Analysis of the PHOBOS PMC Simulations

 
                    Barbara Wosiek
                Barbara.Wosiek@ifj.edu.pl
                           March , 1999
 
 

1. Hijing  inclusive events
2. Hijing  semi-central events, b < 7 fm
3. Hijing  central events, b = 0
4. Hijing  central + plasma 15 %
5. Hijing  central + plasma 30 %
6. Hijing  central + HBT R(q_inv) = 10 fm
7. Venus  central

 Different characteristics of each data set are averaged over the eta range from -6 to 6 and 2 pi in azimuth. The following track categories are considered:

• all tracks                                       (T)
• all tracks with nhits >0             (TH)
• all primaries                                (P)
• all primaries with nhits >0       (PH)

• fractions of pions, kaons and charged nucleons increase slightly  with increasing centrality of Hijing events,
• contributions of electrons and positrons (mostly secondaries) decrease with centrality,
• plasma events show larger fractions of pions and kaons as compared to normal central Hijing event
• Hijing HBT data sample is very similar to Hijing central events
• relatively large differences are observed between central Venus and central Hijing events; Venus events have larger fraction of pions (~2%) and kaons (2.5%) compensated by smaller contributions of charged nucleons and electrons.

The overall ratio of TH/PH tracks (all particles) decreases with centrality (by about  2% ) and is still smaller for plasma events. Again we see that the ratio calculated for Hijing HBT events coincides with that obtained for Hijing central. Comparing the TH/PH ratios for central Hijing and Venus events we observe significantly smaller (~6%) value for Venus data.

Alternatively one can study the ratio of all tracks with hits to all primaries, TH/P, which accounts for the acceptance losses.  From the Table below one can see that the TH/P ratios behave similarly to the TH/PH ones, although the absolute values are different.
 
 

3. The reconstructed overall multiplicities
 
The observed above differences should be reflected in the reconstructed total multiplicities. However one has to keep in mind that the present reconstruction code was tuned to central Hijet events and that so far we have neglected possible differences in the average energy deposited per particle. Except of inclusive and semi-central events the reconstruction underestimates total event multiplicities (see Table V), especially for the data samples having different shapes of the dN/deta distributions (plasma events). A large discrepancy is observed between generated and reconstructed multiplicities for Venus events. The relative amount of this underestimation (for plasma 15%, plasma 30% and Venus central with respect to the Hijing central) can  be, at least partially explained by the observed differences in TH/P ratios (the reconstruction uses larger value for this correction therefore gives smaller multiplicities). One can expect that tuning the reconstruction code to e.g. Venus central events we  would obtain overestimated total multiplicities for real data if they would look like central Hijing  events.

We are of course interested in reproducing the single particle distributions in eta and phi. The limited statistics of the investigated data samples allows only for the study of eta dependence in delta_eta windows of  2 eta units wide. The results of this study are presented below.

The first 4 figures show fractions of particles with respect to all TH tracks (Fig.2a),  average momenta per particle (Fig.2b) and ratios of the TH/PH tracks and TH/P (Fig.2d) as a function of pseudorapidity  calculated for Hijing inclusive, semi-central and central data samples.

• Fig. 3a - c  :  inclusive/central,   semi-central/central
• Fig. 4a -c   :  plasma 15%/central,  plasma 30%/central
• Fig.  5a-c   :   Venus central/Hijing central

• CENTRALITY DEPENDENCE (FIG. 3a - 3c)

Particle composition, average momenta as well as ratios of all tracks to primaries do not differ by more than 2-3% for inclusive or semi-central events as compared  to the central events sample. Therefore if we tune our reconstruction to central Hijing , that size of systematic uncertainty  should be expected. It seems to be quite satisfactory. It has to be noted that these three samples show the same shape of dN/deta distribution (with a plateau region extending from -2 to 2, see Fig.1).
Warning: the analyzed data samples are not independent, and in addition the statistics for inclusive events is too small.
Needed: studies of larger statistics independent data sets with different centralities, i.e. different impact parameter ranges.
 
