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L0). The L2 Υ trigger makes the decision by looking for calorimeter signatures consistent with the production of a high invariant mass electron-positron pair. (Since the L2 trigger uses BEMC information only and does not distinguish electrons from positrons, we will refer to electrons and positrons simply as “electrons” in all dis- cussions of the L2 trigger.) At a minimum, one pair of candidate electrons is required. They are processed as follows. (We will denote kinematical quantities obtained in the L2 stage with the superscript “L2” to distinguish them from similar quantities obtained during the offline analysis.) 

The algorithm starts by searching for all towers above the L0 High Tower threshold. Each of these is treated as a seed for a 3-tower cluster. To produce the clusters, we search in the η - ϕ region around each High Tower, with a search window of 3 × 3 towers. This area is smaller than the TP size in order to focus on electron finding, as our simulations show that electrons will likely have most of their energy contained in only 3 towers. We sort these 8 surrounding towers according to their measured energy and pick the two highest- E$_{⊥}$ towers in this list to pro- duce a 3-tower cluster. This L2 tower clustering gives a better estimate of the electron energy compared to a single tower due to possible shower leakage into neighbor- ing towers. If the energy of this 3-tower cluster is greater than 4.0 GeV it is considered for further processing, and we label such clusters as “L2 Cluster-1”. 

We next look for additional electron candidates in the 

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event. While it is possible for an event to have two tow- ers above the HT threshold, the majority of events will have only one. We select additional electron candidates by starting with towers which have E$_{⊥}$ ≳ 0 . 7 GeV (10- bit ADC of at least 75 counts after pedestal subtraction). Starting from these second seeds, we again construct 3- tower clusters (L2 Cluster-2) using the procedure out- lined above. We require that the L2 Cluster-2 energy be E L 2 2 > 2 . 5 GeV. After the complete iteration to find electron clusters, we make all possible cluster pairs (where each pair must have at least one L2 Cluster-1) and calculate two pairwise quantities: the opening an- gle and the invariant mass of the pairs. These are cal- culated under the approximation that the vertex loca- tion is in the center of the detector and that the elec- trons travel in a straight line. Since the majority of the e $^{+}$e − pairs from Υ decays have a large opening angle ( θ ), we look for pairs with cos( θ L 2 12 ) < 0 . 5, where θ L 2 12 is the angle between the two clusters calculated in the L2 algorithm. With the combined information on the energy of the two clusters and their opening angle, we reconstruct the invariant mass via the approximate for- mula M L 2 12 ≈ √ 2 E L 2 1 E L 2 2 (1 − cos θ L 2 12 ). We can neglect the electron mass of 0.511 MeV /c 2 as it would only con- tribute ≈ 1 MeV /c $^{2}$, which is small for ultra-relativistic electrons. For comparison, the straight-line approxima- tion and the energy resolution result in a mass resolution of ≈ 900 MeV /c 2 as will be discussed in the following sec- tion. We select events with cluster-pair invariant masses in the range 6 < M L 2 12 < 15 GeV /c $^{2}$. If there is any pair 

