Track/pi0 Cluster Likelihood Ratios

Following Carla’s work deriving a likelihood for jet based identification, I have implemented a similar scheme for track/pi0 clusters. I make a series of parameterized likelihood for y(i)=B(i)/S(i), where i is a particular variable, S is the signal Higgs sample, and B is the combined W+jets sample. Then I multiply all the y’s together as uncorrelated likelihood ratios and create the final likelihood as L=1/(1+y). The plots of each y are given below.

  • N(live) – The value of y is obtained for each bin of N(live) up to N(live)=9. Beyond that, y(Nlive>9)=y(Nlive=9).

y(Nlive)

  • N(tracks) – The value of y is obtained for each bin of N(tracks) up to N(tracks)=10. Beyond that, y(Ntracks>10)=y(Ntracks=10).

y(Ntracks)


  • N(pi0s) – The value of y is obtained for each bin of N(pi0s) up to N(pi0)=9. Beyond that, y(Npi0>9)=y(Npi0=9).

y(Npi0)

  • pT(cluster)- The value of y is obtained by fitting the distribution to the functions
    • if(pT<12) f1(pT)=exp(C+s*pT)
    • if(12
      <40) f2(pT)=p0+p1*x+p2*x^2+p3*x^3+p4*x^4
    • if(pT>40) f3(pT)=f2(40)

y(pT)

  • kpar(cluster) where kpar is the 1st longitudinal mechanical moment. The value of y is obtained by fitting the distribution to the functions
    • if(kpar<11.25) f1(kpar)=p0+p1*x+p2*x^2+p3*x^3+p4*x^4
    • if(11.25<30) f2(kpar)=exp(C+s*x)
    • if(kpar>30) f3(kpar)=f2(30)

y(kpar)

  • fEM, Em fraction, using only towers that are hit by tracks or have pi0s identified in them. The value of y is obtained by fitting the distribution to a 6th order polynomial across the entire range [0,1].

y(fEM)

After multiplying all of these ratios together and forming the combined likelihood, we obtain distributions of this combined variable for signal, W+jets, and ttbar.

Combined Likelihood Comparison

We then make a plot of efficiency versus fake rate for a series of cuts on this variable. The fake rate is determined from the W+jets sample.

Efficiency vs. fake rate for combined likelihood

Remember, this is a per cluster efficiency and fake rate. I did not use the mass of the cluster as a variable in the likelihood because I was worried about biasing the mass distribution. However, if we are not using the cluster mass to do the signal extraction (supposing we have one), then it is not a problem. I want to add that variable and see what the effect is as well as variables that are specific to clusters containing a soft electron.

–Dan