Measurement of σWbbWjj
M. Soderberg, S. Miller, D. Gerdes

Table of Contents

Talks

These are the talks scheduled in support of this analysis

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CDF notes

These are the CDF notes released in support of this analysis.  Note:  We will post an updated note (v2.0) ASAP.


A measurement of the ratio of the detector-level cross-sections of W±bb and W±+ jets in the lepton+jets data sample is described. The method relies on fits of invariant mass to measure the b-fraction of the SECVTX tagged jets. The ratio is determined to be 0.0072±0.0024±0.0022, where the first uncertainty is statistical and the second is systematic.


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Questions/Comments and Answers

Questions regarding this measurement will be answered here. To submit a question, email Mitch Soderberg.  All figures and tables referred to in the questions/answers refer to v1.0 of the note.

  1. General Questions/Comments
  2. SECVTX Mass Template Questions/Comments
  3. Method II Related Questions/Comments
  4. Systematic Uncertainty Questions/Comments

General Questions/Comments:

1.1) Does your estimate of ttbar events depend on HF fractions? - Steve L. and Jaco K.

Yes, in v1.0 of the note we used the measured ttbar cross-section of 8.4pb to estimate ttbar related quantities.  This measured cross-section is dependent on the Method II HF fractions though, so to truly decouple from this we should use the theoretical cross-section of 6.1pb (top mass = 178GeV).  We will make this change in v2.0 of the note.

1.2) Could you show us your fits to the Isol>0.1 region for electrons and muons separately? - Steve L.

Yes.  Electrons(Charm-Only, Charm+Light, Charm+Neg. Tags)  Muons(Charm-Only, Charm+Light, Charm+Neg. Tags).  The b-fraction measured in the muon channel is consistently 10% higher than that of the electron channel.  This is telling us that we should be more careful when estimating the QCD b-fraction.  We should be fitting separately for the electron and muon QCD b-fraction, and applying the respective b-fraction to the tagged QCD event estimates for electrons and muons.  We've updated our estimate of QCD b-jets to reflect this (will put in v2.0 of the note).

1.3) Is the b-fraction in the high-iso region the same as the low-iso region?  Could you show us the Region B fits? - Un-Ki

No, we see that the fit in Region B (Iso<0.1, MET<15GeV) is upwards of 20% lower than in the high-isolation region.  We assign a systematic uncertainty to our estimate of the tagged b-jets from QCD due to this discrepancy (see section 10.1.5 of our note).  The plots for Region B are as follows: Electrons(Charm-Only, Charm+Light, Charm+Neg. Tags)  Muons(Charm-Only, Charm+Light, Charm+Neg. Tags).  Again, it can be seen that the muon channel has a higher (10% or more) b-fraction than the corresponding electron channel.

1.4) Charm tagging efficiency? - Jaco

We assume the same MC/data scale factor as for b-jets but use a larger systematic error for charm jets.

1.5) In your notation, you should replace "W+N jets" with "W+jets" - Jaco

Okay, we can do this.  The "W+N jets" nomenclature was used in section 9 of our note since we were comparing the results for the cross-section ratio in various N-jet bins.  This analysis is a "detector-level" analysis, so there should be no ambiguity about using "N-jet".  In the future, when we measure the physics-level ratio, it would be more confusing to use "W+N jets".

1.6) Can you fit for the charm fraction? - Weiming?

This is a good idea, and one we would like to pursue in the not-to-distant future, but we won't have it done by the blessing talk.  The main issue in doing this would be to determine if we really trust the Mistag component of our fits, since we would need to know this to separate the Charm contribution out of the "non-b" fraction of the data.  Assuming we do trust the Mistag component (which we should, since it is a well studied estimate taken from the data), we then would need to have a method for determing what fraction of the tagged QCD events are from charm. 

We have found that the pseudo-ctau does provide some discrimination between charm and light flavor - but using this requires a careful handling  of the resolution effects for mistags (such as subtracting off the negative tag shape). We have looked at a 2-dimensional fit using SECVTX mass and pseudo-ctau, but won't pursue that until after the
blessing.

