Final Systematic Error Analysis of - PowerPoint Presentation

1. Final Systematic Error Analysis of HMS Scaler-based Fall ‘18 Boiling Slopes D. Mack10/28/20 Abstract Using Hem’s scaler reports from the Fall ‘18 lumi scan, I get boiling slopes for C, LH2, and LD2 with total errors of ~+-0.3% . Results are consistent between the 2 pre-triggers El LO-CER and EL HI, and the 2 triggers El Real and El Clean. Additional scalers like PR LO, PR HI, and SH LO appeared to work quite well at the higher rates for LH2 and LD2, but I dropped them because for carbon – where the rates were relatively low – the slopes were too sensitive to the beam off offsets.

2. Final Fall ’18 Results 2TargetMeasuredEl RealSlope(%/100muA)El Real Slope with Window Correction(%/100muA)Total ErrorC-0.10n/a+-0.2 LH2-2.26-2.50+-0.30 LD2-2.71-2.84+-0.32 Measured slopes are consistent with preliminary slopes I reported last month.Scalers are much more consistent now. (Next few slides.) I did the randoms corrections which were a little larger than I expected. Also, analysis of the gate timings showed the CER DT correction I was making was too large. So I no longer need a bizarrely large DT correction to get CAL-dominated scalers to agree with CER-dominated scalers. Uncertainties remain ~same as last month: while I no longer have to inflate errors to allow for discrepancies between different scalers, the std dev of the slope from better fits indicates there are systematic issues which are larger than the statistical errors. But I’m done. I added corrections for dilution by the Al windows.

3. Final Fall ‘18 Results And More of the Elephant 3TargetMeasuredEl RealSlope(%/100muA)El Real Slope with Window Correction(%/100muA)Total ErrorStd Devof Slope(stat+nonlin+model)Slope Error from BCM OffsetMaximum El RealRandoms Correction Max El Real DT CorrectionCorrection for Window DilutionAve H3of4 Rate(kHz)Ave El LO-CER(KHz)AveCER-CER0 Rate (KHz)C-0.10n/a+-0.2+-0.04+-0.2-0.07+0.02n/a4.43.625.6 LH2-2.26-2.50+-0.30+-0.23+-0.2-0.24+0.05+0.238.36.745.9 LD2-2.71-2.84+-0.32+-0.25+-0.2-0.28+0.10+0.1314.312.475.8 Measured slopes are consistent with preliminary slopes I reported last month.Scalers are much more consistent now. (Next few slides.) I did the randoms corrections which were a little larger than I expected. Also, analysis of the gate timings showed the CER DT correction I was making was too large. So I no longer need a bizarrely large DT correction to get CAL-dominated scalers to agree with CER-dominated scalers. Uncertainties remain ~same as last month: while I no longer have to inflate errors to allow for discrepancies between different scalers, the std dev of the slope from better fits indicates there are systematic issues which are larger than the statistical errors. But I’m done. I added corrections for dilution by the Al windows.

4. Fan Speeds in Context4RunLH2 fan speedLD2 fan speedSpring ‘184040Fall ‘185040I'm using Hem's runs he listed on his slide 2 at https://hallcweb.jlab.org/doc-private/ShowDocument?docid=1087 You can check the fan speeds using first_epics_30.results which is attached to the Run Start entries in the hclog. (But Dave G and Eric C helped clarify things for me.) So, ignoring beam spot size variability, in terms of magnitude:The magnitude of my LH2 slope should be smaller than the corresponding Spring ’18 slope.The magnitude of my LD2 slope should work for Spring ’18 or Fall ’18.

