Figure 2: Probability of including the second muon from J/ψ decays RoI as a function of the extended RoI size for different samples. Open squares are from J/ψ decays where one muon has p_T>6 GeV and the other p_T>3 GeV. Full squares are from J/ψ decays where one muon has p_T>4 GeV and the other p_T>2.5 GeV.

Figure 3: The η direction of muons at the intercation point vs. the difference in η position between the inner detector and the middle station of the muon spectrometer, for muons with p_T=6 GeV. The lines indicate the choice of η regions for the parameterization.

Figure 4: Distribution of the vertex χ² for true J/ψ decays (shaded) and for fake di-muon triggers (open histogram).

Figure 5: Efficiency of TrigDiMuon relative to muons identified by Atlas.MuGirl for the higher p_T muon (left) and the second muon (right).

Figure 6: Efficiency for muons from K and π decays as a function of p_T for the baseline muComb selection, compared to the optimized muComb selection described in Section 5.1 for the 4 GeV threshold (left) and the 6 GeV threshold (right).

Figure 7: Efficiency of the tight window match on single muons simulated with the aligned detector setup. The efficiency drop for the 6 GeV threshold is shown according to different σ cuts.

Figure 8: Efficiency of the tight window match at 2.7 σ on single muons simulated with the misaligned detector setup. The relative efficiency is shown for the 6 GeV threshold.

Figure 9: The distribution of ΔR between the level-1 RoI and the offline muon track, (a) using the offline track parameters at the perigee and (b) by extrapolating the offline track to the RoI position. The dashed line shows the value where the cut was applied for the matching.

Figure 10: The distribution of ΔR between the level-2 muon and the offline muon track. The dashed line shows the value where the cut was applied for the matching.

Figure 11: The overall efficiency of the level-1 single muon trigger with respect to the offline selection obtained by the tag-and-probe method (filled circles) and the efficiency estimated from a single muon Monte Carlo sample (open circles). The curve is a fit to the efficiency obtained by the tag-and-probe method from Equation 4.

Figure 12: Fit parameters (A, α and b in Equation 4) of the efficiency curve in different η and φ regions.

Figure 13: Distributions of J/ψ variables, p_T, η and cosθ*. The open histograms are for all reconstructed J/ψ´s with the generator level cut of p_T^μ₁>6 GeV and p_T^μ₂>4 GeV. Filled histograms are distributions of events passing the level-1 di-muon trigger.

Figure 14: Di-muon trigger efficiency with p_T^μ>6 GeV. Open circles are the result obtained from decision of the level-1 di-muon trigger and filled circles are the efficiency obtained using the parameterization shown in Figure 12.

Figure 15: The overall efficiency of the level-2 single muon trigger, (a) with respect to offline reconstruction, (b) with respect to level-1.

Figure 16: The overall L2/rec single-muon trigger efficiency as a function of p_T, η and φ. Efficiency is calculated using the trigger efficiency map (black circles) and it is compared to the one calculated using matched level-1 and level-2 trigger objects (open triangles).

Figure 17: The overall di-muon J/ψ trigger efficiency as a function of p_T, η, φ and cosθ*. Efficiencies from the trigger decision bit (open triangles) and the ones calculated from the trigger efficiency map (black circles) are shown.

Figure 18: The overall di-muon J/ψ trigger efficiency as a function of ΔR. Efficiencies from the trigger decision bit (open triangles) and the ones calculated from the trigger efficiency map (black circles) are shown.

Table 1: Summary of MC samples.

Table 2: Efficiency, relative to level-1, of the two di-muon trigger algorithms for a trigger threshold of 4 GeV. In parenthesis is the efficiency calculated relative to J/ψ events that passed the single muon trigger that selects the input to TrigDiMuon. To estimate the efficiency we used a sample of Λ_b -> J/ψ Λ, where J/ψ-> μ(p_T>2.5 GeV) μ(p_T>4 GeV).

Table 3: Efficiency, relative to level-1, of the two di-muon trigger algorithms for a trigger threshold of 6 GeV. In parenthesis is the efficiency calculated relative to J/ψ events that passed the single muon trigger that selects the input to TrigDiMuon. To estimate the efficiency we used a sample of Λ_b -> J/ψ Λ, where J/ψ-> μ(p_T>2.5 GeV) μ(p_T>4 GeV).

Table 4: Fake rate of the TrigDiMuon algorithm for muons from different sources and total fake rate using a trigger threshold of 4 GeV, at a luminosity of 10³¹cm^-2s^-1. The b and c components were estimated from a sample of bbbar -> μ+X$ with p_T^μ 4 GeV and the K/π component from the minimum bias sample with forced decays.

Table 5: Fake rate of the TrigDiMuon algorithm for muons from different sources and total fake rate using a trigger threshold of 6 GeV, at a luminosity of 10³³cm^-2s^-1. The b and c components were estimated from a sample of bbbar -> μ+X with p_T^μ 4 GeV and the K/π component from the minimum bias sample with forced decays.

Table 6: Total rate and efficiency relative to level-1 of the TrigDiMuon algorithm including the vertex cut χ²<30, and of the topological di-muon trigger. The efficiency is estimated from a sample of Λ_b -> J/ψ Λ, where J/ψ-> μ(p_T>2.5 GeV) μ(p_T>4 GeV).

Table 7: Efficiency of the TrigDiMuon and Topological di-muon algorithms for J/ψ reconstructed by Atlas.MuGirl. To estimate the efficiency we used a sample of Λ_b -> J/ψ Λ, where J/ψ-> μ(p_T>2.5 GeV) μ(p_T>4 GeV).

Table 8: Expected rate with a 6 GeV single muon threshold from the muComb algorithm for the π and K decays. The rejection with respect to the baseline muComb algorithm is shown in parenthesis. These rates were estimated from the forced-decay minimum bias sample.

Table 9: Expected rate with a 6 GeV single muon threshold from the muComb algorithm for the b component. In parenthesis is the percentage rejection with respect to the baseline muComb.

Table 10: Expected output rate of muFast and muComb for a 4 GeV threshold at the 10³¹cm^-2s^-1 luminosity.

Table 11: Expected output rate of muFast and muComb for a 6 GeV threshold at the 10³³cm^-2s^-1 luminosity.

Table 12: The rates after level-1 and level-2 using the proposed calibration trigger for a luminosity of 10³¹cm^-2s^-1 with the threshold of p_T>6 GeV. The contribution of J/ψ-> μ₊μ_- process to the rate is also shown in parentheses.