Comments/Responses on PRL
"B -> D** mu nu X"

2/15/2005
answering two more questions from Alice:

1)  Discussion on the available experimental information:
from hep-ex/0112028 "Combined results on b-hadron production rates and decay properties"
this is to give more background information on the previous individual measurements of Br and R (called R** below).



Observations: the CLEO data is in fact the upper limit and does not give meaningful measurement of R**.
For DELPHI R**=0.64+-0.41. ALEPH did not quote Br for D*2 in the original paper only upper limits.
thus it's contributions from ALEPH and CLEO (which are in fact only upper limits) that lower the current
estimate of R** to 0.37+-0.14. i am not sure i agree with this approach but anyway that's what people currently use.

another interesting piece : from Belle's paper hep-ex/0307021 - this explores the B->D**pi   decay modes (and not semileptonic modes as we do) .
however they have some useful comments on H (we currently use the estimate of H from hep-ex/0112028 : 71+-7%).


2) how the fact that the inclusive Br is measured influence the result on R?

we indeed neglect the dipion modes of decay for D** and assume that the D(*)pi modes saturate the D** decays. 
this does not affect interpretation of the Br mesurement but for the estimate of the ratio R this implies that we assume
that the B->D** munu decay is exclusive. this assumption was used by LEP experiments and it is supported by
the DELPHI result which was shown closer to the bottom of this page.

2/6/2005
back to fitting : here are the fits, numbers and systematic errors for 

Belle parameters, chi2 of the fit 46.28/46


N(2420) = 514.733 +/- 43.4245 (8.43631%)
w1 systematics : -52.5453 ( -10.2083 %) 53.7897 ( 10.45 %)
w2 systematics : -3.6791 ( -0.714759 %) 4.99449 ( 0.970306 %)
dm systematics : -20.2661 ( -3.9372 %) 16.6185 ( 3.22858 %)
sigma systemcs : -22.3901 ( -4.34984 %) 24.1417 ( 4.69014 %)
total systemcs : -60.7171 ( 11.7959 %) 61.4595 ( 11.9401 %)
N(2460) = 192.737 +/- 49.2999 (25.5789%)
w1 systematics : -37.239 ( -19.3212 %) 38.1987 ( 19.8191 %)
w2 systematics : -15.8694 ( -8.23374 %) 12.4726 ( 6.47134 %)
dm systematics : -16.371 ( -8.49394 %) 19.6407 ( 10.1904 %)
sigma systemcs : -18.963 ( -9.83879 %) 16.0804 ( 8.34318 %)
total systemcs : -47.6045 ( 24.6992 %) 47.5294 ( 24.6603 %)
N(2420)+N(2460) = 707.47 +/- 59.7276 (8.44242%)
w1 systematics : -14.3445 ( -2.02757 %) 16.5456 ( 2.33871 %)
w2 systematics : -13.507 ( -1.9092 %) 12.7063 ( 1.79601 %)
dm systematics : -1.54076 ( -0.217785 %) 1.00573 ( 0.142159 %)
sigma systemcs : -6.3016 ( -0.890724 %) 5.21042 ( 0.736487 %)
total systemcs : -20.7434 ( 2.93205 %) 21.526 ( 3.04267 %)
N(2460)/N(2420) = 0.37444 +/- 0.100852 (26.9342%)
w1 systematics : -0.100928 ( -26.9544 %) 0.125217 ( 33.4411 %)
w2 systematics : -0.0341325 ( -9.1156 %) 0.0271013 ( 7.23783 %)
dm systematics : -0.042521 ( -11.3559 %) 0.0550677 ( 14.7067 %)
si systematics : -0.0519649 ( -13.878 %) 0.0496892 ( 13.2703 %)
total systemcs : -0.125936 ( 33.6332 %) 0.148038 ( 39.5358 %)