5. Results (not corrected for window dilution)5Same vertical scale for all 3 targetsNo parameters adjusted between targetsErrors are correlated, but not identical

6. Results (not corrected for anything)6Same vertical scale for all 3 targetsNo data-driven randoms correction No almost model-independent CER DT correctionNo (slightly sketchy) CAL DT correction

7. Results (not corrected for anything)7Same vertical scale for all 3 targetsNo data-driven randoms correction No almost model-independent CER DT correctionNo (slightly sketchy) CAL DT correctionRandoms correction turned off(was ~ -0.24%)

8. Results (not corrected for anything)8Same vertical scale for all 3 targetsNo data-driven randoms correction No almost model-independent CER DT correctionNo (slightly sketchy) CAL DT correctionCAL DT correction turned off(was ~ +0.46%)

9. Results (not corrected for anything)9Same vertical scale for all 3 targetsNo data-driven randoms correction No almost model-independent CER DT correctionNo (slightly sketchy) CAL DT correctionCAL DT correction turned off(was ~ +0.46%)CER DT correction turned off(was ~ +0.05%)

10. Results for Other Scalers That I Dropped(not corrected for window dilution)10Same vertical scale for all 3 targetsNo parameters adjusted between targetsI chose to focus on El LO-CER, El HI, El Real, and El Clean.The simpler, non-coincidence scalers work pretty well too, at least at high rates.But for carbon, the slopes were sensitive to changes in the offsets in Pr LO, etc, at the 1 Hz level. So after wasting a lot of time, I used only coincidence scalers.

11. LH2 Slope Plots(not corrected for window dilution)11The apparent slight curvature here may be due to statistical errors which are just below 0.1% per point.At a given beam current, the stat errors are highly correlated between these 4 scalers, modulo PID. Pion fraction was ~ 25%. Since pions were above CER threshold: El LO-CER and El Real count e + all piEl HI and El Clean count e + some pi.

12. LH2 Systematics Checks12In the ratio of corrected scalers, the boiling – and a lot of statistics - cancel out. This checks for false slopes due to correction errors.Vertical scale now zoomed into 1 +- 0.5% . LH2 (here) and C look excellent. For LD2, the El HI scaler is an outlier.

13. LH2 Systematics Checks13In the ratio of corrected scalers, the boiling – and a lot of statistics - cancel out. This checks for false slopes due to correction errors.Vertical scale now zoomed into 1 +- 0.5% . LH2 (here) and C look excellent. For LD2, the El HI scaler is an outlier. The plot I flagged in pink looks a little odd.But it’s just telling us that, when I made theseveral % randoms correction to El LO LO, I made O(0.1)% systematic errors. Same thing happens for all 3 targets. That’s OK.The randoms contribution to El LO LO-Cer is much smaller.

14. Misc Rates in HMS During Fall ‘18 Lumi Scan14El Real(clean trigger, so ~ “tracks”)S1X2-ended rate in a hodo planeis ~10x larger than the track rate.1-ended rates ~30% higherCER ~380KHz offset from light leak. Subtracting offset, CER rate is ~ 5xlarger than the track rate. LD2 beam-induced rates are >3x larger than 1.5% Carbon “flat control”.Need a thicker Carbon target.

15. Motivation15The yields extracted from scalers are potentially attractive for measuring boiling slopes because of their small statistical errors and generally small size of the rate-dependent corrections. Plus, a scaler analysis is in principle simpler than an event mode analysis, and there’s no loss of statistics from computer live time or pre-scaling. Still, a scaler extraction of the boiling slopes may not be feasible: one has to first determine whether the scalers are linear after corrections, whether they suffer from excess noise, and whether systematic errors are under control. In an event-mode lumi analysis, the contribution from a liquid target boiling slope will combine with potential errors in ELT and/or tracking efficiency and/or FADC deadtime. (I assume CLT is perfectly known.) Interpretation of event-mode lumi slopes may be ambiguous even when the boiling contribution is known.Ideally, if the boiling contributions could be determined from scalers, then one could use event-mode lumi analyses to study the MUCH more complicated problems such as ELT, tracking efficiency, and FADC deadtime.

