Transverse momentum fluctuations in nuclear collisions at $158A\mathrm{GeV}$

Results are presented on event-by-event fluctuations in transverse momentum of charged particles, produced at forward rapidities in $\mathrm{p}+\mathrm{p}$, $\mathrm{C}+\mathrm{C}$, $\mathrm{Si}+\mathrm{Si}$, and $\mathrm{Pb}+\mathrm{Pb}$ collisions at $158A\mathrm{GeV}$. Three different characteristics are discussed: the average transverse momentum of the event, the ${\Phi }_{p_T}$ fluctuation measure, and two-particle transverse momentum correlations. In the kinematic region explored, the dynamical fluctuations are found to be small. However, a significant system size dependence of ${\Phi }_{p_T}$ is observed, with the largest value measured in peripheral $\mathrm{Pb}+\mathrm{Pb}$ interactions. The data are compared with predictions of several models.

Figure 1

The experimental setup of the $\mathrm{NA}49$ experiment [38] with different beam definitions and target arrangements.

Figure 2

$\mathrm{NA}49$$\varphi -p_T$ acceptance of positively charged particles (standard configuration of magnetic field) for two selected rapidity bins at $158A\mathrm{GeV}$. The solid lines represent the analytical parametrization.

Figure 3

The dependence of ${\Phi }_{p_T}$ on the allowed distance $\Delta z$ of the reconstructed event vertex from its nominal position. Note: the values and their errors are correlated.

Figure 4

The dependence of ${\Phi }_{p_T}$ on the upper cut in the impact parameter $\mid b_x\mid$. For each point, the cut on $\mid b_y\mid$ was equal half the cut on $\mid b_x\mid$. Note: the values and their errors are correlated. The dashed line indicates the cut used in the analysis.

Figure 5

The dependence of ${\Phi }_{p_T}$ on the fraction of randomly rejected particles.

Figure 6

Additive correction $\Delta {\Phi }_{p_T}$ for limited two-track resolution effect versus multiplicity $⟨N⟩$ of accepted particles. Different points correspond to positively charged, negatively charged, and all charged particles. The presented corrections have been determined using $\mathrm{p}+\mathrm{p}$, $\mathrm{C}+\mathrm{C}$, $\mathrm{Si}+\mathrm{Si}$, and three centralities of $\mathrm{Pb}+\mathrm{Pb}$ collisions at $158A\mathrm{GeV}$. The lines represent the analytical parametrization: $\Delta {\Phi }_{p_T}\left(⟨N⟩\right)=-a\sqrt{⟨N⟩}+b$ with $a$ and $b$ being parameters of a fit to the data points.

Figure 7

Distributions of mean transverse momentum for real (data points) and mixed events (histograms). Data points are not corrected for acceptance and limited two track resolution. Events with accepted particle multiplicity equal to zero are not used.

Figure 8

${\Phi }_{p_T}$ versus mean number of wounded nucleons $⟨N_W⟩$. Data points were corrected for limited two-track resolution. Errors are statistical only. Systematic error is smaller than $1.6\mathrm{MeV}∕\mathrm{c}$.

Figure 9

(Color) Two-particle correlation plots using the cumulant $p_T$ variable $x$. After each charged particle pair $(x_1,x_2)$ was entered into the plot, the bin contents were normalized by dividing with the average number of entries per bin. The data are plotted with different color scales.

Figure 10

${\Phi }_{p_T}$ versus mean number of wounded nucleons calculated using the HIJING model with geometrical acceptance cuts included (black lines) and without geometrical acceptance restrictions (gray lines). Results are compared to data (points) corrected for limited two-track resolution (the markers are the same as in Fig. 8). The panels represent: all charged, negatively charged, and positively charged particles. Data points contain both short and long range correlations. The effects of short range correlations are not incorporated in the HIJING model.

Figure 11

Mean transverse momentum versus multiplicity of all accepted particles. The closed symbols represent $\mathrm{p}+\mathrm{p}$ data at $158A\mathrm{GeV}$ (data are not corrected for limited two-track resolution effect) and the open symbols corresponds to $\mathrm{p}+\mathrm{p}$ events simulated using the HIJING model (the effects of the limited NA49 acceptance are included). Events with accepted particle multiplicity equal to zero are not used.

Figure 12

(Color) Two-particle correlation plots using the cumulant $p_T$ variable $x$. Results are shown for all charged particles for $\mathrm{p}+\mathrm{p}$ data (a) compared to: simulated $\mathrm{p}+\mathrm{p}$ HIJING events with limited NA49 acceptance (b), simple random-generator model, which reproduces $M\left(p_T\right)$ versus $N$ correlation for $\mathrm{p}+\mathrm{p}$ data (c), and model of fluctuations of the inverse slope parameter for $\mathrm{p}+\mathrm{p}$ data on the level of about 10% (d).

Figure 13

(Color) Two-particle correlation plots using the cumulant $p_T$ variable $x$. Results are shown for simulated $\mathrm{p}+\mathrm{p}$ (a) and $\mathrm{C}+\mathrm{C}$ (b) collisions from the HIJING model. Limited NA49 acceptance is taken into account.

Figure 14

(Color) Two-particle correlation plots using the cumulant $p_T$ variable $x$ for the most central $\mathrm{Pb}+\mathrm{Pb}$ collisions. The experimental result is shown in (a) and compared to the inverse slope parameter fluctuation model (b)–(d). In the model the mean value of the inverse slope parameter was set to 190 MeV. The dispersions of the Gaussian shaped inverse slope parameter distributions were set to: ${\sigma }_T=5\mathrm{MeV}$ (b), ${\sigma }_T=10\mathrm{MeV}$ (c), and ${\sigma }_T=20\mathrm{MeV}$ (d).

Figure 15

Predicted dependence of ${\Phi }_{p_T}$ on $T$ fluctuations [34] compared to the measured ${\Phi }_{p_T}$ for the 5% most central Pb+Pb collisions. The uncertainty of the measured ${\Phi }_{p_T}$ value is represented by the bands for statistical (gray) and systematic (dark gray) errors.