| E08-010 ~ N-Delta Luminosity Calculation |
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Introduction In its simplest form, the cross section in this experiment is a measurement of how often a Δ is formed when an electron encounters a proton. To accurately measure this, then, one needs to know both how many real events occurred, as well as how many electrons were fired at the proton target. This last term is the basis for what is known as luminosity. In its simplest form, the luminosity is the product of the beam current, the target density, and the target length. It is this definition, with current in µA, density in g/cm3, and length in cm, that is used in the MCEEP input file. For example, for run 2451 in kinematic 12, the beam current was approximately 80 µA, the target density was a fairly consistent 0.0723 g/cm3, and the target length was 4 cm, giving a luminosity of 23.136 µA⋅g/cm2. For the purposes of obtaining a cross section from the data, the "total" luminosity is needed. The final units on such a term should be something like cm−2 or fm−2, to account for the final units on the cross section itself. The first step is to multiply the luminosity above by the beamtime for a run, preferrably in seconds, which was approximately 1050 seconds for run 2451. The seconds will cancel out the time component of the µA, leaving µC. We can eliminate the Coulombs by dividing by the electron charge (1.602×10−19 C). We can remove the grams by dividing by the atomic mass of the target (1.0 g/mole) and multiplying by Avogadro's number (6.02×1023). Aside from units like "electrons" or "atoms", this leaves us with just cm−2 and quite a few powers of ten. Using the numbers above and making the appropriate conversions, this would give us an end result of 9.129×1040 cm−2. If you prefer, without the beamtime factored in, the result is 8.7×1037 cm−2⋅s−1, which is the exact result given in the summary file of the MCEEP simulation. |
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Charge Calculation Because the current fluctuates over course of a run, it cannot be taken as a constant. The exact beamtime should also be taken into account. Both of these problems are dealt with by examining a run event by event and effectively integrating the current as a function of the beamtime to determine the overall charge, which will then be used as a factor in the overall luminosity. Each event has a recorded current, via the BCM monitors, and a timestamp, via the scaler clocks. One way to calculate the charge for each event would be to assume that the current remains relatively constant between events, with the time calculated as the time difference between the current event and the previous event. This would produce a series of effective charges for each event, which could then simply be added up. The table below shows information about production run 2451, including number of recorded events, beamtime, average beam current, charge, and luminosity. Corresponding information for all of the production runs are available here.
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Trigger Efficiency and Livetime In addition to the luminosity, an accurate measure of real events from the data is needed to calculate the cross section. However, the count of good events may be limited by the detector systems, requiring calculation of the trigger efficiency and livetime. Trigger efficiency is a measurement of how effective the detectors are at triggering on an event. Livetime (or conversely, deadtime) is a measurement of how often an event could be occurring while the detector system is busy recording the previous event. In both cases, the assumption is that there may be events occurring that are not properly recorded. To take these possibilities into account, the total count of good events in the calculated yield are divided by the two percentages, increasing the total count to something assumed to be closer to reality. The trigger efficiency is, as you one might assume, the efficiency of the triggering system, which consists primarily of two layers of scintillator bars, labeled S1 and S2. S1 is a set of 6 scintillator bars, and S2 is a set of 16 scintillator bars. The triggering system is only activated if one bar in both layers detects a particle, producing the T1 trigger signal in the right HRS or a T3 trigger signal in the left HRS. To measure the efficiency of this system, a third layer, S0, consisting of a single scintillator bar, is used. The logic of the system is that a secondary trigger, known as T2 (T4) in the right (left) HRS, produces a signal only if S0 and either S1 or S2 produces a signal. That is, if both S1 and S2 produce a signal, no secondary trigger is formed. This effectively measures how often one of the primary triggering layers detects a particle while the other doesn't, with S0 acting as confirmation of the particle. To measure the efficiency of the detectors layers, then, one simply measures the total number of T1 (or T3) events divided by the number of T1 and T2 (or T3 and T4) events as measured by the scalers. For run 2451, the scalers recorded a total of 138 million T1 triggers, 1.65 million T2 triggers, 479 million T3 triggers, and 112 thousand T4 triggers. This produces a trigger efficiency of 98.8% for the right arm and 99.8% for the left. Likewise, the deadtime (or livetime) can be calculated by looking at the total number of T5 coincidence events recorded by the data aquisition system (DAQ) and dividing by the total number of T5 coincidence events measured by the scalers. For run 2451, the DAQ recorded 868,097 T5 events and the scalers recorded 894,676 T5 events, giving a livetime of 97.0%. Like the lumonisity above, the trigger efficiency and livetime for each production event can be found here. |
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Luminosity Factor Taken together, the luminosity, trigger efficiency, and livetime produce a weighting factor that can be used to produce yield histograms, similar to the weights used to produce yields in the MCEEP program. For run 2451, this factor is 1.11435 × 10−15 fm−2. |