16. Yield FormalismThere’s no such thing as a simple analysis if you’re trying to keep systematic errors below the 0.5% level. Let’s look closely: A fairly general* expression for the scaler rate is R_msr = r_signal*I_true + R_offset + r_randoms*I_true^2The average BCM signal, allowing for nonlinearity as well as errors in gain and offset, is I_msr = I_true*(1+ΔI_gain) *( 1 + f(I_true) ) + ΔI_offsetThe yield is therefore approximately Y = R_msr/I_msr = r_signal + R_offset/I_true + r_randoms*I_true --------------------------------------------------------------- 1+ ΔI_gain + f(I_true) + ΔI_offset/I_trueExpanding to first order, and dropping any products of two small terms, we get Y = r_signal *[ 1 - ΔI_gain – f(I_true) - ΔI_offset/I_true ] + R_offset/I_true + r_randoms*I_true16* I’ve neglected the target windows and rate-dependent DT corrections. I’ll do those separately later; the above is messy enough.

17. Yield Formalism and Magnitude of Slope Contributions From the previous slide we had: Y = r_signal *[ 1 - ΔI_gain – f(I_true) - ΔI_offset/I_true ] + R_offset/I_true + r_randoms*I_trueTo keep things from getting even messier, I won’t differentiate this to get dY/dI and normalize the result. But there will be half a dozen additional contributions to our normalized slope, including the signal of interest, dr_signal/dI : No. Yield ContributionNaive Magnitude of Slope ContributionEstimate of the Uncertainty from Slope Contribution1r_signal0%/100muA for C to -”5”%/100muA O(0.1)%/100muA statistical error2-r_signal*ΔI_gain < 0.05%/100muA< 0.05%/100muA for gain error of 1% 3-r_signal*f(I_true)Potentially +-O(0.5)%/100muA 0.1% if BCM4B is not used (see “flavor dependence” slides later)4-r_signal* ΔI_offset/I_true +-0.75%/100muA for a BCM offset uncertainty of +-0.1muA. roughly +-0.2%/100muA for Fall ‘18 due to1) a smaller 0.050muA offset uncertainty, and 2) tuning of the offset to reduce the residuals. This may be the largest, irreducible systematic error. 5r_randoms*I_true 0%/100muA in single detectors like PreSh LO,< 0.1%/100muA in higher level electron triggers, O(1)%/100muA in Hodo 3of4, O(10)%/100muA in STOFVaries over a huge range. Can be accurately corrected if small. STOF and Hodo3of4 are unusable for lumi scans.6scaler DT correctionsWorst case 0.7%/100muA for LD2Worst case 0.14%/100muA for LD2 assuming 20% uncertainty on the DT corrections 7target window correctionsO(0.5)%/100muA for a –”5”%/muA slope <0.1% assuming 10% uncertainty on the window correction For many scalers, it should be possible to achieve a systematic uncertainty of +-0.3%/100muA for carbon where rate dependent DT corrections are small, and +-0.4% for LD2 where those corrections are larger. 17

18. BCM Systematic Uncertaintiesoffset, gain, flavorIf we have already removed the small rate offsets from cosmics, then Y = r_signal *(1 - ΔI_gain – f(I_true) - ΔI_offset/I_true )18

19. Effect of BCM OffsetThe BCM offset injects a 1/I_true term into the normalized yield: Y = r_signal *(1 - ΔI_offset/I_true )In Fall ’18 the BCM offset had an uncertainty of +-0.05muA. This is the a made-up example of how it would affect the Yield:19

20. Effect of BCM OffsetThe BCM offset injects a 1/I_true term into the normalized yield: Y = r_signal *(1 - ΔI_offset/I_true )In Fall ’18 the BCM offset had an uncertainty of +-0.05muA. This is the a made-up example of how it would affect the Yield:And this is the normalized Yield:This systematic error would be significant for interpreting whether the carbon slope is “flat”. 20

21. Effect of BCM OffsetIn principle, the residuals to a linear fit provide smoking gun evidence for an incorrect BCM offset which could then be tweaked within its uncertainty. But in this example with a +-0.05muA residuals, it is unlikely any lumi dataset would have enough statistics to see this curvature. Options are to stick with a +-0.35% slope error for Fall ‘18, or reduce/constrain this uncertainty better with an offset tweak which achieves better linearity for all 3 targets. 21Take the plot from the previous page (below), and calculate the residuals (right):

