WARNING: Those answers were written at the time we received the questions and have not been updated since.

Questions from Pre-Blessing on December 02^nd @ the Top Meeting

During preblessing

1. What is the typical away jet et in bb ?

        In the electron sample it is ~25 GeV(~26GeV)  before(after) SVX tagging. In the muon sample it is 28 GeV(29 GeV) before(after) SVX tagging.

2. Is the number of double svx tag event 10k ? (Jason)

    yes 2233 and 7726 in the electron and muon samples respectively

3. p15: do you determine k from that plot of from w+jets ?  Looks like you have very few event. (Evelyn)    

    yes, it is high ht region C, but we still get a decent uncertainty between this and the extrapolation.

4. Do you have uncertainty for ht in the k factor (Taka)

    yes we move the ht cut by 20GeV.

    we also changed the template between taggable >=3 etc...

5. Any plot for ht dependence of k (Taka)

    yes p 14 (integrated over all jet but dominated by 1 &2 jets bins)

In W+jet it is fairly flat.

6. Which plot do we want blessed. (Evelyn)

    will put the plots on the web page

Questions from Taka 12/02/04

1. Can you make a table for the uncertainties of k factors, k_e and k_{\mu}? I know k_e = 1.4+-0.3 and k_mu = 0.6+-0.4 include
   uncertainties due to (a) fit error from stat, (b) template distibution of taggable tracks, (c) Ht cut itself, but I would to like to know how large each component is. If you already have numbers in CDF note 7381, I missed it.

For the electron case: fit uncertainty: ± 0.2
>>=4 template: ± 0.1
Ht moved by 20 GeV: ±0.2
--> final ± 0.3

For the muon case: fit unc: ±0.4
>>=4 template: ±0.0 (the function is flat)
Ht moved by 20 GeV: ±0.0 (Ht falls more sharply for mu and plateau's earlier)
--> final ± 0.4

Questions from Jason 12/02/04

1. Part of the improvement in the uncertainty comes from improved statistics now that you have shown the tag rate depends on the MET-Track angle and not on jet mutiplicity. How do you know that dependence is the same for all of the jet multiplicity samples.
   
   (answer during the meeting): This plot is Fig. 2 in CDF-7381. Even though the 1- and 2-jet bins are combined in principle, the 1-jet bin doesn't really exist in the Jet 20 sample, so a comparison of 2- and 3-jet is enough.
   

Questions from Taka 12/07/04

I have following questions / comments for CDF note 7381. If possible, can you make inputs on your analysis to me?

1. If you fold the fitted ratio to the dphi distributions, it looks to me that we have more than 1.4+-0.3 as a k_e since you have around 3.8 as meas./pred. around dphi=0, which dominates the taggable dphi distribution. Am I wrong?

    dphi=pi equally dominates the distribution

2. How do you choose the function for fit (in Fig.7)? Choosing the one function, you assume correlation between bins. I think it does not affect the final uncertainty so much, but function selection does not look like a priori.
   

    The function (an exponential) is taken from our model of understanding of the rate vs angle seen in Jet20 (and all generic jets) data, in figures 2 and figure 3.

3. Similar question for Fig.8. You say that you fit the distribution with linear, but I wonder why flat function is not a candidate for electron case. You may have larger uncertainty with  a flat function. 
   

    In the case of the muon channel in fig 8, an exponential fit ends up like a constant

4. CDF note mentioned that you changed +-20GeV for Ht to attach the systematic error. I would like to know this is for fit region changing or/and other effects. This is just to clarify.
   

    It was to check the effect of bin migration across the cut.

5. Jet multiplicity extrapolation includes systematic error, but MET extrapolation doesn't have. I'd like to know how  you combine these two, which might have different quality. 

    Just statistics average

         So, this means that systematic error from MET extrapolation is small enough compared to the Stat. error?

Yes, the stat. uncertainty is larger but mainly the MET extrapolation has less assumptions. There are >=3 TJ events, and Ht>200 already, so it's
purely looking at the trend at lower MET. The Dphi-Met variable has the njet independence assumption (based on the knowledge from jet20 data), and a folding procedure with a fitting function. Those elements we felt needed to be checked for the effect and size of a systematic bias.

6. I still don't understand why you have now only 2.7% uncertainty for non-W prediction while you once had 19% for non-W prediction
   and 13% for non-W fraction. At slide17 of your talk, currently N_{QCD}=1.5+-0.3 (ele) and 0.12+-0.08 (muon) while old one is 1.91+-0.58(ele) and 0.44+-0.23 (muon). It seems that error did not become 1/5. If you can, can you explain?
   

    The mathematical explanation is anti-correlation. The quoted uncertainties on the QCD are anti-correlated with the uncertainty on W+jets.

