Slide 1: Used CSC data

• use CSC 5205 AcerMC without duplication problem

Slide 2: Measuring ttbar spin correlation code for these slides

• Measuring method:
  • Atlfast data: distribution of in reconstruction level divide that in parton level to obtain a correction function (pol(n) fit).
  • Full sim data: the distribution in reconstruction level divide the correction function to recover to its parton level.
  • The mean of the recovered distribution multiplying (-9/0.51) is taken as the estimator of the ttbar correlation parameter A
• The expected value of A=0.42 in SM and measured value is 0.82+/-0.16

Slide 3: Why it looks like bias

• Two analysis with the same technique and entirely different samples
  • Analysis 1: "rome" TopRex, full simulation sample 730/pb and early fast simulation high statistics (10/fb?).
  • Analysis 2: "CSC" AcerMC, full simulation sample 220/pb and atlfast1 fast simulation 220/pb.
• The measurement results (only statistical error)
  • Analysis 1: 0.67 +/- 0.10 deviation>
  • Analysis 2: 0.82 +/- 0.16 deviation>
• SAME and LARGE deviation from the expected value on the same side. What does it mean:
  • Bias is introduced due to discrepancy between fast and full simulation
  • In fact, statistical error

Slide 4: Bias comes from full sim electron in crack? NO!

• remove events with electrons reconstructed in calorimeter crack (bad reconstruction) (1.37 < abs(etaele) < 1.52 ), nothing changed for the results
• this is not the reason

Slide 5: Bias comes from error of correction function? looks not.

estimation method	Change for each parameter of the fitted correction function. 5 parametersmany measurements. take as error	reset each bin with randomly gaussian according to its error bar and re-fit the correction histogram. do 5000 times, take as error	Statistical error	Systematic error	total error	exist bias
Previous analysis 1	0.09 plot2	---	0.10	0.08*	0.16	0.22
now analysis 2. Which method is reliable?	0.39 plot1	---	0.19	0.15**	0.45	0.40
	---	0.18 plot3			0.30

Slide 6: Compare correction functions from different samples

• Difference are clear.
  • This difference is considered as one source of the bias.
  • We still don't understand why and what make the difference, except statistics.
    

• As stated below, 2 independent aflfast data give different measurement, here compare their correction functions
  • different bins are used to see the bins effect (code)
  • fast data 2 is the reprocessing of the same fast data, but change random seed.

6bins	7bins	9bins	13bins	19bins	25bins

More fast data are produced, A are deduced from them (same data set, different random seed for b tagging)

• the correction functions:
  

Slide 7: Pure measuring resolution effect on correction function

• Fast simulation: according to measurement resolution, we add a small value to the truth as its reconstructed value
  • We can do many times and make many different correction function.
• The measurement distribution is as blow
  • Take as error: 0.15 (left plot) for analysis2. 0.07 for MCNLO (right plot) means it's smaller with higher statistics,
  • so <<0.07 for Analysis1.
• These error are actually part of error above, can't explain the deviation
  

Slide 8: Evidence 1 for not-bias

• Use MCNLO events, same statistics as "rome" data, the measurement shows no obvious bias.
  

log

Show Hide

open new data...$HOME/analysisResults/forplots_3_jcali_Moore_MCALO_atlfast_btagemulation_jetprecalibration/ANA.ntuple.root
open the 3nd data...$HOME/analysisResults/forplots_3_jcali_Moore_MCALO_btag60_HLT_AODlevelbugfix/ANA.ntuple.root
In CalculateAndSetCorrectionFunction()
 in recons level, events=6104    A=-0.0178893
 in parton level, events=253416  A=0.00158521
Correction function is 1.119092+(0.007044)*x+(-0.004921)*x*x+(-0.000065)*x*x*x+(0.000012)*x*x*x*x
full A:   mean: -0.0238551+/-0.0845253

Slide 9: Evidence 2 for not-bias

• Use the 340 AcerMC events, where fast and full simulation both reconstructed ttbar events correctly (pure signal).
• Plot the difference of between fast and full simulation, the mean is 0.013 that bias doesn't exist in these events. (0.097 for MCNLO 1675 events)
  

• Use the 340 events to repeat the measuring method, got A=0.07. Even larger error from correction function?

