7 FIG. 5: The distribution of cosine of L2 opening angle θ L 2 12 for accepted events. The line histograms show the Υ distribution after acceptance requirements (solid line), and after all trig- ger requirements (dashed line). The vertical line shows the location of the trigger threshold. Normalization and scaling factors are the same as in Fig. 3. FIG. 4: The distribution of L2 Cluster-1 energy E L 2 1 for all towers above the HT threshold in a trigger patch above the TP threshold. The L2 trigger requires E L 2 1 > 4 . 0 GeV (vertical line). The line histograms show the Υ (from simulation) af- ter acceptance requirements (solid line), and after all trigger requirements (dashed line). The normalization and scaling factors are the same as in Fig. 3. IV. Υ ACCEPTANCE AND TRIGGER EFFICIENCY ulated Υ’s. This again reflects the fact that the triggered distribution is dominated by back-to-back π $^{0}$’s. The ma- jority of these are rejected offline when requiring the pres- ence of a corresponding electron track in the TPC. The L2 invariant mass distribution shown in Fig. 6 is peaked at ≈ 8 GeV /c 2 due to the cluster energy require- ments. The vertical lines depict the lower and upper thresholds at 6 and 15 GeV /c $^{2}$. The histogram shows the simulated Υ(1S) before any trigger cuts (solid) and after passing all the previous thresholds (dashed). The trigger preferentially rejects lower L2-mass Υ events, be- cause these can happen when the energy clusters mea- sured in the calorimeter are lower than their average, and these clusters are preferentially rejected by the algo- rithm. From these simulations we estimate the Υ mass resolution of the L2 trigger to be 849 ± 8 MeV /c $^{2}$. It is dominated by the BEMC energy resolution and by the straight-line approximation used to calculate the open- ing angle in the L2 trigger algorithm. This is about an order of magnitude larger than the offline mass resolu- tion, where the electron trajectories and momenta are obtained from tracking. Since all the Υ’s that reach this stage are contained within the invariant-mass limits, this invariant mass cut serves mainly to reject background. In addition, the L2 information (such as that shown in Figs. 4–6) is available online after every run. These distributions serve as useful diagnostic tools during data taking. To determine the geometrical acceptance of the detec- tor for measuring Υ → e $^{+}$e $^{−}$, we combined two types of events in the following way. For the first type, we performed GEANT simulations of the Υ → e $^{+}$e − de- cays and propagated them through the detector geome- try. The simulations were done with uniform population of the p$_{⊥}$ - y phase space, folded with a Gaussian in y ( σ = 1) and a realistic p$_{⊥}$ distribution. We chose the form dN/dp$_{⊥}$ ∝ p$_{⊥}$/ (exp( p$_{⊥}$/T ) + 1) with the parameter T = 2 . 2 GeV /c obtained from a fit to CDF data [24]. The dependence of the acceptance on the choice of p$_{⊥}$ distri- bution is negligible. This was verified by using functional forms derived from data at lower energy. Each simulated decay was combined with a simulated p + p minimum- bias event using the PYTHIA event generator [25] with CDF Tune A settings [26]. For the second type, we used a set of data collected by triggering on a RHIC bunch crossing. These were labeled “zero-bias” as they do not require signals in any of the STAR detectors. These zero- bias events do not always have a collision in the given bunch crossing, but given that in the 2006 p + p run the dominant contribution to the TPC occupancy was from pileup, these events will include the pileup from out-of- time collisions and all detector effects. When the zero- bias events are combined with simulated events, they pro- vide the most realistic environment to study the detec- ) L2 cluster pair cos( -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1  equivalent -1 Counts, scaled to 1 pb 10 2 10$^{3}$ 10  Trigger I, with Trig II cuts  Trigger II /dy 100 pb): Simulation (BR d  500 (1S) in acceptance   500 (1S) triggered  L2 cluster 1 energy (GeV) 2 4 6 8 10 12 14 16 18 20  equivalent -1 Counts, scaled to 1 pb 1 10 2 10$^{3}$ 10$^{4}$ 10  Trigger I, with Trig II cuts  Trigger II /dy 100 pb): Simulation (BR d  500 (1S) in acceptance   500 (1S) triggered 