• PLASMA EVENTS VS. CENTRAL EVENTS (FIG.4a - 4c)

Here we compare the samples with practically the same event mutliplicities, but exhibiting different shapes of dN/deta distributions.
CENTRAL REGION (eta = -2 to 2):
We see differences in particle composition - generally plasma events are enriched in pions (enhancement up to about 10% as compared to central events). On the other hand pion momenta are smaller. So I would guess (speculate) that differences in energy deposits may be rather small. The ratios of all tracks to primaries for plasma events is smaller by about 7% than in central events. I think that this difference is mainly caused by different shapes of pseudorapidity distributions in this central region. Therefore if we tune the reconstruction to central Hijing, the reconstructed particle density in the central region would be underestimated.
ABS(eta) > 2:
In this eta region the differences in particle compositions are much larger (less pions and more other particles in plasma events). Note that particles other than pions constitute about 38% of all particles with hits for central events and ~44% for "plasma 30%" events. Some differences in particle momenta can also be seen.  However in this eta region all particles are relativistic, so neither differences in particle composition nor small differences in momenta should play a role. Ratios of all to primaries are larger for plasma events and this would lead to the overestimated multiplicities in this eta range if reconstructed with the help of the code tuned to central events.
 
• VENUS CENTRAL VS. HIJING CENTRAL (FIG.5a -5c)

Now we have different event multiplicities and different dN/deta shapes. For reference in Figs.5 also the data for "plasma 30%" events are plotted.
CENTRAL REGION (eta = -2 to 2):
Particle composition - Venus events show enhanced fraction of kaons,  but kaons represent only ~8.4% (Venus),  ~5.1% ("plasma 30%") and ~ 5.6% (central) of all tracks with hits recorded in the central eta region. Kaon momenta are also smaller. By inspecting Fig.5a and 5b it is hard to estimate whether energy deposited per particle in Venus events differs from that for Hijing  events (we have more pions but with smaller momenta, more kaons with smaller momenta, less protons but with higher momenta and less electrons). Clearly energy deposited per particle should be studied separately.
Smaller ratios of all tracks to primaries for Venus events will result in the underestimated reconstructed central densities. This underestimation should be somewhat larger than for "plasma 30%" events.
ABS(eta) > 2:
All characteristics of Venus central events are different than those for "plasma 30%" events. So in general we may expect that if the reconstruction of plasma events gives overestimated particle densities for abs(eta)>2, we should not observe the same effect for Venus events.  And again the main factor is the ratio of all to primaries, since no difference in energy deposited per particle is expected for relativistic particles recorded in this eta range.
 
 
 
• HIJING + HBT VS. HIJING CENTRAL (NOT SHOWN)

There is no sizable differences between HBT events and central events.
 
 
 

5.  Final remarks

Evidently more detailed study, based not on PMCTracks, but rather on responses of the detector elements, including the analysis of the energy deposited per particle and using larger and other as well data samples is in order. The results of this first glance at PMC simulations show differences between various event samples which are important for the multiplicity reconstruction. They clearly indicate that the shape of dN/deta distribution plays an important role (it affects ratios of primaries to secondaries).
However if we are satisfied with systematics of the order of 10 - 15% (prime Mark's assumption) then we may say that even with the present non ideal tuning we already achieved this goal (assuming that real events would not be different from those studied). My opinion is, however, that we should aim to reduce the systematics to the level of 5% or even smaller if possible. Now we are investigating only total multiplicities and dN/deta distributions. 10-15% systematic uncertainty in these observables may seriously affect more advanced analyses like e.g. correlation studies, or event-by event studies.
It is already clear that tuning to central Hijing events should result in smaller systematics for other data samples, even for Venus events.
We may also consider two adjustments, one to central Hijing and the another e.g. to the sample with the same multiplicities but different dN/deta shape, or even to central Venus events.
At the same time, all efforts which may reduce model dependency are necessary to undertake.