Updates for version 2.4
***********************

Martin Grunewald <mwg@fnal.gov> (comments on version 2.3)
===============================================================

> mu/jets:

> p.7 Do the ALPGEN W+njets samples overlap with W+n+1 jets in the
> W+n+1 jet phase space? Is that taken into account to avoid double
> counting?

We do not use any matching procedure. We use the W + njets exclusive
Alpgen samples for the n-th exclusive jetbin (n = 1,2,3), and
W+>=4jets sample for the fourth inclusive jetbin. "Jets" should be
read as "light parton" in our MC naming scheme. By using this
primitive pseudo-matching procedure we are not risking any double
counting, but we might be missing parts of the
phase-space. Unfortunately, Alpgen version with built-in matching was
not available at the time our samples were produced.

> p.7 bottom: poisson mu is different: state in text whether this
> explicitely treated later or ignored or included in some systematics

This information is absolete. In this analysis we used samples
generated within D0 Common Alpgen Production which all have 0.4
minimum bias events overlayed.  Both notes are updated.

> p.9 eq.(1) more explanation needed: this is a SF applied to dca? pt?
> q/pt?

This SF is applied to q/pt. Added in the text.

> p.16 discussion: what is the (residual) systematic assigned to this
> discrepancy?

We do not assign any systematic uncertainty since we believe that the
non-perfect modelling of MET (and the W transverse mass) is due to the
way we estimate the QCD contribution for these distributions.

The QCD shape is modeled by using the "loose-tight" data sample (as
described in Section VI, i.e. by using loose preselected events with
an inverted tight muon isolation cut) and the total amount of QCD is
estimated with the Matrix Method, using a single number for epsSignal
and epsQcd. However, as can be seen from Fig. 11 & 12, epsQcd and
epsSignal depend strongly on the muon pT. This is the expected behaviour 
since muon isolation criteria includes muon pT. Therefore a better way to
describe the muon pT distribution is to determine both epsQcd and
epsSignal as a function of the muon pT and apply the Matrix Method bin
by bin. We have used this approach in the *_MMbased.ps plots in the directory:

http://www-clued0.fnal.gov/~gollub/SSR_ANALYSIS/sanity_muoJets/

The shape of the QCD contribution of the muon pT distribution is then
significantly different from the one predicted by the "standard" method
described above. The "loose-tight" sample fails to describe the shape
in case of a strong correlation between the variable under consideration 
and epsSignal or epsQcd.

The muon corrected missing ET (MET) is composed out of the calorimeter
missing ET (JESMET) and a correction due to the muon. As can be seen
on the last pages of the sanity_jb*.ps files, the JESMET distributions
are described rather nicely. Adding the muon degrades the background
description which can however by explained by the failure of
describing the QCD background shape in the muon pT as described
above. Unfortunately we can not parameterize epsQcd as a function of
MET by construction, since a MET<10 GeV sample is used to determine
epsQcd.

In summary: We came to the conclusion that the observed slight
degradation in modeling of muon pT, MET (and therefore also W
transverse mass) is due to the method used to describe the QCD
background and not due to a problem in the MC. We checked that the
likelihood template QCD shape is stable when switching from the
standard loose-tight QCD sample to one determined by using the Matrix
Method bin by bin. This is the only thing that matters for the cross 
section extraction. There is no strong dependence of the likelihood
discriminant on either epsQcd or epsSignal. If we use the Matrix
Method bin by bin on the likelihood template, we fit a cross section
of
* sigma(tt) [pb] = 4.10 +1.85 -1.70 (errors statistical only)
* sigma(tt) [pb] = 4.10 +45% -41%
which is consistent with the result using the "standard" method (3.6
pb as quoted in the note).

> p.25 some errors seem inconsistent: 2nd table Njet=3 line, 4th table
> Njet>=4 line p.26 Njet>=4 line likewise.

We derive the error on the efficiency by sigma(eff) =
    sqrt(eff*(1-eff)/N),
where eff=n/N (i.e. n events pass out of N) and sigma(eff) is the
quoted error on the efficiency. If eff==0 or eff==1, then the error is
0. Of course this is not true, but since we are not too interested in
the efficiency error, we decided that using the simple formula is good
enough here. 

> p.33 - see comments on e/jets note
> (these also apply to mu/jets): - more explanations needed:
> bullet 2: state the transformation used (function, to what range
>  of new values, ...)
> bullet 3: fit range of what? the likelihood?
> last bullet: improve the explanation: what is x and what is i in x_i?
> Eg, x is value of variable i in event j? where is index j?
> Or is x a vector of variables for an event?

Updated the text and made the recommended clarifications regarding the
likelihood formalism and construction. Also added a reference to Mark
Strovink's D0Note 3989 on which the likelihood construction is based.

> p.34: where is sigma_PDF - which is included in the e/jets analysis?

The FoM for the likelihood optimization is given in Eq. 21 on page 36
and includes the sigma_PDF (which is called sigma_Wmod in (21)). 
Eq. 20 is only used to preselect promising variables to be used in the 
final likelihood optimization. In principle it would be a good idea to
include the PDF uncertainty already at this stage.

> p.36 reason to use LLH2 instead of LLH1: drop the reason
> that because the expected error shrinks with number of
> variables, you pick LLH2 instead of LLH1: this argument
> applies only to the average of manny LLHs with the same
> number of variables, but you need to find and use one LLH,
> not an ensemble of several. You have just shown that LLH1
> is the best. So this argument to drop LLH1 and use LLH2
> is invalid - drop it.

We have removed this statement from the text.

> p.46: see e/jets comment on correlations of the same source
> affecting both eps and Nttt
> "correlations taken into account" those are not just different but
> correlated sources of errors (SSR stuff), but I hope also the
> correlation between Nttt and eps due to the same systematic error
> affecting both Nttt and eps?

Yes, when evaluating the influence of a source of uncertainty on the
cross section, we vary at the same time the preselection efficiency
and the number of fitted ttbar events. So the correlation between the
effect on the efficiency and the number of fitted ttbar events is
taken into account.

> p.54 2nd para after eq.(37): add reference to Fig.49.
> Even if Njet=3 is not used: is there some systematic
> to be assigned for propagating this discrepancy in the
> Nj=4 bin?

The reference to the Figure has been added to the text. When looking at the
signal sample (four or more jets, Fig. 57), the feature observed in
the 3rd jetbin is not visible at all. Therefore we are convinced that
the problem is confined to the third exclusive jetbin and we did not
add a systematic uncertainty due to this one distribution. The problem
observed in the 3rd jetbin was also the reason for not including
events with three jets in the signal sample.

> p.54 3rd para after eq.(37): "statistical"

Fixed.

dhiman chakraborty <dhiman@fnal.gov> 
=============================================

Editorial:
---------

> p5: Last sentence before "Method Overview": remove one "both".
Fixed

> p16: d_phi(mu,MET) cut: either "MET[GeV]/50" or "MET/(50 GeV)", not "MET[GeV]/(50 GeV)".
Fixed. Chose MET/(50 GeV).

> p28: "Using Ed. 12 ..." -> "Using Eq. 12 ..."
Fixed.

> "Figure" is sometimes abbreviated to "Fig.", sometimes not.
Changed everything to "Fig."

> p33: Sec VII.A:
> "The likelihood discriminant is build ..." - "The likelihood discriminant is built ..."
Fixed.

> p36: just above Eq. 21
> "build" -> "built".
Fixed.