Analysis of PHENIX Data

During the first run period RHIC provided Au-Au collisions at $\sqrt{s_{NN}} = 130$ GeV. The primary interaction trigger was based on information from the two BBC. The trigger required a coincidence where at least two photo-multipliers on each side fired. From simulations it was found to correspond to 92% of the nuclear interaction cross section of 7.2 barns. A total of about $5\cdot10^5$ such minimum bias events were used in the net charge fluctuation analysis, which is based on information from the drift chamber and the first pad chamber plane in the west tracking arm. These detectors cover approximately 0.7 units in pseudorapidity and 90 in azimuth. The vertex positions of the collisions were mainly retrieved from time measurements in the two BBC. A rather tight vertex cut of $\vert z\vert<17$ cm was applied to get a homogeneous event sample, where background from interactions in the magnet iron was avoided.

Results from the data were compared to simulations using the RQMD [21] event generator, PISA and detector response code. The simulations also gave information on reconstruction efficiencies and background contributions. The reconstruction efficiency was shown to fall rapidly for particles with $p_T$ below 0.2 GeV/c, implying exclusion of tracks with $p_T<0.2$ GeV/c from the real data sample. The overall efficiency for detecting charged particles was then found to be about 80%, both for positive and negative particles. Background contributions, e.g. from interactions in detector material and weak decays, were estimated to about 20% of the reconstructed tracks.

The acceptance coverage $p_a$ of the detectors was estimated from the simulations to be 0.018. A value of $\varepsilon=0.078$ was measured from the data sample, and charge asymmetry effects for $v(Q)$ can be shown to be negligible. The expected reduction in the net charge fluctuations, due solely to global charge conservation, then yields

$$v(Q) = 1 - p_e \cdot (1-f_{bkg}) \cdot p_a$$

$$= 1-0.8\cdot(1-0.2)\cdot0.018 \quad \approx \quad 0.988$$ (44)

Fig. 3.9 shows $4 \cdot v(Q)$ and $v(R)$ for each value of $n_{ch}$.

Figure 3.9: $4 \cdot v(Q)$ and $v(R)$ for fixed values of $n_{ch}$. Solid curves show the stochastic behavior, calculated using equations (3.33) - (3.36).

The data points are compared to a purely stochastic behavior (solid curves), calculated from

$$\<Q\> \quad=\quad \sum_{i=0}^{n_{ch}} (2i-n_{ch}) \left(\begin{array}{c} n_{ch}\\ i \end{array}\right) p_+^{n_{ch}-i} \cdot p_-^i$$ (45)

$$\<Q^2\> \quad=\quad \sum_{i=0}^{n_{ch}} (2i-n_{ch})^2 \left(\begin{array}{c} n_{ch}\\ i \end{array}\right) p_+^{n_{ch}-i} \cdot p_-^i$$ (46)

$$\<R\> \quad=\quad \frac{1}{A} \sum_{i=1}^{n_{ch}-1} \frac{n_{ch}-i}{i} \left(\begin{array}{c} n_{ch}\\ i \end{array}\right) p_+^{n_{ch}-i} \cdot p_-^i$$ (47)

$$\<R^2\> \quad=\quad \frac{1}{A} \sum_{i=1}^{n_{ch}-1} \left(\frac{n_{ch}-i}{i}\right)^2 \left(\begin{array}{c} n_{ch}\\ i \end{array}\right) p_+^{n_{ch}-i} \cdot p_-^i$$ (48)

where $A = 1 - p_+^{n_{ch}} - p_-^{n_{ch}}$ is the new normalization needed when discarding events with $n_+$ or $n_-$ equal to zero, in the case of $R$. The figure shows that the use of $v(R)$ introduces complications. $v(R)$ has a strong dependence on $n_{ch}$ and $\varepsilon$. The values are understood only when comparing to the stochastic curve, but for event classes with varying $n_{ch}$ it is not straightforward to calculate such a curve.

Figure 3.10 displays $v(Q)$ as a function of increasing centrality. The centrality is divided into 20 classes, which are determined from the BBC and ZDC information as shown in fig. 3.11. The rightmost data point in fig. 3.10 corresponds to the 0-5% most central events.

Figure 3.10: $v(Q)$ as a function of centrality.

Figure 3.11: The centrality classes determined by the charge in the BBC and the energy in the ZDC.

The magnitude of the fluctuations does not depend on centrality. For the 10% most central events, the value is $v(Q)=0.965 \pm 0.007$. If the difference when applying (3.19) is taken to be a systematic error the result is

$$v(Q) = 0.965 \pm 0.007\mt{(stat)} - 0.019\mt{(syst)}$$ (49)

However not as drastic as was predicted with a QGP transition, there is a clear reduction compared to the expected value from (3.32). Taking the limited geometrical acceptance of the detector into account, the result is consistent with the resonance gas prediction mentioned on page . With larger acceptance the probability to detect both charged decay particles from neutral resonances increases. This is seen in fig. 3.12, where $v(Q)$, for the 10% most central events, is displayed as a function of $\Delta \varphi _r$. (Here $\varphi _r$ denotes the reconstructed azimuthal emission angle of a particle, and $\Delta \varphi _r$ defines the region where particles are accepted in the analysis, explained further by fig. 3.13.) Above $\Delta \varphi _r$=40 the behavior of $v(Q)$ clearly deviates from what is expected solely from global charge conservation (the solid curve). Fig. 3.12 also shows good qualitative agreement between the data and the RQMD simulation.

Figure 3.12: $v(Q)$ for the 10% most central events as a function of $\Delta \varphi _r$. For data, the error band shows the total statistical error, and the error bars the uncorrelated part.

Figure 3.13: $p_T$ vs. $\varphi _r$ for a sub set of the detected particles. There is one band for positive particles and one for negative, due to the opposite bending in the magnetic field. The $\Delta \varphi _r$ region is centered around the $\varphi _r$ corresponding to the mid-point of the detector.