22. Effect of BCM Gain ErrorThe BCM gain error basically only tweaks the units of the beam current: Y = r_signal *(1 - ΔI_gain ) It cannot create a slope, but if a slope exists then an N% error in the BCM gain will produce a -N% relative error in the boiling slope.Given the short duration of the lumi runs, I think an uncertainty of +-1% is reasonable. Here is a made-up example, with an exaggerated +-5% BCM gain error,of how a -3%/100muA boiling slope would be affected:22

23. The systematic error from a 1% BCM gain uncertainty would be below the statistical errors on the slopes.Effect of BCM Gain ErrorThe BCM gain error basically only tweaks the units of the beam current: Y = r_signal *(1 - ΔI_gain ) It cannot create a slope, but if a slope exists then an N% error in the BCM gain will produce a -N% relative error in the boiling slope.Given the short duration of the lumi runs, I think an uncertainty of +-1% is reasonable. Here is a made-up example, with an exaggerated +-5% BCM gain error,of how a -3%/100muA boiling slope would be affected:23

24. Effect of BCM “Flavor” Dependence - CarbonRecall the nonlinearity term in the Yield eqn: Y = r_signal *(1 – f(I_true) ) It is very hard to measure absolute nonlinearities below the 0.5% level, but it is easy to measure differential nonlinearity. Here’s the carbon data normalized to 5 different BCMs:24Note the vertical scale is only +-0.5%. All these BCMs have good linearity,but several seem a bit odd at lower beam currents. Let’s separate them intoanalog receivers and digital receivers (dropping BCM4B):

25. Effect of BCM “Flavor” Dependence - CarbonRecall the nonlinearity term in the Yield eqn: Y = r_signal *(1 – f(I_true) ) It is very hard to measure absolute nonlinearities below the 0.5% level, but it is easy to measure differential nonlinearity. Here’s the carbon data normalized to 5 different BCMs:25Note the vertical scale is only +-0.5%. All these BCMs have good linearity,but several seem a bit odd at lower beam currents. Let’s separate them intoanalog receivers and digital receivers (dropping BCM4B):

26. Effect of BCM “Flavor” Dependence - CarbonRecall the nonlinearity term in the Yield eqn: Y = r_signal *(1 – f(I_true) ) It is very hard to measure absolute nonlinearities below the 0.5% level, but it is easy to measure differential nonlinearity. Here’s the carbon data normalized to 5 different BCMs:26Note the vertical scale is only +-0.5%. All these BCMs have good linearity,but several seem a bit odd at lower beam currents. Let’s separate them intoanalog receivers and digital receivers (dropping BCM4B):Hmm…. Maybe the digital receivers are a little less linear?

27. Effect of BCM “Flavor” Dependence – LH2And for LH2: 27Note the vertical scale expanded by a factor of 3 to accommodate the boiling slope. All these BCMs have good linearity. Let’s separate them into analog receivers and digital receivers (dropping BCM4B):Analog and digital receivers look similar here. I’m assigninga nonlinearity errorfor all BCMs of 1E-3 (or 0.1%).

28. El Real Trigger Stuff28

29. 29From Carlos’s trigger doc: https://hallcweb.jlab.org/doc-private/ShowDocument?docid=1028El LO-CER2/2Small change of nomenclature to be consistent with Eric P scope shots in the hclog … and sanity.El LO2/3

30. Scaler DT Corrections30

31. EL HIEL LO -CERYesEELHINo1-EELHIYesEELLO*ECERYYEELLOLO*ECER*EELHIYNEELLO*ECER*( 1-EELHI )No1 - EELLO*ECERNY[ 1 - EELLO*ECER ]*EELHINN[ 1 - EELLO*ECER ]*( 1-EELHI ) EElReal (the OR) = anything with at least one “Yes” = EELLO*ECER + [ 1 - EELLO*ECER ]*EELHI EElclean (the AND) = has to be “YesYes” = EELLO*ECER*EELHIElReal (the OR) and ElClean (the AND)31El Real efficiency is ~100% due to redundancy. El Clean is awesomely clean, but is subject to multiple inefficiencies.