Slide 10: Evidence 3 for not-bias

• 220/pb AcerMC full simulation samples is split into 2 parts, according to its event number even or odd.
  • Calculate correction function with events of even event number
  • Apply on the events with event number odd.
• The measured A=-0.84 and 1.10 when exchange the 2 samples . （-0.78 and 1.16 if change correction function bins to 9)

• Although no bias in the samples, the deviation is more than . Do same to MCNLO events, deviation larger than is observed too: 0.296882+/-0.118093 and -0.275076+/-0.115798.
• The correction function is from very low statistics, with large uncertainties around 0.6 and 0.8, which can explain the very large deviation of above. The estimation of the MCNLO sample shows the error are around 0.3 too, to be able to explain the deviation in MCNLO sample.
  

log MCNLO Hide

In CalculateAndSetCorrectionFunction()
 in recons level, events=2523    A=-0.180958
 in parton level, events=253416  A=0.00152187
Correction function is 1.109897+(-0.009322)*x+(-0.004660)*x*x+(0.000038)*x*x*x+(0.000012)*x*x*x*x
full A:   mean: 0.296882+/-0.118093

In CalculateAndSetCorrectionFunction()
 in recons level, events=2534    A=0.0872601
 in parton level, events=253416  A=0.00152187
Correction function is 1.067744+(0.002200)*x+(-0.002326)*x*x+(-0.000007)*x*x*x+(0.000000)*x*x*x*x
full A:   mean: -0.275076+/-0.115798

Slide 11: Cut effect

• We use quality cut to remove non-well-reconstructed events to improve S/B, use cut on ttbar mass to enhance the asymmetry A.
  • There are obvious difference on these quantities between fast and full simulation. Using same quality cut on both will mean different operation
  • As below, the green is the measurement difference between full simulation and fast simulation (correction function from fast simulation), with the same quality cuts, and the blue use specific quality cut for fast and full respectively.
• Specific cuts helps to reduce the deviation.

AcerMC sample and MCNLO sample

Meaning of number

Show Hide

• Measure with different quality cut for fast and full simulation: w and top mass cut around peak value.
• A=0.557148+/-0.176043, But can't believe it so much because the best correction is from cut on leptonic top mass, but actually this is the least difference between fast and full.

Slide 12: Continue with above

• With the same selection and quality cuts on the reconstructed quantities, but this time, use to remove the resolution effect, the discrepancy between full and fast simulation is much smaller, means resolution is part of the reason of the deviation.

AcerMC and MCNLO

• However, we see that
  • The deviation is smaller but still larger than the error bar
  • MCNLO sample: deviation larger than error bar emerges, don't understand! does it mean bias is there introduced by cut and reco procedure effect but is compensated by resolution uncertainty in MCNLO and extended in AcerMC?
• Take 1300 truth value as measured one (removing reconstruction effects) randomly for 45 times to calculate the correction function and applied on the same sample containing 1192 events of truth value (no reco info, too). The resulted 45 times of measurement (left plot) shows a error 0.005. If we try the shift on parameters of correction function, we have 243 times of measurement(right plot), shows a error of 0.35, which is consistent with above: . The question is which error is reliable? For the first error estimation, 0.005, it's clear that bias is from cuts and reconstruction procedure. for the second, the statistics conceal any possible bias in it.
  
• ttbar mass is lower measured in atlfast than full simulation, this makes small bias as 0.07 (farther from truth value). With this cut, we cut 30% of ttbar events, 34%(33%) reconstructed events and 44%(41%) well-reconstructed events for atlfast and full simulation respectively. High-mass ttbar events are easier be reconstructed, may give up this cut.

