt{s}=2760$ GeV are compared to hydrodynamic model predictions. Results are shown for different choices of pseudorapidity bins where the average transverse momentum is calculated.

Figure 2

Preliminary data from ALICE Collaboration [37] on the correlation coefficient $b\left({\left[p_T\right]}_F,{\left[p_T\right]}_B\right)$ in two pseudorapidity bins ($0.4<|{\eta }_{F,B}|<0.8$) in Pbb+Pb collisions at $\sqrt{s}=2760$ GeV. Hydrodynamic model results are shown for $100\%$ (squares), $80\%$ (circles), and $50\%$ efficiency (crosses).

Figure 3

Transverse flow-transverse flow correlation coefficient $\rho \left({\left[p_T\right]}_F,{\left[p_T\right]}_B\right)$ predicted in the hydrodynamic model plotted as a function of collision centrality. Results are shown for two choices of pseudorapidity intervals $0.4<|{\eta }_{B,F}|<0.8$ (crosses and dashed line) and $0.6<|{\eta }_{B,F}|<0.8$ (circles and dotted line). Symbols represent the results obtained from events generated with realistic multiplicities and nonflow correlations from resonance decays, while the lines are obtained by integrating the particle spectra and include only correlations from flow.

Figure 4

Transverse flow-transverse flow correlation coefficient $\rho \left({\left[p_T\right]}_{\eta },{\left[p_T\right]}_{-\eta }\right)$ plotted plotted as a function of $\eta$ for three different centralities. Symbols are for results from realistic finite multiplicity events and lines are obtained from spectra integration (see caption of Fig. 3).

Figure 5

Transverse flow-transverse flow correlation coefficient $\rho \left({\left[p_T\right]}_{\eta },{\left[p_T\right]}_{-\eta }\right)$ plotted as a function of $\eta$. We compare results of hydrodynamic calculations with assumed efficiency $100\%,80\%$, and $50\%$, all with bin width $\delta \eta =0.5$. Squares denote the results obtained with bin of width 0.25 and efficiency $100\%$.

Figure 6

Factorization breaking coefficient ${\text{r}}_{p_T}\left(\eta \right)$ of the average transverse momentum at different pseudorapidities. Symbols are for results from realistic finite multiplicity events and lines are obtained from spectra integration (see caption of Fig. 3).