Using the exact weightings for the muon multiplicity distributions as described below, I made a plot of the change in the number of background events with respect to variations in the tag and fake rates.

Variations in the muon tag rate have more of a systematic effect on the background estimate than corresponding variations in the pion/kaon/proton mistag rates. In addition, the change in the number of background events is linear with respect to tag rate variations in all cases.

Next I take the 10% variations of both the real and fake rates and run a Bayesian limit calculator using 1000 pseudoexperiments drawn from the null hypothesis. We ask for 95% credibility level. The program returns the scale factor on the signal model that is excluded at this level. The output is as follows:

Observed : 0.305
Expected : mean=0.284 +1sig=0.396 -1sig=0.222 +2sig=0.589 -2sig=0.185

The observed exclusion is slightly stronger than expected, but completely within the 1 sigma bands. The signal model is excluded at 95% credibility at a cross-section of 30% of that provided.

I think one of the problems with the limit setting that I attempted to do last week was that I was using a random number generator to decide if a particular MC soft muon candidate is tagged. In the tail of the multiplicity distribution where the yields are small, we can get incorrect systematic estimates this way due to random fluctuations. Below is a comparison of the number of events with 2 and 3 extra muons in a W+b MC sample between using and RNG and exact weighting.  The systematic yields are calculated using exact weighting while the central yields have both techniques.

The systematic variations are symmetric with respect to the exactly weighted central values while they are sometimes asymmetric with respect to the rng value. Using exact weights eliminates the false asymmetry.

After applying the extended soft muon matrices shown below and performing the pTrel/d0Sig fit, we fix the number of additional single soft muons to the results obtained from the fit and then take the absolutely normalized prediction as a systematic error for the higher multiplicity bins.  The result is shown below.

I ran a limit-setting program using the bins with N>1, taking the central value from the fit to the single lepton pTrel/d0Sig, and using the tag rate and fake rate variations as systematics. The CLs returned was 0.0714 with an expected value of 0.002. I am suspicious of this value because the Bayesian limit calculator failed using the same inputs. I have contacted the experts for advice.

In the previous post, soft muon tag rates were extended into the pT>15 GeV region by plotting the efficiency as a function of pT for different eta bins and then taking the efficiency function as constant beyond the point for which there are no J/psi events.  An improvement on this is to use high-pT Z events to extend the efficiency function.

Below is the mass of trigger muon + taggable/tagged track for opposite-sign and same sign combination.

We can see that there is no Z peak in the same-sign data.  We use the same-sign as an estimate of the background under the Z peak, defined as 86.5<M(Z)<95.5 GeV.  We then obtain the efficiency as a function of pT in the same 3 eta bins as was done previously.

We use these functions to fill in missing bins for the muon tag rate matrix, as before.  The matrix obtained is:

We use this tag rate to obtain the absolute background prediction and pTrel/d0Sig templates.  We then use the results of the fit as an estimate of the systematic error for N(mu)>1.  The result is below.  Note that only the W has the systematic error currently estimated because the pTrel/d0Sig fit has not been performed for the Z events yet.

The tag/mistag matrices for soft muons had some holes in them due to insufficient statistics at higher pT in the J/psi, D*, and lambda samples.  I did a rough correction for this by fitting the efficiency as a function of pT in 3 eta bins for pions, kaons, protons, and muons separately and then using this fitted function whenever data was unavailable for a particular (pT,eta) bin of the matrix.  The result of this procedure is shown below.

The old tag rate matrix is on the left and the extended one is on the right.  Since we observed that the background prediction is low for the single muon bin and the data excess grows as a function of pTrel, I was hoping that filling these holes in the tag rates would fix some of this discrepancy.

The number of absolutely predicted SM background events in the single muon bin is now N(bg,W)=5386 for the W and N(bg,Z)=340.  Before the tag rate matrix extension, these numbers were N(bg,W)=5145 and N(bg,Z)=304.

The pTrel plots now look like this.

There is still an excess, but it climbs more slowly with respect to pTrel than before.  We can see this clearly if we compare the data/MC ratio plot to the one obtained before the tag rate extension.