1.7) You say there does not appear to be any benefit gained in using the MLM matching scheme.  But how would you decide that based on the plot of Jet ET you have in Figure 2 of your note?  Shouldn't you study how the MLM scheme changes the SECVTX mass to decide if it's worth using or not? - Chris Neu/John Paul Chou

The MLM matching scheme should have more an effect on the Jet ET spectrum than the SECVTX mass.  The MLM matching scheme really tells you nothing about the decay of the hadrons which go into our SECVTX mass shapes.  The MLM scheme could certainly effect the relative numbers of double vs. single HF jets that we have in the MC, but we've tried to show that the SECVTX mass is fairly similar for single vs. double HF jets (more true for bottom than charm) and doesn't change the measured b-fraction by much.  

1.8) What non-b model is used for the "Measured" numbers in Table 7 of your note? - Chris Neu

The "Measured" numbers in this table are the average of the three non-b models we use.

1.9) Did you get 0.386±0.026 for the tag muliplicity factor by summing all the nWbb numbers and dividing by the sum of the NWbb ?  Could you show these numbers for each Wbb+Np sample individually? - Chris Neu/Catalin Ciobanu

     Yes, the 0.386 number comes from adding all the nWbb numbers and dividing by the sum of the NWbb.  The numbers for each individual sample are shown here.  The 1-jet tag multiplicity factors are fairly consistent between samples.  The 2-jet tag multiplicity factors show a trend of decreasing as more partons are added to the events.  There are several explanations for why this trend appears.  In order for a BB+1p or BB+2p sample to end up with 1 or 2 jets, partons have to merge into the same jet, or fall outside of our kinematical acceptance region, or be too soft to be counted as a jet. 
     In the case of events with 1 jet, we see that the tag-multiplicity is fairly constant between samples even though the number of pretag events with one b-jet decreases as more partons are added, indicating that the number of tagged b-jets is falling at the same rate.  In the case of events with 2 jets, the number of pretag events with at least one b-jet increases (though this is more true for muons than electrons) as more partons are added, as does the number of tagged b-jets.  Here however, we see that the tag multiplicity falls as partons are added, indicating that perhaps more of the b-jets in the higher N parton samples contain two b-quarks, or perhaps that more of the b-jets in these 2-jet events are not-taggable.


1.10)  I would suggest removing the "charm only" non-b model from your list of non-b models.  It does nothing but bias your results and inflate your uncertainties, and you know it is not correct anyways. - Catalin Ciobanu/John Paul Chou

This is a good suggestion.  We know we don't really trust the "charm-only" non-b model, and we think we've given good evidence for that (poorer fits to the data in the signal region and in the high-isolation region), but we'll leave it in for the time-being instead of changing our technique so close to the blessing. 

1.11)  When fitting, why do you constrain the light-flavor (or negative tag) shape to the Method II result?  Why not let the light-flavor be fixed to many different values in different fits, and see which one maximizes the KS statistic? - Catalin Ciobanu

The charm and mistag shapes are close enough that we cannot let the mistag fraction float in the fit. Using the Method II mistag fraction gives us a better control of this background. We use a gaussian constraint on the mistag fraction in the fit. In the future, using additional variables we should be able to fit the charm and mistag fractions separately.

1.12)  Are the errors in Table 12 of your note statistical only? - Catalin Ciobanu

These are the HF fractions from the SECVTX ttbar cross-section PRD.  The errors on these HF fractions include systematic uncertainties.

1.13)  Are there other discriminating variables besides SECVTX mass that you could use for this type of analysis? - Catalin

Yes, there are several you could use (pseudo-ctau of the SECVTX tagged jet, "neutral-particle-corrected" SECVTX mass, #tracks in SECVTX tag, etc...), all of which probably have their pros and cons.  We chose the SECVTX mass since there was some history of using at CDF (notes #6538,6675,6865) and the results seem to be somewhat insensitive to what you use for the non-b component of the data (since charm and mistags are similar in their SECVTX mass shapes).  If  we were to use pseudo ctau, for example, it might not be the case that the mistag and charm shapes are so similar and you would have to be more careful about making your templates. 

