• Redone analysis with MU and SMT bad runs removed

• Found minor bug in the asymmetry calculation 

• Systematics from fitting procedure

• Removed fiducial cut DL<1.8 cm

• Charge asymmetry (consider tag muon+ and tag muon- separately)

• Other systematics

worsened resolution by factor of 2  :   dM = 0.518724 ; IST eff = 0.730528
improved resolution by factor of 5   :  dM = 0.496095 ; IST eff = 0.725683
increased B lifetime by 10 um :           dM = 0.494735 ; IST eff = 0.725536
set all relative MC efficiencies to 1 :    dM = 0.515511 ; IST eff = 0.730347

the final table with systematic errors now looks as follows

• Simultaneous fit of D0 and D* samples

  Here are the results of the combined (D0+D* samples) fit for opposite 
side muon tagging:

  1) purities for B0 and B+ are different:

FCN = 7.261267

dM = 0.495362 +- 0.0453544
pur0 = 0.74696 +- 0.0239902
pur+ = 0.695649 +- 0.0185146

2) purities for B0 and B+ are the same:

FCN=   9.677110

dM = 0.498221 +- 0.0496028
pur0 = pur+ = 0.715805 +- 0.0131498

• from Vivek Jain
  

thanks for the note (well in advance of the deadline!).
> 
> a couple of quick comments.
> 
> 1) Shouldn't eqns. 6 and 7 be derivable from (4) and (5)? If so, they 
> seem to be backward.

thanks - typo fixed

> 
> 2) You asymmetry is presented as a function of VPDL. But you've taken 
> the K factor into account when you calculate
> A_expected. Shouldn't you be using the K factors for data too?

K-factor is already used for the data by nature, we can't change it.
All we can do is to describe it by introducing K-factor in 
the expected distributions.

• from Christos Leonidopoulos

Technical stuff:

(1) I really don't like the fact that the analysis does not use muon-id
certified muons. I agree 100% with the arguments previously made, that
the way the ID groups work forces everybody to go back and reprocess
their data & redo their analyses. A great inconvenience, to say the
least. We all had to do this at some point. Also, it is not true that
the muon quality definitions were optimized for high-pt physics. The
muon guys have spent considerable time for low-pt folks, like us (they
have asked us for feedback many times, by the way). I did see better
results with the certified muons.

• 
  
• at least two A layer wire hits
• a A layer scintillator hit
• at least three BC layer wire hits
• at least one BC scintillator hit
• a converged local fit (chi2loc>0)

(2) There is no mentioning of systematic effects due to the K-factor
(maybe you are already working on this). My studies show this to be the
most significant contribution. Also, another significant uncertainty
(which I think you are underestimating) is the charged B contribution.
This is NOT the uncertainty that one gets by varying by one sigma the BR
from the PDG book.

(3) The resolution function should be given either analytically or
numerically (e.g. 3 gaussians with relative weights X and Y, sigmas s1,
s2, s2 and means m1. m2, m3). This is not important for the Bd
measurement (as discussed many times before), but it is important for
the methodology. We do this only to prove that we can do Bs mixing.
After all, Bd mixing was discovered in 1985.

(4) I am curious how you feel about the very low chi²/Ndof = 1.7/5. Was
that "massaged"? I also noticed that Sergey in his talk yesterday gives
numbers like chi²/Ndof = 4/12, etc. Where do all these low chi²'s come
from?

(5) Summary/conclusion: A Bd mixing measurement of 0.050 ps^-1 is not a
precise measurement. Precise measurements are done by Belle and Babar
(sigma < 0.010 ps^-1).

well, then let's put it this way - it matches the best CDF single measurement in run 1. so we are doing well for hadron colliders

Ok, now my opinion on how to proceed with the analysis.

You are mentioning in the note something along the lines: we found out
that if we loosen-up our D0/D* cuts, we can gain 50-100% more
statistics. However, keeping the conference deadlines in mind we decided
not to change the cuts at this point.

I could not disagree more with this statement. You quote a statistical
uncertainty of 0.050 ps^-1 by using just soft-muon tagging. Compare this
with:

(a) An uncertainty of 0.033 ps^-1 I got by using soft muons and 0.052
ps^-1 by using jet-charge.
(b) An uncertainty of 0.055 ps^-1 Sergey got by using same-side tagging.

It can't be more obvious to me that our priority should be to get out
there a mixing measurement with three taggers (or three measurements).
Keep in mind that CDF has about 1/4 of our semileptonic statistics with
much worse soft muon AND SST tagging. What could be better for D-Zero
than a mixing machinery that *already* produces numbers better than the
CDF Run-I result by a factor of two? I don't understand why we should
give them the opportunity to think "oh, we suck, but so does D-Zero".

Reg the B+ contribution i did not quite understand what you mean - could you explain?
do you mean sample composition or purity or both or something else?

I meant that there are many things to check to make sure that that the B+- contribution is what one expects it to be, e.g.

- there are different contributions from all the D, D*, D** animals as Jan has been saying (side note: why is Jan NOT working for the B group?
we could use at least his expertise with electrons, if nothing else)

- there could be possible differences in the way the jet algorithm (that defines the totality of the tracks one does analysis with)
could be dealing with tracks from B+/- and B0

I looked at your last Bd mixing talk on the web (the note has, I think, some inconsistencies: more & more data added, but result/uncertainties do not change)

So, you have:
# of D* events: 21'400, soft-muon dilution = 48.6%, efficiency: 4.7%, sigma(Delta m) = 0.049 ps^-1

I have:
# of D* events: 32'500, soft-muon dilution = 50.0%, efficiency: 4.5%, sigma(Delta m) = 0.033 ps^-1

If I do the math, I expect to have sigma_1/sigma_2 = 1.24. Instead, we have sigma_1/sigma_2 = 1.48.

I can think of three explanations:

(1) You overestimate the error (on the event populations for different decay lengths, and therefore, Delta-m). I don't know why that would be,
but low chi²'s point towards that direction.
(2) I underestimate the errors. One thing to check is, what happens if I change the way I determine the # of signal events
(as you pointed out at the meeting last Thursday). This may change not just the # of signal events, but more importantly, the uncertainty of that #.
(3) A combination of the above, and/or a statistical fluctuation. The estimation of the statistical sensitivity by using a set of input parameters
(# of events, tagger efficiency & dilution) works only on average.

Is your number consistent with what Sergey gets for SST? I am not sure how I can get from n_0, n_+ to dilution.

• from Brad Abbot

(4) I am curious how you feel about the very low chi2/Ndof = 1.7/5. Was
> that "massaged"? I also noticed that Sergey in his talk yesterday gives
> numbers like chi2/Ndof = 4/12, etc. Where do all these low chi2's come
> from?

 The probability for  chi2/Ndof = 1.7/5 = 0.8889
 and the probability for chi2/Ndof = 4/12 = 0.983436

 So they aren't too unreasonable.  The probability distribution is
 basically flat so having a probability of 50% is ~ the same as having
 90%.
 

> It can't be more obvious to me that our priority should be to get out
> there a mixing measurement with three taggers (or three measurements).

  We should make 3 independent measurements and them add them
 together to get our final number.  If our error is ~ .02-.03 we
 aren't too far from the best individual measurements.

 Brad

we thank everybody for the comments - we think it will help to improve this analysis!