32. Explanation:The CER sum pulse had a worrisome, high dark rate of spe’s. It takes ~20ns for a CER spe pulse to drop below the -11mV threshold and re-arm the discriminator. Only then can the discriminator update.Conclusion: Based on the scenarios at right, looks like any DT effects from the high CER sum spe rate will be very small. There is a ~1ns wide corner case at 20ns where the discriminator update might be blocked and the coincidence missed. Another corner case is if some pulses are slightly longer than 20ns. I’m going to set this CER sum DT time constant somewhere in the 0-5 ns range. For the 0-19ns earlier window, the lingering analog pulse from the earlier noise hit will paralyze the discriminator, but the 20ns nominal timing overlap means we still fire the El LO-CER scaler.For the 21-40ns earlier window, the discriminator has time to re-arm, we get a good update, and we still fire the El LO-CER scaler.For the >40ns earlier window, there’s no interference and we fire the El LO-CER scaler.From Eric P’s scope shot in the hclog: yellow is El LO,blue is CER sum. Why El LO-CER DT is So Small

33. Dealing with Hodo 3of4 Randoms33Get a preliminary slope from El Real. It will be a good approximation to the true slope, but it needs an O(0.1)% Hodo 3of4 randoms correction.Get a preliminary slope for Hodo 3of4. It will be batshit crazy, something slightly positive due to several percent randoms. Using your favorite Hodo 3of4 randoms model, which will be data-driven using actual S1X rates, etc, tune this model until the randoms-corrected Hodo 3of4 boiling slope roughly matches the preliminary El Real slope. Now that you have an estimate for the Hodo 3of4 randoms, by logic the same rate of Hodo 3of4 randoms has leaked into El LO LO.Estimate randoms in El LO LO-CER from the product of the CER rate, the random leakage calculated above, and the appropriate time window (2*50ns in my case). By logic, the same rate of El LO LO-CER randoms has leaked into El Real. Correct El Real for randoms. Calculate the new El Real slope and you’re done.(You could iterate this procedure once, but the changes to the El Real slope will be at the O(0.01)% level so not much point.)

34. Just Some Notes34(Pre)TriggerLogic Content Efficiency for giving one scaler count per (pre)trigger (logical true isn’t enough, need a new pulse)Quick estimate which tries to include correlations Predicted DT Slope Contribution for Carbon?commentsEl LO LO2of3{Pr LO, STOF, Hodo 3of4}Proportional to 1- DTELLOLO - DTPRLO*DTH3of41 - DTELLOLO for e or pi.1E4Hz*50ns= -0.05%/100muAGarbage. Has ~5% randoms bkg from H3of4. El LO LO-CER2of2{El LO LO, CER}ECER *( 1- DTELLOLO ) for e or pi if ELOLO = 100%. 1 - DTCER - DTELLOLO for e or pi 1E4Hz*50ns= -0.05%/100muA+5E4Hz*20ns=-0.1%/100muATotal = -0.15%/100muADensity changes cancel in scaler ratios. The ratio El LO-CER/El LO should test the CER DT model but mostly tests the randoms subtraction in El LO . El LO-CER/ElHI lets me test CER DT / CAL DT corrections. El HI3of3{Hodo 3of4, PrHI, ShLO}EH3of4EPrHIEShLO for e (pi’s are excluded)1 - DTH3of4 - DT<PrSh>1E4Hz*200ns=-0.2%/100muAThe ratio ElClean/ElHI lets me test the CER DT model. El Real1of2(El LO LO-CER , EL HI)Proportional to 1 – DTElReal + DTCER*DTELHI1 – DTElReal 1E4Hz*50ns= -0.05%/100muAEl Real trigger DT is small!!! El Clean2of2{El LO LO-CER , EL HI}ECEREH3of4EPrHIEShLO for e (pi’s are excluded) 1 - DTH3of4 - DT<PrSh> - DT<CER> 1E4Hz*200ns=-0.2%/100muA+5E4Hz*20ns=-0.1%/100muATotal = -0.3%/100muAThe ratio ElClean/ElReal lets me test the product of the CER and CAL DT models. The higher level triggers are quite the headache: each needs to be examined for DT sources, then one has to come up with a first order DT correction which does not double-count. The slopes of ratios provide validation (or not). I won’t swear I’m done yet!