1.14)  You presume that the Wbb and Wjj efficiencies are equal in equation 1 of your note.  I don't see why that should necessarily be true. - John Paul Chou/Chris Neu/Steve Mrenna/Jason Nielsen

The way equation 1 is explained in version 1.0 of the note is inccorrect.  First of all, it is not necessarily true that the efficiencies for Wbb and Wjj cancel out, and we don't assume they do (contrary to what is written in the note).  We only assume that the luminosity factors cancel out.  We then say that we are going to measure the "observed" numbers of Wbb and Wjj events.  By this we mean that we are not going to model any acceptance/efficiencies, but rather will just say that the observed number of Wbb (Wjj) events is equal to the true number of Wbb (Wjj) events divided by the corresponding efficiency.  So we are then dealing with a ratio of "observed" (or detector-level) cross-sections, which can be written as the observed number of Wbb events divided by the observed number of Wjj events.

Futhermore, we redefine the observed number of Wbb events in terms of the observed number of tagged b-jets in the data, and necessarily introduce a "tag-multiplicity" (not an efficiency, as is written in the note) factor to allow us to go from a number of jets to a number of events.  We define this tag-multiplicity in such a way that our ratio is directly comparable to the Method II HF fractions.  Specifically, we define the tag-multiplicity as the number of tagged b-jets from Wbb divided by the number of Wbb events with an identified b-jet.  The requirement in the denominator of this tag-multiplicity that there be an identified b-jet makes our definition of the cross-section ratio comparable to the Method II HF fractions.

1.15)  Figure 1 is hard to read.  Could you fix this? - Many

Yes, this will be updated in v2.0 of the note. 

1.16)  SECVTX mass plots need coarser binning universally.  - Chris Neu

We'll have to think about this.  This will change the b-fraction slightly (ex. - The b-fraction when using the non-b model of charm+neg. tags is 25.4+4.4-4.1% with a chisq/dof of 29.86/34.   The b-fraction using a binning twice as coarse is 25.6+4.4-4.1% with a chisq/dof of 14.78/18).  One effect of using a binning twice as coarse is that the "peaks" in the charm template of SECVTX mass are smoothed out somewhat.

1.17)  How do you account for jets which may have two vertices (one bottom, one charm), giving rise to the possibility of tagging the charm vertex in a b-jet? - Jason Nielsen

Any jet with a b quark is considered a b jet and so would end up in the b jet template and be counted as a b jet from the fit. We assume the MC models this correctly in making the templates.

1.18)  Please clarify what fraction is given in Table 3 of your note. Is it the jet fraction or the event fraction?  - Jason Nielsen

This is the jet fraction (i.e. - the fraction of tagged jets in our data which come from b decays).

Questions/Comments about SECVTX Mass Templates:

2.1) Do you use only Wcc for double vs. single heavy-flavor jet plots? - Un-Ki

We would allow any sample to contribute to the double and single heavy-flavor plots.  However, it turns out that only the Wcc samples contribute to the double HF charm plot.  The other samples (Wc) have massless charm quarks, and a generator level cut of dR>0.4 between any massless quarks from gluon splitting, so they cannot contribute to our double HF jet plot (which by definiton are jets with two HF quarks within 0.4 of the same jet).  This might be the origin of some of the systematic uncertainty we assign to differences between the single and double HF jet plots (see question 2.2).

2.2) How sensitive are your fits of SECVTX mass if you use only single or double HF jets? - Un-Ki

We studied this by changing the amount that the double HF charm-jets contribute to the overall charm shape.  The double HF bottom-jets are more consistent with their single HF counterparts, which is not the case for charm, so we don't vary the double HF bottom-jet contribution.  We let the number of double HF charm-jets vary from 0 to 2 times the value we use in our final templates.  This variation changes the b-fraction as shown here.  This plot show the resulting b-fraction with the various scaled double HF charm-jet contributions (in these fits, we used the charm+light non-b model).  The b-fraction varies from 27.1% to 24.5% as the double HF charm-jet component is varied from 0 to 2 times its normal contribution.  We will assign an additional systematic uncertainty for this effect in v2.0 of our note.