Slide 13: New method

• From above:
  • We didn't found any clear sign that a bias exist in the measurement
  • We should find out all potential errors which may resuts in this large deviation
• A clear sign is statistical fluctuation, especially on the tail of the distribution, contributes much to the deviation, and may be amplified by correction function obtained from other sample.
• What we learned from the w polarization study is the parameters extracted from fit is not very sensitive to these occasionally happened fluctuations. So we can try to use fit to measure it.
• Look at the ttbar correlation function

• Measurement, * code :
  • The Y axis is scaled with (-4) * bins/2 /0.51 after normalization, because first of all, the last formula above is normalized, second, (-4) is the proportional constant; thirdly, the histogram is divided to bins/2 bins each x-axis unit; last, 1/0.51 is the spin analyzer power.
  • integral , of the hadronic decayed top side: A=0.39+/-0.19. The plots are fast truth, fast reco, fast correction function and full measurement.

• • integral , of the leptonic decayed top side: 0.31+/-0.19. The plots are fast correction function and full measurement.

• • test it with MCNLO sample, we got 0.05+/-0.11 and 0.09+/-0.11 for each side integral.
  • Test the sensitivity to "different physics", correction function from AcerMC is used on MCNLO samples, we got 0.17+/-0.11, exchange the samples we have 0.30/-0.18 , it means when the physics changed, we can get the sign
    

Slide 14: Use fitting method for Ad code

• Although the fitting method works well for A measurement, how doest it work for Ad?
• Ad measurement has been taken as the Mean of 1-D distribution of . now use the fit of the theoretical funcition
  
• We got for AcerMc sample Ad=-0.39+/-0.10 ( Mean method gives -0.45+/-0.10 ), the plot below are fast correction function, full measurement and fast measurement (correct itself). Fitting method works well too.
  
• Try on the MCNLO sample, Ad=-0.11+/-0.06 (Mean method gives -0.07+/-0.05), the plot below are fast correction function, full measurement and fast measurement (correct itself). The Fitting method is even worse, one fact is the fitting method gives fast measurement 0.08+/-0.05, it means that the error from the correction function is large
  

Slide 15: bug found for the new method.

• Bug:
  • The distribution of the above is plotted with and scale factor for both reconstruction and parton levels.
  • But in the correction function application, only is used, other than
• After bug fix. the measurement A=0.66, similar as the exist method. (plot 4)
  • 
• Summary:
  • This method doesn't solve the bias problem, but prove that old method is reliable.
  • The possible reason for bias is explored, see coslep>0 suppressed in full sim.
  • Coshad_lej is slightly affected, so the new method with coshad_lej work better, it is ~0.15 closer to SM value than on coslep.

log Hide

open new data...$HOME/analysisResults/5205_12605_jcali_atlfast/ANA.ntuple.root
open the 3nd data...$HOME/analysisResults/5205_12605_jcali_fullsim_truthHardProc/ANA.ntuple.root
In CalculateAndSetCorrectionFunction()
Correction function is 0.958208+(-0.196741)*x+(0.183672)*x*x+(0.070694)*x*x*x+(-0.159684)*x*x*x*x
the slope is: -0.391749+/-0.0914739
full A:   mean: -0.446723+/-0.0966451
the slope is: -0.263819+/-0.0863646
fast A:   mean: -0.281153+/-0.0906166
Info in <TCanvas::Print>: GIF file AcerMC_fitAd_measurement5.gif has been created

open new data...$HOME/analysisResults/forplots_3_jcali_Moore_MCALO_atlfast_btagemulation_jetprecalibration/ANA.ntuple.root
open the 3nd data...$HOME/analysisResults/forplots_3_jcali_Moore_MCALO_btag60_HLT_AODlevelbugfix/ANA.ntuple.root
In CalculateAndSetCorrectionFunction()
Correction function is 0.975217+(0.039795)*x+(0.051875)*x*x+(-0.176321)*x*x*x+(0.018757)*x*x*x*x
the slope is: -0.108361+/-0.05298
full A:   mean: -0.0732559+/-0.0472294
the slope is: 0.0759533+/-0.0486825
fast A:   mean: -0.00752075+/-0.0432925
Info in <TCanvas::Print>: GIF file MCNLO_fitAd_measurement5.gif has been created