I am attempting to use the pTrel/d0Sig fit in the single muon bin either as a systematic or as a central result.  I fixed the Drell Yan fraction relative to the W+heavy component using the number obtained from the absolutely normalized sample,  15% for TCE.  The fit looks like this:

The fit output is as follows:

N(h)=1805 +- 50

N(DY)=319

N(l)=1262 +- 59

There is still a large discrepancy with the absolutely normalized result.  The corresponding absolutely normalized pTrel and d0Sig plots are below.

The numbers for this are:

QCD=303

W+b=198

W+c=537

tt=155

Diboson=49

Z+heavy=22

Z->tau tau=100

Drell Yan=36

W+jets=1497

Total background=2897

Total data=3494

Summing the contributions to compare to the fit, we get

N(heavy absolute)=890

N(DY absolute)=158

N(light absolute)=1849

There is twice as much heavy and Drell Yan from the fit and less light.  Also note that the absolute prediction is low by a factor of 20%.

I varied the real and fake tag rates for soft muons for the standard model background and dark Higgs signal MC.  In addition, 5% of the taggable MC tracks were thrown away to model the 5% Monte Carlo tracking overefficiency systematic. I then plot the fractional change in background or signal population with respect to the variation for both the W and Z samples. The population plotted is the number of events containing 3(2) or more additional muons in the W(Z) sample.

Note that the signal MC tends to vary in the same direction as the background SM MC.  This implies the limit will be relatively stable with respect to a systematic variation in tag rate.

Below is a first attempt at listing all of the systematic errors we need to calculate and proposed techniques for calculating them.

• QCD rate – maximum variation found in CDF 6636 is 26% for N(jets)>3.  This may be overly conservative.
• Lepton & trigger ID – can be obtained from the R-ratio as done by Sasha.
• MC modelling for soft lepton ID – Some possibilities are
  • Use top selection. Take delta(1 mu) as a starting point for the uncertainty.  See if the difference changes as a function of N(mu) and blow up the error by this slope.
  • Do the single lepton fit using pTrel & S(d0).  Use this as a starting point for the uncertainty.  Blow up by Delta(Nmu) slope obtained from the top selection.
  • Take the maximum variation in N(taggable), pT(taggable), eta(taggable) in the single lepton bin and then feed the difference through the tag rate/mistag matrices.
  • There is expected to be a 5% tracking over efficiency in the MC.  Depending on how we estimate this uncertainty, it may be covered.  If it is not, I can throw out 5% of the tracks (possibly depending on pT) and rerun the prediction.
• Soft muon tag rate –
  • propagate fit errors from J/psi.
  • fit epsilon(pT) in 2 bins of eta and vary fit function.
• Soft muon mistag rate –
  • take largest (Observed-Predicted)/Observed from various jet samples.

Last week, I produced “final” 4 panel plots combining all the triggers for W and Z selections.  Here is the 4 panel Z plot I showed last week

There are 2 issues with this plot:

1. The jet overlapping the 2nd loose lepton is not being removed from the jet list.  This causes the funny bump in the Et(jet) plot in the bottom right.
2. All of the plots are for dilepton events across the whole mass spectrum.  We should be plotting the Z region, since this is “W/Z + additional leptons”.

Both of those issues were fixed this week to give the following plot. Note that the mass plot still shows the whole range.

The other plot produced last week was the N(muons) plot, shown below.

There are 2 issues with this plot as well:

1. The count of muons in the Z plot is over the entire mass region, as above.
2. We are counting muons coming from the W and Z as well.  This causes weird shapes because we are combining electron and muon triggers.

We fix these issues by, as above, only counting inside the Z window and by ignoring leptons coming from the W or Z.  In addition, the signal expectation is added.  The new plot is below.

The absolutely normalized prediction for the heavy component of the single muon final state and the fit results differ widely.  Below are pTrel and d0 significance plots obtained from absolute normalization.

And here is a corresponding fit result for mu+.

The fit returns N(W+heavy)=1861 +- 65 while the absolute prediction is 897.  The reason for this may become apparent when we plot some of the absolutely normalized components below.

Continue reading Discrepancy Between Absolute Normalization and Fit Result in Single Muon Bin →