PDG parameters , chi2 of the fit 46.89/46

N(2420) = 467.216 +/- 38.9868 (8.3445%)
w1 systematics : -37.419 ( -8.00894 %) 49.9893 ( 10.6994 %)
w2 systematics : -6.20293 ( -1.32764 %) 7.65924 ( 1.63934 %)
dm systematics : -13.4835 ( -2.88592 %) 11.9909 ( 2.56646 %)
sigma systemcs : -19.2428 ( -4.11861 %) 19.9182 ( 4.26317 %)
total systemcs : -44.6178 ( 9.54972 %) 55.6607 ( 11.9133 %)
N(2460) = 176.392 +/- 37.1593 (21.0664%)
w1 systematics : -28.2629 ( -16.0228 %) 22.09 ( 12.5232 %)
w2 systematics : -20.3856 ( -11.557 %) 18.3753 ( 10.4173 %)
dm systematics : -9.75269 ( -5.52899 %) 10.4084 ( 5.9007 %)
sigma systemcs : -8.07395 ( -4.57728 %) 5.67724 ( 3.21854 %)
total systemcs : -37.0766 ( 21.0194 %) 31.0835 ( 17.6218 %)
N(2420)+N(2460) = 643.606 +/- 37.6465 (5.84931%)
w1 systematics : -15.329 ( -2.38174 %) 21.7282 ( 3.37602 %)
w2 systematics : -12.7435 ( -1.98002 %) 12.6446 ( 1.96464 %)
dm systematics : -3.57022 ( -0.554722 %) 2.67975 ( 0.416365 %)
sigma systemcs : -13.5622 ( -2.10722 %) 11.8432 ( 1.84014 %)
total systemcs : -24.3732 ( 3.78698 %) 27.9185 ( 4.33783 %)
N(2460)/N(2420) = 0.377538 +/- 0.0855458 (22.6588%)
w1 systematics : -0.0911357 ( -24.1394 %) 0.0842656 ( 22.3197 %)
w2 systematics : -0.0490178 ( -12.9835 %) 0.0449383 ( 11.903 %)
dm systematics : -0.0297987 ( -7.89288 %) 0.0341587 ( 9.04774 %)
si systematics : -0.0320114 ( -8.47898 %) 0.0288904 ( 7.65232 %)
total systemcs : -0.112344 ( 29.7569 %) 0.105459 ( 27.9333 %)

Observations :
- both fits are ok
- systematics errors for the ratio (which is the most interesting parameter for the theory) are smaller when PDG values are used.
the reason is smaller errors on w1 (width of D(2420)).

remaining questions from EB :
  - effects of the 6MeV mass shift on the formfactors will be investigated

this could be important for calculation of k used in the formfactor (see eq.5 in the d0note 4324). shifted the mass variable by 6 Mev
(which overestimates the effect because k is estimated in the D** rest frame and at the resonance when m = M D** is at rest and the wrong momentum scale is not relevant). The Br and ratio numbers changed by less than 1%. Conclude this is a small effect.

  - inconsistencies in the parameter r values from different fit
approaches will also be investigated. Alan has pointed to a 6% difference

Parameter r was defined before normalizations and integration of signals so as defined it does not need to be equal to the ratio of events in two peaks. Since this parameter is not used in the analysis (eq. 11 has been corrected) the discrepancy is no issue.

1/30/2005
- implemented  weighting when for final selections subtract averaged lower [2.25-2.35] and higher [2.55-2.65] sidebands from the signal region [2.35-2.55] for the data (rows 2c, 5a in the table). this approach gives somewhat harder pt spectrum for everything but the statistics in the data is low.. in any event the efficiency and resolutions do not differ much. it was proposed that this weighting should be used as central value for the analysis.
- thus, i will use resolutions 8.2 Mev for D1 and 9.4 for D*2. Ratios of 2nd-to-1st gaussians widths and the fraction of the 1st Gaussian will be taken from MC
- here is the new fit of data
 fit version 6.0

1/23/2005

- re the difference between method a) and b) : it appears that the difference in mass resolution between the two methods can be explained by too coarse binning used for method b). initially the bin size was 10 Mev which is larger than the resolution so the resolution was overestimated.  when the bin width is decreased the fitted resolution goes down (rows 1, 1a, 1b in the table below). with adequate binning the resolution from method a) and method b) agree within errors.

- tryed several weighting options, see the table below, rows 2, 2a, 2b. Among others tryed weighting obtained taking into account side bands of D** signal in data. For final selections (so D** signal is obvious in the data) subtracted pt(D meson) distribution in a side band (2.55-2.75 Gev) from the pt(D meson) distribution in the signal region (2.35 -2.55 Gev).

- the observed variation of resolution  [6.7 - 7.5 Mev] is covered by the assigned 20% systematic error
- the observed variation of efficiency [45.4 - 47.1 %] can be converted to a systematic error ~ 1.5% which should be added to the statistical error.