35. Discussion on OffsetsTo get highly linear behavior out of the scalers it was important to subtract offsets from EDTM and “cosmics”. The physics trigger rate was only 1.7KHz at the lowest beam current setting on carbon, so one could not ignore 10 Hz of EDTM . When the beam is off, high level electron trigger rates (eg for El Real and El Clean) are ~zero, so these only need EDTM subtraction. Individual detector rates generally need both EDTM and “cosmics” subtraction. 2. Possibly the largest systematic is due to the BCM calibration offset error. (This will contribute in event mode analyses as well.) If several BCM calibrations were averaged, then the weighted average uncertainty on the BCM offset should be ~+-0.05muA . For this lumi dataset, which covered 20-65 muA, the resulting slope uncertainty would have been +-0.35%/100muA. But by adjusting the offset while minimizing residuals (the Christy method), I was able to bound the offset error to 0.025muA +-0.025muA. The contribution of the BCM offset to the uncertainty on the boiling slope was less than +-0.2% . 35

36. Discussion on Noise and RandomsIndeed, some scalers cannot be used due to excess noise and too-large random contamination. But a lot of them work fine:The calorimeter scalers work well presumably because their -15mV to -65mV thresholds rejects soft backgrounds (that’s roughly 30-130 pe’s). I didn’t see any slopes that could be attributed to gain shifts in the calorimeters, but this might change with a much worse pi/e ratio. Scalers for individually discriminated detector channels like Pr LO, Pr HI, and Sh LO have no randoms by definition, but their slopes can be too sensitive to their beam off offsets. ii. The CER was too strange to use. But that’s not too surprising since beam halo scraping upstream of the BCMs can produce spe backgrounds that vary with time (excess noise). And the dark rate offset may have been changing with time and activation (hysteresis). iii. The hodoscopes are also sensitive to soft backgrounds (the paddle rates in these lumi kinematics were 6x higher than the track rates), which is why the hodoscope trigger is formed by multiple coincidences like STOF and Hodo 3of4 and El LO LO. Nevertheless, these scalers still have significant randoms background (~+75%/100muA for STOF and ~+5%/100muA for the latter two) which is either too large or too difficult for me to accurately correct. Higher level electron triggers have very little randoms contamination so can be accurately corrected for this. A logical OR like El Real has non-negligible randoms contamination but higher efficiency than an AND like El Clean. 36At least 6 scalers are useful for precision boiling studies.

37. Other Findings The 1.5% carbon in this dataset was a useful but not a great control. The rates are too low. It is somewhat helpful for understanding the rate-dependent systematics in LH2 (where the rates are 2x higher) but it is a big extrapolation to the LD2 regime (where the rates are 4x higher). Assuming we don’t melt anything, it would be nice to use a thicker carbon target as the control for lumi scans with 10cm liquid targets. A small BCM gain error turns out to be relatively harmless: in lowest order, it cannot create a false slope, but will scale the slope. Since a typical gain error is O(1)%, the uncertainty on a -3%/100muA slope would be +-0.03%/100muA, hence negligible.A simple model suggests the El Real is the most interpretable scaler for lumi work, with very small corrections. While the DT corrections are below 0.1%, the randoms corrections are ~0.1% due to ~5% of H3of 4 randoms bleeding into El LOLO, then leaking into the El LO-CER coincidence due to the high CER sum rate. In the end, to get consistency between the CER-dominated and CAL-dominated (pre)triggers, I used a CAL DT of ~360ns. This is not too crazily larger than what one sees on the scope from the huge, volt-scale pulses. The CAL linear summer chain is surprisingly complicated, so I don’t think its performance can be dead-reckoned at the 0.1% level. Still, the struggle to get agreement between the El Real and El Clean scalers helped me to realize the CER DT correction in El Clean was too large, and that El Real needed some tiny corrections for randoms. 37