    Here is how it works: say 85% of data has a fake rate of 1 and 15% has a fake rate 1.2 (20% higher). Now if 15% is measured with an uncertainty of ±5% the uncertainty on the total is not ±5%, but it is: 0.2*5%=1% Where is the catch then ? the catch is in the fact that the reduced uncertainty is only on the sum of the two contributions, not on each separately. If the 15% had a rate ==1 there wouldn't be any uncertainty on the sum at all from the ±5% !, while there would remain ±5% on each separate contribution.
Hence, even though there appear to be no huge improvement in the single estimate of the QCD or the W+j, the procedure is thought such that the sum of the two is known with better precision. The ability to tell how much is W+j
and how much is QCD remained on the same scale.

7. By the way, I don't think smaller number of events in W+1, 2 bin than that of expected is not a serious problem because  control sample does not have to match within 0 sigma between these two.  Instead of that, I guess calculating the probability that two bin  (W+1 and 2 jets bins) has small observed events with 1.2 and 1.3 sigma is good enough.
   

    oh sure, thanks.

Questions from Evelyn 12/07/04

1. Tables and plots to be blessed - you said you would send or post these before the blessing? 
   The plots & tables are here.
   

2. Comment - Interesting that the QCD background was off by 100% before in the 1 and 2 jet bins - eg for 1-jet, the estimate has changed from 21.1 +-9.9 to 46.8+-12.9 events. That now makes QCD about 28% of the tagged events in the 1 and 2 jet region. However, the HT cut removes most of the QCD events in the >=3jet region, eg for >=3jet the estimate has changed from 2.0+-1.2 to 1.6 +- 0.3. Maybe the delta-phi cut between MET and the leading jet could buy you something now in the 1 and 2 jet region!
   
   As promised at the PB, we've re-evaluated the QCD in the 1,2 jet bins. This is described in the revised note, but the gist of it is that the k factor is a very strong function of Ht for low Ht and F_nw has an Ht dependence in 1,2 jets as well. As a result you cannot take the product of their average values when calculating the QCD background. Instead, you have to convolute them as functions of Ht. So we've done this and the agreement is much better in 1,2 jets.
   

3. Question - In Table 7 of note 7120, do the uncertainties on NQCD (last line in electron and muon sections) really include the uncertainty on F_NW, k and the fake rate matrix? Can you put statistical and systematic errors on F_NW in the table so that it is easier to follow the numbers?
   
   For instance, the uncertainty in the 1-jet bin seems too small. In the text, you say you take 35% as the uncertainty on F_NW in electrons in the 1 and 2 jet regions. So, the uncertainty on F_Nw is 5% statistical and 35% systematic. Then, the uncertainty on k_e is 13% and the fake rate matrix is another 10%. So the uncertainty on N_QCD should be 39%, i.e. 42.1 +- 16.4 instead of 42.1 +- 12.5? Sorry if I'm missing something obvious here.
   
   It's a little tricky. There are correlations so you can't just add the fractional uncertainties in quadrature. The uncertainty on the 42.1 works as follows:
   The QCD prediction is k*F_nw*P, where P is the total number of fakes from applying the fake matrix to the taggable events.
   Write this as P*F_nw F_nw*P*(k-1). The uncertainty on the P*F_nw is 10% due to the fake matrix. There is no F_nw uncertainty attached because this is exactly cancelled by the fake+W+HF prediction (which is (1-F_nw)*P). The uncertainty on the second term is the quadrature sum of the uncertainties on F_nw, P and k. But it applies only to the excess (that is "k-1") part of the total background.
   

4. Question - Is figure 6 in note 7381 for all W+jet events? Can you split it up into different jet multiplicities?
   The new Fig 7 has already nj=1 and nj=2 separately. I don't think there is enough in >=3 to make much Ht dependence, but we'll try.

5. Question - Section 4.1 of note 7381 says that you extrapolate from low to high jet multiplicity in region C. But with HT>200 GeV required, do you really have any 1 or 2 jet events left? You have very poor statistics for the plot in the upper left-hand corner of figure 7, with some bins having 0 entries.

Yes, there are 1 and 2 jet events left, in fact most of them are 2TJ. In the electron ch. there are 1 in 1TJ, 8 in 2TJ and 3 in >=3TJ. In the muon ch. there are 0 in 1TJ, 3 in 2TJ and 1 in >=3TJ . As for the zero entries bins, they have 0 tags but about 1-2 predicted, so they do contain useful information for the fit.

6. Comment - The difference in tag rate for the QCD background between low and high HT makes me wonder about the relevance of the 1 and 2 jet events as a control region. Is there something else one could do, like compare data/MC for different jet ET thresholds, that would allow extrapolation from the 1 and 2 jet region towards the signal region? I suspect at low HT, the QCD events are dominated by jets in cracks and real b-decays, whereas at high HT, the events are dominated by the energy resolution.
   
   We have resolved this with the convolution procedure mentioned above. Albeit at the cost of a fairly large uncertainty.