1/18/2005 

Mass resolution and MC scaling

at the last meeting we decided to use two Gaussians to describe the mass resolution. Implementing the smearing of BW with two Gaussians i found a bug in the way the smearing was done for one Gaussian (effectively  a flat distribution was used instead of a gaussian) - this bug has been fixed. In addition the fitting of the resolution histogram is done now using the likelihood option in Minuit (i.e. "L" in root) and the means of two gaussians in method a) were fixed at 0. Thus the resolution numbers all changed - the most significantly because of the bug fix.            

table with resolution/efficiency for different cases of MC



efficiency, %
method a) sigma 1, MeV
method a) sigma 2, MeV
method a) fraction
method b) sigma
comments
1
D1, weighting 1
46.8 +- 1.1
7.1 +- 0.5
16.7 +- 1.8
0.77 +- 0.08
9.2 +- 0.8
b) sigma ratio 2.4; fraction 0.77
1a
D1, weighting 1

7.2 +- 0.5
17.1 +- 1.8
0.80 +- 0.06
8.2 +- 0.7
same but finer binning of mass/resolution histos 60->120
1b
D1, weighting 1

7.2 +- 0.5
17.1 +- 1.9
0.81 +- 0.06
8.0 +- 0.8
same but finer binning of mass/resolution histos 60->180
2
D1, weighting 2
46.5 +- 1.1
7.1 +- 0.5
16.7 +- 1.8
0.78 +- 0.07
9.3 +- 0.8
b) sigma ratio 2.5; fraction 0.8
2a
D1, weighting 3
47.1 +- 1.2
7.5 +- 0.4
19.3 +- 2.7
0.88 +- 0.05
9.1 +- 0.8
b) sigma ratio 2.6; fraction 0.88
2b
D1, weighting 4
45.4 +- 1.6
6.7 +- 0.9
12.6 + -2.4
0.73 +- 0.20
8.5 +-  0.7
b) sigma ratio 2.0; fraction 0.73
2c
D1, weighting 5
47.7 +-1.0
6.8 +- 0.4
16.4 +- 1.2
0.72 +- 0.06
7.5 +- 0.7
b) sigma ratio 2.4; fraction 0.72
3
D1, no weighting
44.0 +- 1.1
7.8 +- 0.4
23 +- 3
0.90 +- 0.04
9.2 +- 0.8
b) sigma ratio 2.5; fraction 0.8
4
D*2, weighting 1
45.7 +- 1.4
8.7 +- 0.5
23 +- 4
0.91 +- 0.05
10.4 +- 1.1
b) sigma ratio 2.6; fraction 0.9
5
D*2, weighting 1

7.9 +- 0.4
17.9 +- 1.2
0.77 fixed
9.7 +- 1.0
b) sigma ratio 2.4; fraction 0.77
5a
D*2, weighting 5
45.9 +- 1.2
7.8 +- 0.4
17.4 +- 1.0
0.72 fixed
9.4 +- 0.8
b) sigma ratio 2.2; fraction 0.72
6
D*2, no weighting
44.9 +- 1.3
9.1 +- 0.4
38 +- 11
0.94 +- 0.02
9.0 +- 1.1
b) sigma ratio 2.5 ; fraction 0.8
7
D*2, no weighting

7.9 +- 0.3
21.1 +- 1.4
0.77 fixed


 
Weighting :
- use the weighting obtained from the pt distributions of D meson as shown below. "Weighting 1" vs "weighting 2" is different in describing of the first bin which is considerably higher than the polynomial fit (row 1 vs 2) - makes little difference.
- Weighting 3 :  apply final D** selections in data and MC to get the weighting function.
- Weighting 4 : same as weighting 3 but for data subtract the distribution for the side band from the distribution obtained for the signal region.
- Weighting 5 : same as weighting 4 but the upper [2.25-2.35] and lower [2.55-2.65] sidebands are used for subtraction

Observations :
1) resolution for D1 and D*2 compares ok (row 1 vs 5) if the fraction of the second Gaussian for D*2  is fixed at 0.77 (determined from D1). Then the mass resolution is different by ~10% between D1 and D*2 as expected. if the fraction is not fixed (row 1 vs 4) then the first gaussian for D*2 is wider but covers larger fraction of events.
2)  methods a) and b) are still different. one needs to fix the second gaussian width and the fraction for this fit to have sensible results - i used parameters from method a) to do so. changing the binning (rows 1a, 1b) makes difference for method b) so i presume that the fit is not very stable since the BW width and Gaussian width are strongly correlated. Results of method a) are stable wrt binning.

Proposal : use resolution from method a) , scale it up by 20% to account for difference data/MC. 20% is the same as difference data/MC for D* - more i think about it more i like this option since it is simple to describe and justify.

thus use
sigma1  D1 = 8.6 Mev, ratio sigma2/sigma1 = 2.4, fraction sigma1 = 0.77
sigma D*2 =  9.5 Mev, ratio sigma2/sigma1 = 2.3, fraction sigma1 = 0.77

data fit with the above parameters (all 6 of them are fixed) :  
 

the Br and Br ratio did not change much. 