38. SummaryScaler rates are attractive for measuring boiling slopes because of their small statistical errors and small corrections. To get highly linear behavior out of the scalers it was often important to subtract offset rates from EDTM and/or cosmics and/or activation. The BCM calibration offset uncertainty is non-negligible systematic. After tweaking the above offsets, it appears that at least 7 scalers can be useful for lumi scans: those with calorimeter-dominated deadtime like Pr LO, Pr HI, Sh LO, El HI ; one with Cerenkov-dominated deadtime, EL LO-CER; one with both calorimeter and Cerenkov deadtime, El Clean; and one with very small deadtime corrections because it is the OR of calorimeter and Cerenkov based pretriggers, El Real . The HMS CER had a light leak when these data were taken. (At a threshold of ~ 0.5pe, the CER sum was firing at 381 kHz.) It’s now fixed, thanks to Chuck. The light leak had consequences, but didn’t hurt us as badly as I initially feared; the high HMS CER rate is not the dominant systematic in this lumi scan. But it meant I had to make some small randoms corrections to El LO-CER and El Real which should not have been necessary. The DT in the CAL sum discriminators is large and not fully understood. This scaler analysis cares because it is the largest correction for CAL-heavy scalers like El HI and EL Clean. An event mode analysis may care becausethese same discriminators presumably drive TDCs which are used to form the time differences cuts and are therefore a source of effective FADC deadtime, andif an insufficient number of EDTM events is taken during a run, then the ELT may have to be modelled. 38

39. backups39

40. Elclean = E_ELLOLO*E_CER*E_ELHIElreal = E_ELLOLO*E_CER + [1 - E_ELLOLO*E_CER]*E_ELHIElclean/elreal = E_ELLOLO*E_CER*E_ELHI ----------------------------------- ~ E_ELLLO*E_CER E_ELLOLO*E_CER + [1 - E_ELLOLO*E_CER]*E_ELHIUsing Scaler Rates and the Model to Probe Efficiencies40

41. 41

42. Using Scaler Rates and the Model to Probe EfficienciesEl Real is an OR. In principle, it should be equal to the input with the higher rate.However, El Real is higher than El LO LO-CER. How to interpret this?This suggests El LO LO-CER missed some good electrons tagged by EL HI. Because the redundant El LO LO trigger is highly efficient, it may be dominated by Cerenkov DT.El Clean is an AND. In principle, it should be equal to the input with lower rate. However, El Clean is lower than El HI. How to interpret this? This confirms El LO LO-CER missed some good electrons tagged by El HI. 42

43. Using Scaler Rates and the Model to Probe EfficienciesDTElReal= (ElReal - El LO LO-CER)/El HI DTElClean = (El HI - El Clean)/El HI = E_ElHI - E_ELLOLO*E_CER*E_ELHI ---------------------------------------------- E_ElHI = 1 – E_ELLO*E_CER = 2.1%= E_ELLOLO*E_CER + ( 1 - E_ELLOLO*E_CER )*E_ELHI - E_ELLOLO*E_CER --------------------------------------------------------------------------------------------- E_ElHI = 1 - E_ELLOLO*E_CER = 2.0%According to the model, these two DT’s should be the same, and are. However, much of the 2% offsetcould be caused, not by rate-dependentmechanisms, but by the CER simply having a smaller acceptance than the hodoscope. 43

44. Trigger Logic VariableConstructed from the Following Trigger or Detector Variables Possible problem in lumi scanPossible problem in absolute measurementsPreSh HI PreSh Hi gain shifts inefficiency due to shower statistics and threshold?EL HI (3/3)Shower LOShower LO gain shifts ? Hodo 3of4Rate dependent deadtimeUncorrected rate dependent deadtime CERRate dependent deadtime Randoms promoting pions into electrons. Uncorrected rate dependent deadtimeEL LO(2/2)PreSH LOPreSH LO PreSh LO gain shifts inefficiency due to shower statistics and threshold?EL LO-LO(2/3)STOF Random coincidences HODO 3of4HODO 3of4Rate dependent deadtimeUncorrected rate dependent deadtimeElreal Trigger Systematics == EL HI .OR. EL LO (Elclean is the .AND.) For a lumi scan, the EL HI pre-trigger looks tighter and less efficient, so I presume EL LO has a slightly higher rate than EL HI. The weakest link in the EL LO trigger is probably the CER, but it also contains Hodo 3of4 . (The Elclean scaler is arguably the worst of all worlds for a lumi scan, being subject to problems in all the detectors: eg, not only the CER systematics in EL LO but also the PreSH HI systematics in EL HI.) 44

