Evidence for production of single top quarks
and first direct measurement of |V_tb| at DØ

Fall 2006

Frequently asked questions

1. In the ME method, why don't you use the ttbar ME and why not use a NLO ME for everything?
   We don't use ttbar in our discriminants. This does not mean that our discriminants are wrong, but just that they are not as effective as they could be. You can see this mostly in the ME output for the events in the 3rd jet bin, where a lot of ttbar events end up in the high discriminant region. The main reasons for not including some diagrams are that the theoretical calculations do not exist, or that they require too much computing power while doing the integrations. We are working on including ttbar for the next round of the analysis.
   As regards the shapes from NLO vs LO, the difference is not large, it's more of an overall normalization difference.
2. Why don't you use the latest world average m_top=171.4±2.1 GeV? And how big is the error on your ttbar yield?
   We use m_t=175 GeV throughout this analysis, because the MC was generated before this new world average was made. It also takes a long time to generate and reconstruct the MC events. A top mass of 171 GeV would affect three things:
   
   a) The ttbar cross section would be higher. When we calculate the ttbar yields, we apply an 18% relative error on the ttbar cross section, which includes the theoretical uncertainties as well as the uncertainty on the 175 top mass. That 18% error covers the shift in cross section from 175 to 171 GeV (see numbers below).
   
   b) The single top production would change. We looked at the kinematic distributions of single top events at parton level with a top mass of 170 GeV and the only noticeable difference appeared in the pT of the forward b-jet in the t-channel. This jet is very rarely reconstructed anyway.
   
   c) The kinematic distributions of ttbar samples would be slightly more similar to the W+jets ones. Since the single top kinematics are usually somewhere between the two, there would be slightly less discrimination.
   
   For reference:
   What we use with 175GeV σ(tb): 0.9±0.1pb; σ(tqb): 2.0±0.3; σ(ttbar): 6.8±1.2pb
   New values with 171GeV σ(tb): 0.93pb; σ(tqb): 2.05pb; σ(ttbar): 7.6±0.9pb
   
3. How can you be sure you got the normalization of ttbar right?
   We measure the cross section and mass well enough that our systematic errors will cover any differences. If the shape was significantly different then DØ would not be able to correctly measure the mass.
4. How is c-tagging done and how big is the error?
   We do not have a c-tagger like CDF does. We use both data and MC to measure the tag rate functions for the probability to tag (identify as a b-jet) a charm jet. The TRFs are determined as functions of jet pT and |eta|. The relation used is:
   
   Probability to tag a charm jet =
mu-b-jet efficiency (measured in mu+jet data) *
inclusive-b-jet/mu-b-jet efficiency (measured in MC) *
inclusive-c-jet/inclusive-b-jet efficiency (measured in MC)
   
   In this method, the differences in the shape between b- and c-jets are accounted for as the procedure is used bin-by-bin in pT and eta.
   The c-tagging efficiency is around 10% for central energetic jets.
   
5. How can boosting be more sensitive if the DT outputs are more central for both signal and backgrounds than peaked towards 0 and 1, as is the case with no boosting?
   We will provide a plot of the efficiency for signal vs efficiency for background for different DT outputs when using boosting and no boosting. You can see there that boosting is actually more sensitive.
6. How valid is it to assume |V_tb| is not 1 for production but it is for the decay?
   When deriving |V_tb| we have assumed the following:
   a) No FCNC interactions, or heavy scalar or vector bosons are present: the only production is through a SM W boson.
   
   b) The tbW interaction is CP-conserving and of the V-A type, but it is allowed to have anomalous strength.
   
   c) |V_td|²+|V_ts|² << |V_tb|². This is a very reasonable assumption supported by the direct measurements of |V_td| and |V_ts| (=~ 0.01) and the model independent measurements of R by CDF and D0. This is the assumption that top will decay ~100% of the times to Wb.
   
   The important quantity for the decay is R=|V_tb|²/(|V_td|²+|V_ts|²+|V_tb|²), which is very close to one in all cases: even if there was a 4th generation (and |V_tb| was significantly smaller than 1), the decay would still proceed to tb, but the production would be altered.
7. The fact that you model the low discriminant region well does not mean you understand your backgrounds.
   Indeed, and we have used two cross check samples to make sure our two main backgrounds are well described in the high discriminant region, by selecting events with "soft" W+jets (below our signal in HT) and "hard" W+jets (above our signal in HT). That is: one sample enriched in W+jets and the other in W+jets and ttbar. And there the agreement is also good in the high discriminant region.
8. How can you trust your W+jets modeling? OR You use Alpgen, a leading order MC, to simulate the shapes of W+jets, how big is the NLO k-factor and how does it affect the shape?
   We have looked at many many variables before and after b-tagging and compared the MC prediction with data, and there is a fair description throughout. The variables that are fed to the DT and BNN are specially looked at for any major discrepancies.
   We know the k-factor (NLO/LO ratio) has a kinematic dependence on the jet pTs and the invariant dijet mass in W+jj. But with two flat normalizations: one to normalize the overall W+jets yield to the data before tagging, and another to set the content of Wbb and Wcc in the W+jets yield, we see an adequate description of all the shapes in the data-MC comparisons. And we have checked this in all our discriminating variables before tagging, after tagging, in our cross check samples (W+jets and ttbar enriched), and in the discriminants outputs.

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