12/16/2004 EB023 meeting : remaining issues

  - MC weighting

      * Andrei claimed that weighting MC events changes the MC effic by approx. 10%

relative change of efficiency is 5.4% (weighting ON gives larger eff)

      * He will change the fit in Fig.7 to a 2-nd order polynomial and
will show uncertainties for individual points (editorial request from Brigitte)
      * Andrei will provide data-MC comparison of various kinematic
distributions for pi**, D0 etc

ok, here they are - will be updated in the note. 
parametrizing the dependence with 2nd order polynomial.

Comparison of the kinematic variables before/after weighting.
The ratio of muon pt spectra in data and MC (plot labelled ptle) was used for the weighting.
take good D* candidates after mass cuts but before additional lifetime cuts. the color coding
of histograms is: blue = data, red = MC before weighting, green = MC after weighting



as can be seen the weighting based on the muon pt does not really do the job for other than muon tracks.
apparently the muon pt is not strongly correlated with the D(*) meson.

tryed to normalize to the pt of D meson.  this does better job for the D system.  Note that only pi** is relevant for the
relative efficiency calculation. however other products may enter the mass resolution so they are also important.
Signal efficiency changes by <1% if compared to weighting using muon pt.

.

 - MC vs data efficiencies

     * efficiency of the cuts on hit number N(SMT), N(CFT) will be
established from the data using mass fits with and without these requirements

Response : used D* sample to estimate the efficiency in the data and compare it to MC.
The slow pion was used as a source of tracks close in properties to pi** from D**.
Removed nCFT>5 and nSMT>1 cuts on the slow pion and determined the following efficiencies


selection
eff  data, %
rel. eff, %
eff MC, %
rel. eff, %
D* cuts  
100
-
100
-
D* cuts && nCFT>1
97.6
97.6
96.6
96.6
D* cuts && nCFT>1 && nSMT>1
95.0
97.3
96.0
99.4
D* cuts && nCFT>5 && nSMT>1 
93.2
98.1
94.1
98.0





as one can see data and MC are  different by (94.1-93.2)/94.1 = 0.0096 (i.e ~1%). 
this correction will be used
to scale down the total signal efficiency

     * sensitivity of the efficiency ratio (Eq(7))  to some scaling
factors will be established, in particular the contribution from the
significance cut with respect to the PV for pi** (expected to be small,
based on previous studies)

The ratio of IP significances (wrt primary and secondary vertices) is used as selection
in the analysis.
Thus, scaling them simultaneously will cancel out with good precision.

Scaling IP (wrt secondary vertex) error only (and thus grossly overestimating the effect) :
IP error scaling factor +20% : relative eff change - 5.2%
+40% : -13.9%

  - mass resolution of 6.5 MeV (from MCarlo) or larger (by 30% as AZ suggested)

        * fits to the data with 8.5 MeV look visibly worse, however
the change in chisq is only 43-->46 (see Andrei's new plots)

fits for mass resolution 8.5 MeV +- 30%. we think this overestimates the mass resolution, see reasoning
below why the mass resolution is better than 8.5 MeV.
8.5 MeV
8.5 MeV + 30%
8.5 MeV - 30%
D1 width free, D*2 width 6.5 MeV


        * Rick suggested to establish the data-MC difference in the
mass resolution by using the psi(2S)-->J/psi pipi channel with the
J/psi mass constraint. The experience from the X(3872)
paper indicates that the difference is smaler than 30%.


a) psi(2S) -> J/psi pipi comparison has been done by Brad and Co. (X(3872) analysis)

Width
MC 8.9 MeV
Data 10.4 MeV

difference in mass resolution 14.4%

b) B+ -> J/psi K+ comparison by Ralph (Bs -> mumu analysis)
Mass Width
MC 5.279 GeV 37 MeV
Data 5.273 GeV 41 MeV

difference in mass resolution 9.8%

we think that the case b) is more adequate for the D** case since there is one track (K+) and
the J/psi mass is used as constraint. Therefore we propose to scale the mass resolution by +10% and vary it
+-10% from this value for the systematic error estimate.

