Proper Time Dependence Studies: Update Bhh Meeting, 07'11'06

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Proper Time Dependence Studies UpdateB?hh
Meeting, 07.11.06

• Laurence Carson (with Alison Bates)

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Aims A reminder

• The study of event-by-event proper time will aid
  the understanding of the measurement capabilities
  of LHCb in a number of channels.
• In particular we are interested in the B?hh
  channels.
• This is an update of studies I have done to
  investigate the dependence of the proper time
  resolution on a number of different variables.
  For previous studies see PTMWG meeting of 24th
  August 2006.

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Method A Reminder

• Using DaVinci v12r16 (switch to v12r18 is
  underway)
• Studying event-by-event proper time for 1M evts
  of inclusive J/? ?µµ sample from DC 04 v1 (prev.
  used only 90k evts)
• Preselection code is PreselJpsi2MuMu
• Package used is Luis DecayChainNTuple v5r8
  (with a few modifications)
• Tool used for lifetime calculations is Gerhards
  lifetimefitter()
• Switch to the globalfitter(), which is much
  better suited() to our sample, was implemented
  for DV v12r17, but not yet for v12r18.
• Graphs of distributions of mass, momentum, MC
  mass etc. see Alisons talk of 20.04.06

http//agouldwe.home.cern.ch/agouldwe/ProperTime/P
romptJpsi-3.pdf
()This is because the lifetimefitter() assumes
that the J/? flight direction is in the same
direction as the overall momentum, which isnt
valid for J/? s from B-decays. The
globalfitter() doesnt make this assumption.
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Graphs of proper time and
proper time resolution
Frequency
Proper time of the J/? (ps)
At the moment the fit to the proper time
is only to the prompt part (tlt0.2ps) and uses a
double Gaussian. In future it is planned to use
ROOFit to fit to the entire proper time
distribution.
The proper time resolution (found by
subtracting the true proper time from the
reconstructed proper time) is also a double
Gaussian. The widths are (331)fs and (803)fs.
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Method used in rest of
these slides

• A variable which the proper time resolution might
  be expected to depend on is chosen and plotted.
• This variable is divided into 5 or so bins.
• The proper time distribution is plotted in each
  of these bins.
• A double Gaussian is fitted to the proper time
  distribution in each bin.
• The width of each Gaussian is plotted as a
  function of the binned variable, to see if a
  dependence exists.

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Number of hits in the VeLo

• if(thetrack) SmartRefVectorltTrStoredMeasurementgt
  StoredMeasurements thetrack-gtmeasurements()
• SmartRefVectorltTrStoredMeasurementgtite
  rator itm for(itmStoredMeasurements.begin()
  itm!StoredMeasurements.end() itm ) double
  z(itm)-gtz() if(zltzmax) nvelohit

• Thanks to Yeuhong for the code!
• Note that the code defines a measurement as being
  in the VeLo if it has zlt700mm. This region covers
  all of the VeLo, except for the 3 stations
  nearest RICH1.

Frequency
Number of µ- hits in the VeLo
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VeLoHits The Bins
The number of VeLohits graph has been
divided up into 5 bins.
Frequency
Next, the proper time distribution was
plotted in each bin of VeLo hits
Number of µ- hits in the VeLo
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Proper Time in Bins of Number of
Hits in the VeLo
Freqeuncy
Proper time (ps)
A double Gaussian was fitted to -0.2ps lt
tau lt 0.2ps, which is the prompt part of the
proper time distribution. The sigmas of the
Gaussians are called p2 and p5.
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Sigma of the Gaussians
against VeLoHits

• We see a positive correlation for sigma1 (the
  narrower Gaussian), but the opposite for sigma2
  (the wider Gaussian). Previously I had seen a
  similar trend in sigma2, but the sigma1 trend was
  flat (within errors). As we have strong reason
  to believe that tracks with many Velo hits should
  be reconstructed better and so have smaller
  proper time resolution, this raises questions
  over whether sigma1 has much physical meaning.

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Sigma of the Gaussians against
VeLoHits Different Fit Range
One can also fit the double Gaussian to
-0.3 lt tau lt 0.1 (in ps). This is sensible
because the tault0 isnt affected by B-decays it
should give the pure resolution.
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Sigma of the Gaussians against
VeLoHits Finer Binning
One can also split VeLoHits into 8 bins
instead of 5, and fit to the std range-0.2,
0.2. The conclusion from this and the -0.3,0.1
data is that sigma1 rises with Velohits, while
sigma2 falls then levels off for Velohits gt 10.
The sigma2 trend is plausible beyond some number
of Velohits the resolution must begin to depend
on other factors more strongly.
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Proper Time in Bins of the
Momentum of the Mu-
As for the number of VeLo hits graph,
the p_lab1 graph is divided into 6 bins, and
the proper time distribution is plotted in each
bin First bin is from 3GeV to 9GeV, last
bin is from 60GeV to 120GeV.
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Sigma of the Gaussians Against
Mu- Momentum
For sigma1, we see no simple trend
ignoring the first point it is basically flat.
For sigma2 the proper time resolution gets worse
as the momentum of the Mu- increases.
Is this what we expect from the physics??
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Proper Time in Bins of the
Transverse Momentum of the Mu-
Will this give similar results to those for
the 3-momentum?
First bin is from 0.5GeV to 0.9GeV, last bin is
from 2.9GeV to 4.5GeV.
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Sigma of the Gaussians Against
Mu- Transverse Momentum
For both sigmas, there is a clear positive
correlation with the muons transverse momentum.
Again, is this expected?
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Resolution on (Transverse) Momentum of
the Muon