45. https://hallcweb.jlab.org/doc-private/ShowDocument?docid=1087Hem Bhatt, target “boiling” study (these are mostly negative. he flips the sign of the slope):45

46. EL-LO-LO -> 3/4 yellow, STOF blue, PR-LO magentaElectrons can satisfy 2of3 with PR LO and 2of4, or with Hodo 3of4 and 2of4. These redundant pathways mean efficiency will be ~100%. But there will be some contamination from hodo randoms in the latter, giving a similar positiveslope to Hodo 3of4. Pions are similar but may sometimes be missing the PR LO signal. Still theHodo path means pion efficiency will also be near 100%.From scaler rates it looks like PR LO was rejecting pions at some level, but effectively this older version of EL LO LO had no PID (just like Hodo 3of4) but It does have more redundancy and therefore higher efficiency. 2of3in{3of4,2of2,PreShLO}=2of3in{3.63 , 4.1, 3.06 KHz}  3.67 KHz(this is 1% higher than the 3of4 rate so this might be an unexpected 3of4 trigger inefficiency)46

47. EL LO-CER -> EL-LO LO yellow, CER blue Because Hem’s lumi scan is above threshold for pi’s, there is no PID enforcement by the CER. However, hodo 3of4 randoms will be mostly suppressed. The CER rate is extremely high which raises the question of DT and residual hodo randoms. Although the discriminator is in principle updating, it can’t update until the analog pulse drops below threshold. 20% of the trigger seeds are lost in going from EL LO LO to EL LO (or EL LO-CER). Which I don’t understand yet. It might be a combination of DT, low pe number for the pions, a delta threshold, K- contamination, etc. 2of2in{EL LO LO, CER} = 2of2in{3.67 KHz , 403 KHz}  3.03 KHzHem’s PID plots go here 47

48. EL-HI -> 3/4 yellow, PrSh-HI blue, Sh-LO magentaEL HI is a stringent triple coincidence which should be electron richand virtually free of randoms. Based on scaler rates, SH LO and PreSh HI thresholds are somewhat suppressing the non-showering pions. 3of3in{3of4,Sh LO, PreSh HI} = 3of3in{3.63, 3.14, 2.81 KHz}  2.45 KHz48

49. From the scope shot at right, the rate of EL LO is significantly higher than that of EL HI. This is reasonable since EL LO LO-CER contains pions and electrons, while EL HI is mostly electrons. 1of2in{EL LO-CER, EL HI} = 1of2in{3.03KHz, 2.45 KHz}  3.08 KHzTo the extent EL HI is a clean electron trigger, this slight increase above the EL LO LO-CER rate suggests that the inefficiency of the EL LO-CER branch is 0.05/2.5 = 2.0% . EL-REAL -> EL LO-CER yellow, EL-HIGH blue49

50. Essentially same plot as before, but this is the AND. 2of2in{EL LO-CER, EL HI} = 2of2in{3.03KHz, 2.45 KHz}  2.40 KHz To the extent EL HI is a clean electron trigger, the slight decrease below the EL HI rate might be another reflection of an inefficiency in the EL LO-CER branch of 0.05/2.45 = 2% . EL-CLEAN -> EL LO -CER yellow, EL-HIGH blue50

51. EL HIEL HI = 3of3in{3of4,Sh LO, PreSh HI}The scalers rates suggest that Sh LO and PreSH LO each suppressup to half the pions. EL HI is clearly an electron-enriched quantity,with high efficiency. 51