// the old sample which has duplication problem
open new data...$HOME/analysisResults/5205_jcali_atlfast/ANA.ntuple.root
open the 3nd data...$HOME/analysisResults/5205_forplots_3_jcali_Moore_MCALO_btag60_HLT_truthHardProc/ANA.ntuple.root
In CalculateAndSetCorrectionFunction()
Correction function is 0.908255+(-0.257376)*x+(0.423997)*x*x+(0.301705)*x*x*x+(-0.342519)*x*x*x*x
the slope is: -0.330671+/-0.0951342
full A:   mean: -0.337228+/-0.0999412
the slope is: -0.13286+/-0.0882929
fast A:   mean: -0.15723+/-0.0931127
Info in <TCanvas::Print>: GIF file AcerMC_fitAd_measurement5.gif has been created

Slide 16: Atlfast B tagging effect

• The tagging weights for b-jets and other jets in ATLFAST events are randomly set, emulating the (IP3D+SV1) weight distribution in full simulation as a function of the pT and eta. Because of this, ∼70% of the selected ATLFAST events and full simulation events are not identical events, although they are read out from same data sample. They are regarded as independent.
• I re-process once again the data (same data, same program) and produce a new ntuple file. Between this run and old run , they are statistically same if in large scale, now the difference is
  • weight is re-set randomly again to each jet.
  • for individual event, whether it passes n(bjet)>=2 is random.
• So it is same as a new independent atlfast data is built. To repeat the measurement: run log

• Question:
  • the atlfast random b tagging are not fully compatible with the b tagging in full simulation? b-tagging in full simulation correlated with some variables?
  • or only statistically contribute large error? but in previous analysis 1, there were enough statistics.
• Summary
  • Trigger affect the measurement. in t7 notes, trigger is not considered because the effect is much smaller than the bias.
• Btaging in atlfast is random, means all b jets has the same possibility to be tagged, which is not the case for full data. We compare the truth angle coslep, coehad_lej and their product distribution with btag effect. From the table, we see, that the effect is A_mesur ~= 0.42/0.316*0.394 =0.55, which is biased around 0.13.

• red: fast data, and blue full data
  
• with MC@NLO data (CSC 5200). Question: is the bias propertional to the A?
  

Slide 17: Use Correction function extracted from MCNLO full simulation

• In MCNLO events, although there is no spin correlation infomation, the physics and detector effect on the objects are same to AcerMC events and .... all other CSC samples.
  • So in principle, we can use the correction function extracted from MCNLO samples and apply on the AcerMC events.
• Do it without trigger simulation

	SM value	measured value
A	0.42	0.31	0.16
Ad	-0.29	-0.17	0.10

• Do it with trigger simulation

	SM value	measured value
A	0.42	0.29	0.18
Ad	-0.29	-0.12	0.11

• Extract correction function from AcerMC and MCNLO events:
  

Slide 18: weighted distribution

• A is the mean of the distribution of -9/0.51*coslep*coshad_lej. The contribution to A depend both on the value of coslep*coshad_lej and number of events (bin content). So try to weight the bin content with the value of abs(coslep*coshad_lej).
  • AcerMC (red atlfast, blue full sim, left: truth, right: reco)
  • 

• • MCNLO
  • 

Slide 19: Summary and Conclusion

• For sure that cut on ttbar mass make difference between fast and full simulation, but the induced visible bias can't be clearly calculated out because of the low statistics, but expected too small to be responsible for the bias in the analysis.
• In CSC analysis, the bias can be explained by its large uncertainty from correction function.
  • If the error calculated by the method 1 is more reliable (change of the parameters of the correction function)
• In the ROME analysis, we take all possible error 0.09, 0.10, 0.08 from correction function, statistics of full simulation and systematics respectively, which is 0.16 still smaller than the bias 0.25. Concerning the bias induced by cut on ttbar mass, it can be considered as acceptable result.
• The quality cuts are the possible final source of the bias, reconfiguring quality cut for fast and full simulation respectively, we have a acceptable result A=0.55, but it can't be for sure in the low statistics, either now.
• With the new measuring procedure, which is not sensitive to the occasionally happened statistical fluctuation, we have good results until now.
• To do: produce fast simulation data with higher statistics.

