8 FIG. 6: The L2 invariant mass M L 2 12 distribution for accepted events. The line histograms show the Υ M L 2 12 distribution after acceptance requirements (solid line), and after all trig- ger requirements (L0 HTTP trigger, L2 cluster, L2 opening angle and L2 invariant mass) of the e $^{+}$e − daughters (dashed line). Vertical lines show location of the trigger thresholds. Normalization and scaling factors are the same as in Fig. 3. FIG. 7: Combined acceptance × efficiency as a function of ra- pidity y Υ for the decay Υ → e $^{+}$e − in STAR. Down triangles: BEMC acceptance only; open squares: adding L0 require- ment; upright triangles: adding L2 requirement; open circles: adding TPC acceptance+TPC tracking cuts and TPC-BEMC matching. tor efficiency and acceptance. Each PYTHIA+Υ event was embedded into a zero-bias event. The vertex posi- tion chosen for the simulated event was sampled from a realistic distribution of event vertex positions obtained from the Υ triggered data. With this procedure, we es- timate both the trigger efficiency and the reconstruction efficiency (discussed in Sec. V). For our purposes, a simulated Υ is considered to fall in the acceptance of the detector if each of its decay elec- trons deposits at least 1 GeV in a BEMC tower, as sim- ulated by GEANT. We find that the acceptance depends strongly on the Υ rapidity ( y$_{Υ}$ ), but weakly on its trans- verse momentum ( p$_{⊥}$$_{Υ}$ ). At | y$_{Υ}$ | < 0 . 5 the acceptance is 57%, dropping to below 30% beyond | y$_{Υ}$ | = 0 . 5, and is close to zero beyond | y$_{Υ}$ | = 1 . 0. This is illustrated in Fig. 7, where the downward triangles depict the geo- metrical acceptance of the BEMC detector ϵ$_{geo}$ obtained from the analysis of the simulated Υ decays in the real data events. For those simulated Υ’s that are accepted, we calcu- late the trigger efficiencies. This requires simulations of the BEMC response, digitization, and running the result through the offline reconstruction software chain. The HTTP requirement and the L2 trigger condition cut out an additional fraction of the events, and the combined acceptance and trigger efficiency is shown in Fig. 7. The squares include the effect of the HTTP trigger require- ment ϵ$_{L0}$ and the upright triangles include the L2 trigger condition ϵ$_{L2}$ . The open circles include TPC acceptance plus tracking efficiency ϵ$_{track}$ and TPC-BEMC matching ϵ$_{R}$ . These selections, as well as the particle identification cuts, are discussed in Sec. V. For the region | y$_{Υ}$ | < 0 . 5, the acceptance and efficiencies are given in Table I. The relative systematic uncertainty on the L0 HT trig- ger efficiency was estimated to be +5 . 9% − 7 . 5% and is the domi- nant source of systematic uncertainty of the Υ trigger effi- ciency. The systematic uncertainties for the L0 efficiency are asymmetric because the underlying E$_{⊥}$ distribution of the daughter electrons is not flat in the threshold re- gion (see Fig. 3). A shift to a higher threshold reduces the yield more than a shift to a lower threshold increases it. The L0 HTTP trigger has largest effect on the efficiency, as only 43% of the events in the acceptance remain after the trigger condition is applied. After including the L2 Quantity Value ϵ geo 0.57 ϵ geo × ϵ L0 0.25 ϵ geo ϵ L0 × ϵ L2 0.21 ϵ geo × ϵ L0 ϵ L2 × ϵ$_{track}$ × ϵ$_{R}$ 0.13 ϵ geo ϵ L0 × ϵ L2 ϵ$_{track}$ ϵ$_{R}$ (1S+2S+3S) 0.14 TABLE I: Acceptance, trigger efficiency, and tracking effi- ciency for reconstructing Υ → e $^{+}$e − in STAR in the kinematic region | y Υ | < 0 . 5. The first 4 rows are for the 1S and the last row is for the cross section–weighted 1S+2S+3S combination. All systematic uncertainties are listed in Table IV. ) 2 L2 cluster pair invariant mass (GeV/c 6 8 10 12 14 16  equivalent -1 Counts, scaled to 1 pb 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 3 10  Trigger I, with Trig II cuts  Trigger II /dy 100 pb): Simulation (BR d  500 (1S) in acceptance   500 (1S) triggered  y -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Efficiency 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceptance Acceptance*L0 Acceptance*L0*L2 Acceptance*L0*L2*Tracking