        * Andrei reported that some other methods to extract this
number from MC indicated that the MC  resolution could be actually better, as good as 5 MeV

mass resolution has been estracted from MC using two methods
a) plot (reconstructed mass - generated mass), fit with Gauss
b) plot reconstructed mass, fit with Breit-Wigner convoluted with Gauss. Sigma of Gaussian is a fit parameter.
Width of BW is fixed to the generated value.

the results are (they have changed compared to the note4324 v3.2 because i found that i did not scale the histogram
errors together with contents. so the errors changed, the fits changed and the agreement between two methods
is better now)

method D1(2420) D*2(2460)
a) 5.7 Mev 6.5 Mev
b) 5.1 Mev 5.5 Mev


another set of numbers for the weighting based on the D meson pt
method D1(2420) D*2(2460)
a) 5.4 Mev 7.0 Mev
b) 5.0 Mev 6.4 Mev


in principle the two methods should give the same results but some discrepancy is observed.
the discrepancy is not fully understood though now it almost within errors.
we propose to average two methods and use the difference
between these two estimates
as additional systematic error on the resolution. then and also taking
into account scaling by 10% from data/MC comparison
we have

D1(2420) D*2(2460)
resolution 5.9 MeV 6.6 MeV
for ptD weight 5.7 Mev 7.4 MeV (assigned +-20% error covers this difference)

we propose to vary the resolution by 20% (as currently in the note) to estimate the associated systematic error.
this variation should still cover the uncertainty on the difference between a) and b) and the uncertainty of teh data/MC
scaling.

the new fit assumes different mass resolutions for D1 and D*2 (as above).
also this fit uses the data sample with removed double events (total 2.3% sample reduction)

Dstpi2_v33.eps

the final numbers changed very little - will update later...

  - fixed parameters of the fit Belle vs CDF vs PDF

         * the consensus was to stick with the Belle values
         * results with the PDG value for the D2* width will be added in a footnote

will get to it

  - effects of the 6MeV mass shift on the formfactors will be investigated

will get to it

  - inconsistencies in the parameter r values from different fit
approaches will also be investigated. Alan has pointed to a 6% difference

will get to it

  - D** single- double pi decay modes. a saturation by a single pi decay mode was assumed. 
Andrei will provide more justification for this.

double pion mode is for ex. narrow D**-> D* pi pi. As we don't reconstruct it the Br
we measure could be underestimated.
however it is the usual practice to assume this decay rate is zero.

except from the lifetime ratio note 4280 describing the argument follows.
as one can see the DELPHI measurement is compatible with 0 (line 4 below)

with more data we should explore this mode and try to do the measurement ourselves.

  -  Interpretation of results

      Alice pointed out at the potential differences in the B meson compositions at the Tevatron and LEP,
as discussed at the previous meeting (Bs->uu)

i guess this question is about using LEP data for f_d & f_u. since we normalize to the semileptonic D* signal
we dont' need these numbers for the measurement itself. however it's true that we use the D* Br from
PDG (measured by LEP) to calculate the absolute Br. it looks as statistics increase and we start to
compete with LEP in precision this question will be coming up frequently so may be it's worth to think
about general party line re this issue. to me the fact that we use things approved by PDG is good enough.

re possible Bs contribution :
the only reason Bs production could matter are modes Bs -> mu nu Ds** with Ds** -> narrow D**K which in principle

may exist. They were never observed and are not present in generators. Estimate of the Bs contribution
into the semileptonic B->mu nu D* X sample is 2+-1%. this mode is possible when Bs-> mu nu Ds** with
Ds** -> D*K and the estimate was elaborated in d0note 4280, page 9. so the expected contribution
to the narrow D** sample should be even smaller.

  - Interference effects

* narrow states - the overall efficiency of 50% is primarly due to the
significance cuts, therefore the assumption about
full integration over angles may be justified.
Nevertheless, Andrei will look at the effects of kinematic cuts
on integration over spherical harmonics.

here it's important that the efficiency for D** decay angles is the same for D1 and D*2.
presumably this efficiency could be different only because of different pt spectra for D1 and D*2.
purely geometrical effects should be the same for D1 and D*2. the plot below shows distribution on angle between
the D** flight direction and direction of D* in the D** rest frame for D1 (points) and D*2 (green histo).
the dip at 1 corresponds to the case when pi** is emitted in the opposite direction to the D** flight so
it has small pt and goes under the threshold.




the plot below shows the same cos() for D1 and three values of
the pi** pt cut : 0.18 (green), 0.3(bleu, used in analysis) and 0.5(red) Gev cut.


the above information shows that the effect if small if any but we still need to quantify it.

* narrow-wide states there were no objections to the current estimate for the size of
this effect

  - a PRL draft v 1.0 is ready, it will be distributed to the
B-physics group and the EB only after conclusion of some of the tests
mentioned above.

  - our next meeting is scheduled for Jan. 13, 2005.