2.3) In some cases MC is generated with massless HF quarks.  How does this effect your results? - Un-Ki

The MC decays massive hadrons which form the displaced vertices, so there should not be a significant effect on the template. The samples with massless charm will have a different fraction of single to double charm quark jets because of the delta-R between light partons imposed at generation time.

2.4) How much HF contamination is present in your light-quark shape? - Anyes

There should be very little contamination.  Initially, we included u,d,and s quarks and gluons in our light-quark shape, which produced a very long tail in the SECVTX mass due to the fact that some gluons hadronize into charm hadrons.  This drove our b-fraction down noticeably. We then changed our light-quark shape by only allowing jets matched to u, d, and s quarks to contribute.  We vetoed any jets matched to a gluon, or any jets that had already been matched to a bottom or charm quark.  This removed the long tail.  In the next iteration of this analysis, the more correct thing would be to allow gluons to contribute, but to check the parton shower to be sure the gluons don't produce any charm hadrons.

2.5) Why would you combine the templates from each sample with equal weight?  Why not use the normalizations used elsewhere in the
l+jets group to construct weighted templates? - Chris Neu

We initially weighted each template by cross-section/#Events generated for each MC sample, and then combined these weighted samples into the final b,c, and mistag shapes.  We found the final shapes using this method were very similar to the shapes we get by just adding templates from different MC samples with no weighting.

2.6)  What do you mean when you say you combine templates from different MC with "equal weight"? - Catalin Ciobanu

This means that every tagged jet of a given quark flavor is added to the final template for that flavor with no weights applied.  In other words, for example, charm-jets from WenuC1p don't get weighted more/less than charm-jets from Wenu1p other than the fact that the former sample contains many more charm-jets than the latter.

2.7)  Any idea why the KS between WenuBB1p and WunuBB1p is 0.042?  That seems low to me.  - John Paul Chou

There's no definitive explanation for this, but we feel this is not too bad of a discrepancy.  The mean and RMS are quite similar for both distributions.

2.8)  The numbers of Table 2 seem to suggest more of a discrepancy between SECVTX mass shapes of a give quark flavor than you indicate in the text of your note.  Can you address this? Can you really add these shapes together? How you choose the "benchmark" sample?- Many

Some of the samples are quite small so it might be that the MC statistical error is similar in size to the data statistical error. Unless we see a sample that significantly
disagrees with the others or an obvious trend e.g. between Wcc samples and other samples, then we assume for the moment that the samples are okay and that all of our other systematics will dwarf this possible additional systematic.


2.9)  Charm template statistics are low.  Is genereating more MC part of your plan? - Chris Neu

If you're referring to the "peaks" visible in the charm template on Figure 7, we believe these are real (though we haven't gone through the particle shower yet and figured out which hadron decays cause them) and not just statistical fluctuations.  More MC would always be good.  There is a set of WenuCC+Np that would be nice to have, but is missing the HEPG bank we need to do our parton-jet matching.  Other than that, a set of WmunuC+Np would be great, but I don't think it exists yet.

Method II Related Questions/Comments:

3.1) Is your 'tag multiplicity' consistent with Sal's HF tagging efficiencies? - Steve L.

The answer to this is clear in the 1-jet bin.  Our definition should be exactly the same as Sal's.  Looking at his CDF note #7486 he has a (post scale-factor) efficiency for Wbb (1b) of 35.12±2.42 (see Table 11).  In our note, we show that our tag-multiplicity is 33.5±2.2 (post scale-factor, see Table 9).  So these results are quite similar and give us some confidence that we can compare our answers to the Method II predictions.  The comparison would be harder to make in the 2 jet bin, or 1+2 jet bins, where several efficiencies are present (Wbb_1b, Wbb_2b, Wbb_2b double-tag).

