| Measurement of σWbb/σWjj |
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M.
Soderberg, S. Miller, D. Gerdes
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Table of Contents
These are the talks scheduled in support of this analysis
These are the CDF notes released
in support of this analysis. Note: We will post an updated note
(v2.0) ASAP.
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.
1.1) 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. 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". 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. 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. 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. 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. 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 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. 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 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). 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. 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. 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. 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.
All questions, comments, suggestions etc. should be directed to Mitch Soderberg. Mitch SoderbergOffice: 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 |