Spare Materials Hide

Some discoveries

• ttbar correlation: 0 means flat in cosine distribution of the 2 angles. but combk means flat in angle distribution, so that not flat in cosine plne, but symmetry

Consideration 4 for non-bias

• The signal and the background mix with a fixed ratio in fast and full simulation in AcerMC 73%(576/788) and 74.8%(510/682). But not the same ratio in MCNLO 113.8%(2364./2078) and 105.3% (1883/1788)
• With MCNLO sample, the background effect doesn't make bias. The reason is background (combk and non-ttbar events) doesn't have correlation information and should have the same shape as MCNLO sample, so the different ratio of S/B should not affect
• A similar S/B in AcerMC should not bring effects from background.

Bias on measurement of A code

• As seen, using the correction function obtained in atlfast to apply on full simulation, the measurement on A is biased of around .
• There are 3 type of calculation:
  • dataI, based on truth infomation: no detector and cut effects
  • dataII, based on atlfast measurement: ideal detector and cuts effects
  • dataIII, based on atlfull measurement: realistic detector and cuts effects
• How to understand the bias and what makes the bias.
  • cuts introduced
  • resolution introduced
  • statistics
• Considerations
  • correlation between 2 measurements needs more statistics?
  • other method for measuring?
  • at least using correction function from full simulation for real measurement
  • why effects are larger for product of 2 variables?
  • correlation measurement need how good a resolution? When the resolution is worsen than a limit, the correlation will not be measured? Can I have
  • If a large need a large statistics for precise measurement of A. Can I have have
• Checks and conclusions
  • divide the atlfast data into 2 part. Use the correction function got from part 1 on part 2. Check the bias, if no bias, means not statistical problem; if bias, means statistical problem.

the truth A=0.405,  error 0.03 consistent with SM  (with Mttba<550G)
use data "eventnumber even" to get the correction function and measurement with data "eventnumber odd":
     A=0.48, error 0.23     (change to quality cut specially for atlfast,  A=0.29, error 0.24 )
change the 2 parts of data:
     A=0.43, error 0.22    
means the correction function inside atlfast works well, the bias is not from statisticas only.

• • the same can be done to atlfull

It's fairly bad, before correction, "eventnumber odd" A=-0.01,  "eventnumber even" A=0.51
use data "eventnumber even" to get the correction function and measurement with data "eventnumber odd": 
      A=-0.84, error 0.23
change the 2 parts of data:
      A=1.10 error 0.23 
Means statistical problem in full simulation data.....?
More checks is done to distribution of reconstructed -9/0.51*cos\theta1*cos\theta2 for 2 parts of atlfull data directly without any correction.
The means are -0.02 and 0.51 respectively, error 0.21 for both.
If checks is done to their corresponding truth: 
The means are 0.46 and 0.37 respectively, error are similar.
That means: for the small statistics, .

• • Use dataI , for the truth cuts and atlfast reconstructed cuts, to check whether the resolution bias the cuts much. If yes, change to atlfull reconstructed cuts to see whether larger bias?
  • Artificially put different resolution to truth (dataI), and different statistics, to see whether the correlation disappear without cuts and detector effects? how the angle resolution propogate to the final measurement, and makes needing more statistics. How the resolution bring errors on the final measurement? the resolution may be affect much collaberating with correction function.
  • The correction function from atlfast may bring large uncertainty due to low statistics. The fact is the old correction function is from old atlfast with good statistics, means small uncertainty due to statistics. So the bias should not be from atlfast statistics.
  • The atlfull data may have different composition in least energy jet (different ratio of quarks flavors), so different spin analyzer power , but the fact is there is no effect on Ad, so the effect should be not the reason of the bias.
  • The fact that there is a slope on the ratio between the distribution of full and fast for different data, means the background is not the reason of the bias. but the slope is the reason, what makes the slope?
  • the e event and muon events ratio are different for atlfast and atlfull. As known the e event and muon event have different results(not know why), this may be the reason of the bias. also atlfull has more jets means more combk?