• To know if the proper time correlations with
  (transverse) momentum make sense, we need to know
  how well we measure (transverse) momentum as a
  function of (transverse) momentum. For both
  kinds of momentum I considered (rec. MC) and
  (rec. MC)/rec.
• Recipe is same as for proper time correlation
  plot the variable in some bins, and parameterise
  the resolution in each bin as a Gaussian width.
  Then I plot how the widths vary over each bin.

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Residual of the Muon Momentum Measurement
By the residual of the measurement I mean
the difference between the reconstructed value
and the generated (MC) value. I used the same
bins for the momentum as before. The bad news
is that a double Gaussian does not fit the prec
pMC graph well a triple Gaussian had to be
used!
To further complicate matters, a double
Gaussian had to be used to fit to the highest p
bin (see backup slide for explanation).
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Momentum Resolution as a Function of Momentum
Obviously we now have three graphs, one
for each contribution to the triple Gaussian.
All three graphs show that the momentum residual
is higher at high momentum values. This is not
too surprising, but what about the relative
error? (see later)
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Transverse Momentum Resolution as a
Function of Transverse Momentum
Again, a triple Gaussian was required and
again, the highest bin was problematic (see
backup slide). The trends can be made much
clearer if we omit the last bin
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Transverse Momentum Resolution as a Function
of Transverse Momentum (2)
After omitting the last bin, we can see that
the three Gaussians all get wider as the
transverse momentum increases (although the trend
for the third Gaussian is weaker).
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Momentum Resolution/Momentum as a Function of
Momentum
Plotting (prec-pMC)/prec in bins of prec, a
double (rather than triple) Gaussian can be
fitted . The fit region is ?p/plt2.5.
The first Gaussian gets wider as the momentum
increases, while the second Gaussian tends to get
narrower.
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Momentum Resolution/Momentum as a Function of
Momentum (2)
Since the ?2/ndf was not great for the previous
graphs, I tried fitting a single Gaussian to a
narrower region of the graph (?p/plt1).
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Transverse Momentum Resolution/Trans Momentum as
a Function of Trans Momentum
First, I fitted a double Gaussian to
?pt/ptlt2.5, to be consistent with the ?p/p
plots. Since these look rubbish I then tried
something different.
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Transverse Momentum Resolution/Trans Momentum as
a Function of Trans Momentum (2)
Secondly, I fitted a double Gaussian to
?pt/ptlt2, because the previous fits were going
off outside of 2. This improved the fits a
little, but we could still improve
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Transverse Momentum Resolution/Trans Momentum as
a Function of Trans Momentum (3)
By fitting a double Gaussian to
?pt/ptlt1.5. Now we see some sort of narrowing
of the wider Gaussian for larger pt values.
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Discussion
What is the physical interpretation of the
dbl/triple Gaussian? How does one decide which
interval to fit to? Do these trends make sense
physically? Should we eliminate non-prompt
J/Psis due to the lifetimefitter() momtm
direction assumption?
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Next Steps

• Switch over to DaVinci v12r18
• Switch over to the globalfitter()
• Start using ROOFit to fit to the proper time
  distribution.
• Look at proper time dependence on other
  variables, including measureError().
• Study background effects using a large minimum
  bias sample.
• Apply proper time calibrations to B?hh channels.

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Backup Slides
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The Last Bin of Momentum Resolution Double
or Triple Gaussian?
If you try to fit a triple Gaussian to the
highest momentum bin (see right hand graph), the
parameters for one of the Gaussians are redundant
(height is 86341, width is 728804). So a
double Gaussian (left hand graph) was fitted
instead.
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The Last Bin of Transverse Momentum Resolution
Normally, the narrowest Gaussian is also the
tallest, and the widest Gaussian is the shortest
in height. However for the highest transverse
momentum bin the narrowest Gaussian was the
second tallest. This raises doubts about the
reliability of the fit.
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Proper Time in bins of Residual
of the First Hit in the VeLo
Freqeuncy
Proper time (ps)
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Rogue Point on FirstHitZ Graph
However the fit to the fourth FirstHitZ
bin is just as good as the rest. So this point
is an anomaly rather than a mistake.
Fourth point does not lie on the line