3.2) You don't really know if the discrepancy with Method II is 1.3sigma or not, since you haven't properly studied correlations between the two predictions. - Jaco

This is true.  We haven't done a thorough study, taking into account correlations between this method and Method II, so this 1.3 sigma number is certainly suspsect.  We will not show this number in public talks.

3.3) Should I expect the uncertainties in the Wbb prediction to be smaller than those of MethodII, especially with more data?  Would you, a priori, expect that your uncertainties will be smaller than Method II? - Catalin Ciobanu

Hard to say at this point.

3.4)  Could you explain what you mean about the "K-Factor" in section 9.1 of your note? - Chris Neu/Catalin Ciobanu

The K-factor is explained in detail in CDF note #7007.  It is derived by fitting the pseudo-ctau distribution of Jet20 dijet data with shapes for bottom, charm, and mistags and noting that while the shapes of the HF contributions look very similar to the data, their overall normalization is low (by the K-factor of 1.5±0.4).

3.5)  Can I infer that your final result agrees better with the data than Method II, since data were used to obtain it?  - Catalin

At present the errors are too large to make a strong conclusion in comparing our result to Method II. Our systematic error is currently dominated by how well we believe the MC template shape, and the large correction of subtracting off other backgrounds which contribute about half of the b quarks in the sample. The Method II systematic is dominated by how well we believe the LO MC for Wbb and Wjj production.

3.6)  Is there a way (or will there ever be a way) to work your result into a Method II-like table and get better predictions (lower uncertainties)? - Catalin

  That is certainly one of the goals of this measurement. This is the first time this measurement has been done, so it will be possible to improve on this measurement in the future.

3.7)  You mention briefly in the conclusion that the Method II HF fractions for Wc are not calibrated to data.  Is this a source of deviation between your results and Method II?  Would you be able to comment on how much Wc would need to be different? - John Paul Chou

Wc is only based on the MC and depends strongly on our understanding of the strange quark content of the proton. The Wc MC has not been calibrated to dijet data in the same way that Wbb and Wcc has been. See the answer to question 3.9 below for how much Wc could be increased.

3.8)  The method II "2b" category measures the fraction of events with 2 visible HF quark jets.  This is different than your "double HF jets", which contain 2 HF quarks.  So the discussion of section 4.2 of your note cannot be used to measure the Method II HF fractions.  - Jason Nielsen

This is correct.  We are not trying to say that the number of "double HF jets" is the same as the Method II 2b category.   We are trying to study if "single HF jets" and "double HF jets" have consistent SECVTX mass shapes in order to determine if we can add them together or not.  Our fit method will not be able to separate the 1b and 2b categories of Method II (except for in the 1-jet bin, where the 1b category is the only contributer).  This is why we compare our answers to the sum of the 1b and 2b categories in Table 12 of our note.

3.9)  How can this measurement be reconciled with the F_HF fit in CDF-7536, which seems to indicate a larger W+HF contribution, 20% larger than the nominal W+HF fraction calculated with ALPGEN?  I guess you touch on this question in Section 6.2 on page 17, but how much larger would the charm HF fractions have to be in order to account for this apparent discrepancy? - Jason Nielsen

The F_HF fit in CDF-7536 is applied to Wbb, Wcc, Wc and requires a larger value because of the overall underestimate of the Method II prediction and the observed number of tags. It also assumes thatthis correction should be applied equally across all jet bins.
  Doubling the Wcc HF fraction would reduce most of the uncertainty.  Increasing just Wc by 50% would give good agreement in the 1 jet bin, but would still fall short in the 2 jet bin. In the 2 jet bin, the double tag estimate agrees very well with the data which would indicate that the default Wbb HF fraction is correct, although with only 16 events, one cannot preclude a higher Wbb HF fraction.


Systematic Uncertainty Questions/Comments:

4.1) Why is muon-jet bottom SECVTX mass wider than your bottom SECVTX mass? - Joao

 One possibility is that the muon jet vertex likely contains the muon which should have a higher pt rel than the average track in B decays.  As a result, I would expect a somewhat harder vertex mass on average.  We have overlayed the muon-jet and away-jet shapes with our bottom template, to see if the distributions were really different or if it was a trick of the eye due to the different scales of these plots.  The resuls are shown here and here, respectively.   It is in fact true that the muon-jet is wider, while the away-jet looks more like our template.   
   The plots in v1.0 of the note come from a sample in which Tom requires the away jet to have SECVTX mass of at least 1.5 GeV, and in the data the away jet must be tagged.  He didn't require the away jet to be tagged in the MC.  We've redone the fits using an updated sample where both the MC and data must have a tagged away jet, but no cut is made on the SECVTX mass of the away jet.   The average shift (for the three non-b models) in the b-fraction is about 0.4% when we use the muon-jet from this new sample to do our smearing (compared to about 2.6% using the original sample from Tom), and about 2.7% when we use the away-jet to do our smearing. 
    The final systematic we quote for this effect will be unchanged in our updated note.  This is a conservative estimate at worst.  In the future, we'll study this effect more.  We will also take into account correlations between how the number of signal and background b-jets are effected by this effect, which could lessen the effect.

4.2) Do you understand the low-end discrepancy between the muon-jet bottom SECVTX mass and the data? - Taka

The low-end discrepancy in the overlayed plot of the data's muon-jet SECVTX mass and that of the MC is because the non-b component has a low SECVTX mass.  The discrepancy is just showing that there is more non-b in the data shape than the MC shape.

4.3) Could you fit the "away-jet" mass in Tom W.'s muon-jet sample? - Weiming

Yes, we have done this using updated distributions from Tom.  Plots of the "scale-factor" are shown here, and our smeared b-templates are shown here.  The same plots using the "muon-jets" are shown here and here.  See also the answer to 4.1. 

4.4) Is it fair to compare MC/data mass templates?  Wbb has jets with 2B, muon-jet sample doesn't. - Un-Ki

We are comparing a muon jet for both the data and MC. The difference in vertex mass could be related to small differences in tracking efficiency (i.e. more tracks should give a higher average mass). We think this correction can be applied to the Wbb sample.

4.5)  I am suprised that the MC statistics error is so large.  Which non-b model contributes the most to this? - Catalin Ciobanu

Actually the MC statistics error relative to the data statistics isn't so large. We have about 19K events in the charm template, which can be compared to the 690 events in the sample. With a MC statistics error that is 1/4 of the data statistical error, that corresponds to a MC sample that is 16x the data sample.  Most of the power in the fit comes from the region with vertex mass greater than 1.5 GeV, which has a small fraction of the charm template.

4.6)  There are methods to deal with correlated systematic uncertainties.  You should use one in the next iteration of this analysis.  - Catalin Ciobnau

This is a good point.  We know some of the systematic uncertainties are correlated in our ratio (the MET vs. Isolation method is used for QCD estimate in both the numerator and denominator;  uncertainties due to non-b models are present in the number of measured tagged b-jets and the number of background tagged b-jets; etc...).  For now we have treated all uncertainties as uncorrelated.  In the future we will utilize one of the methods you mention.

4.7)  Please explain the Table 4 caption comment regarding an extra 12.5% QCD background systematic.  - Jason Nielsen

We now use a 25% systematic on the tag estimate of the qcd background.  That is included in the number in the table.

4.8) Why is the systemaic uncertainty on the tagged QCD event estimate 12.5%?  Shouldn't it be more like 50%? - Evelyn

   We originally used a 12.5% systematic on the tag estimate to match what was done for the secvtx ttbar prd. We have now increased the systematic to 25% to be more conservative, as the qcd background is more important for this analysis than for the ttbar cross section.
 The cdfnote will be updated accordingly. You can see http://cdfrh0.grid.umich.edu/~miller/talks/nonw.ps for a previous study used to determine the 25% systematic for the pretag sample.



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Contact

All questions, comments, suggestions etc. should be directed to Mitch Soderberg.

   Mitch Soderberg
  Office: B0 Trailer 170-D
  Email: soderber@fnal.gov
  Phone:   630-840-2114

You can also email the full author list.


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April 13, 2005