this is not the reason. 
1. we give a weight to e and mu events, to adjust them to the same ratio in atlfast as in atlfull. the measure still gives in atlfull A=0.84.  
2. We have tried to correct efficiency function using the fact that reco efficiency for atlfast and atlfull are different, and the correction doesn't work at all to A.

* atlfull has more jets means more combk? * should use different quality cut for atlfast and atlfull, to decrease the bias, because the event reonstruction (mass distribution) are different for them

Use MCNLO data,

1. which has no ttbar spin correlation, to see the and in 2D histogram, which has 2x2 bins. The results is the bin closed to (-1,-1) has events 45200 and the other 3 bins have 45900 events each.

2. To look at , which is the mean of the distribution, in truth, it gives 0.005.

3. Use the correction function obtained from atlfast in the reconstruction level, the bias is 0.26.

4. If I take the cuts officially defined for T7 note and corresponding correction function, the bias is 0.36. The bias is same as study with AcerMC data.

• MCNLO data (T7CSCnot selection) corrected with AcerMC atlfast corr_func red atlfast:
  

• correction with 2D efficiency::
  

• correction with from 2 angle efficiencies:
  

• efficiencies of the 2 anlges:
  

• 2D efficiency for full and fast:
  

• resoultion effects on distribution of angle 1D:
  

• resoultion effects on distribution of angle 2D:
  

Use AcerMC data:

* AcerMC data (selection T7CSCnote) corrected with it's corr_func from atlfast, red atlfast:

* to look at the ratio of distribution of between full sim data and atlfast data. the data used are 3 types: semiemu; semiemu*goodlnb; semiemu*goodlnb*goodjjb and the distribution of ratios are similar and the bias on measurement of A is even larger. It means the background (tau events and cmbk) is not the reason of the bias.

• • full over fast for costheta1costheta2 for 3 different data : semiemu. semiemu*goodlng, semiemu*goodlnb*goodjjb:
    

• • without quality cut, full over fast for costheta1costheta2 for 3 different data : semiemu. semiemu*goodlng, semiemu*goodlnb*goodjjb::
    
• for truth , the events are reserved only if on the reconstruction level, the event is reconstructed. This is to remove the resolution effect. we see that
  • the bias is very small <0.05
  • if we cut the \|Mwjj-Mw\|<20000, we got bias of 0.15. To change Mw to as measured 80.5 for atlfast and 83.5 for full sim, then the bias is smaller as 0.08. which means the cut result in different events for atlfast ans atlfull, resulting in bias.
  • if we cut the \|Mlnb-Mt\|<35000, we got bias of 0.12. To change Mt as measured 172 for atlfast and 173.3 for atlfull. bias doesn't change.
  • if we cut the \|Mjjb-Mt\|<35000, we got bias of 0.07. To change Mt as measured 172 for atlfast and 177 for atlfull. bias is 0.06
  • if we cut the pt_n/pt_miss>0.99, we got bias of 0.26. if cut pt_n/pt_miss>0.9, bias 0.29, if cut pt_n/pt_miss>0.6, bias 0.03. This cut makes big difference as in the following plot
  • et shrink when reconstructing wln:
    

• cut effect to costheta1*costheta2:
  

• cut effects on costheta1_true*costheta2_true:
  

• correction with 2D efficiency:
  

• correction with from 2 angle efficiencies:
  

• efficiencies of the 2 anlges:
  

• 2D efficiency for full and fast:
  

• resoultion effects on distribution of angle 1D:
  

• resoultion effects on distribution of angle 2D: