The Likelihood Method

1. Marco Incagli – INFN Pisa 24-5-2001 for the ppg group The Likelihood Method …or how to distinguish electrons from pions in the energy range 300-500 MeV

2. this is evident in the MTRK distribution defined by the following equation: • the ppg events selected by the online streaming have a large contamination of Bhabha events ppg high M tail of eeg mmg (events are prescaled below 110MeV and above 220MeV) Note that for ppp events q2g = m2p0 . low M tail of p+p-p0

3. In the angular distribution of the charged tracks the Bhabha’s forward-backward peak is evident (the two histograms are not normalized to the same luminosity)

4. Two methods to suppress background • A first solution which has been adopted to suppress this background is to cut on the pion cotq at |cotq| < 0.7 corresponding to |z| < 140cm and to 55o < q < 125o • As a further criterium a likelihood method has been developed which uses the following variables to discriminate between pions and electrons: • TOF • Energy in the last plane vs energy in the first plane of the associated cluster • Maximum energy vs total energy deposited in a given clusters • This definition implies that a track is associated to a cluster • In the ppg group the association is taken from TCLO bank, without any attempt of improving the performances with an offline extrapolation (see Spadaro’s talk)

5. Control samples • In order to discriminate pions from electrons using calorimeter information, it is better not to use MC information since the details of the showers, in particular for pions, are not correctly reproduced • Three control samples have been used: • radiative Bhabha’s having Mtrk<100MeV • p+p-p0 events from the RPI stream • p+p- events from the CLB stream (selected by the MUMUTAG algorithm) • The last sample is used, as described in the following, since the p+p-p0 momentum end point is at 470MeV • Since p+p-p0 and ppg have different momentum distributions, the likelihood is defined in 50MeV momenutm bins

6. Signal and control sample distributions • The distributions for Bhabha’s don’t depend upon the Mtrk cut • Signal and control sample show a different behaviour in the pion sector; for this reason the likelihood has been developed in momentum bins of 50MeV each • In the last bin also pp events have been used

7. The Likelihood Method • the two control samples are used to find the distribution functions that best separate electrons from pions • an analytical function fi(xi) is fitted on each of the chosen distributions and normalized to area 1 • an absolute Likelihood (aL) function is defined for electrons and pions • aLel,pi (x1,..,xn )= Pfi el,pi(xi) • where (x1,..,xn ) represent, for a given event, the values assumed by the selected variables • note that if the functions were indipendent this would be the total probability for an event represented by the vector (x1,..,xn )

8. The Likelihood Method • To take into account correlations a multidimensional function f(x1,x2,…,xn)could, in principal, be used • This approach is limited by the statistics which is needed to fill all the cells of the control sample distribution • We have used the following operative “likelihood” definition • aLel,pi = fel,pi(x1)  gel,pi(x2, x3)  hel,pi(x4, x5) • Where: • fel,pi(x1) = TOF distribution • gel,pi(x2, x3) = energy in the last plane vs energy in the first plane • hel,pi(x4, x5) = maximum energy vs total energy deposited

9. Time Of Flight pions 98% • The variable (t-l/c) is evaluated in the electron hypothesis (b=1) • This variable is the most powerful in the low momentum bins, where bp0.8 17% electrons

10. Energy distribution (1) • High momentum pions behave as MIPs depositing 40 MeV on each plane • electrons release most of their energy in the first plane and almost no energy in the last one

11. Energy distribution (2) p=400-450MeV • Electrons release a large fraction of their energy in just one plane and they have E/p  1 p=400-450MeV

12. Smoothing and building the likelihood • In order to limit the effects due to bin by bin statistical fluctuations a smoothing procedure that uses the multiquadratic function method has been used (Cernlib function built in Paw) • Finally a relative Likelihood is defined as the logarithm of the ratio of the two absolute likelihoods:

13. The last momentum bin • The p+p-p0 momentum spectrum dies out at 466 MeV, therefore in the last momentum bin also p+p- events are used • However these events are selected with the MUMUTAG algorithm that cuts on cluster variables, therefore they cannot be used for the energy related variables • The solution we have chosen is to use the p+p- events for the TOF variable (fpi(x1))and the p+p-p0 in the 400-470MeV energy range for gpi(x2, x3) andhpi(x4, x5) .

14. Absolute Likelihoods

15. Relative Likelihoods • The final relative likelihoods show a good separation between p- and e- . • Similar results are obtained for the positive tracks.

16. Signal Efficiency • The final efficiency on the signal is quite high (between 98% and 99%) and flat in the pion momentum given a positive TCA • This allows to cut on the OR of the likelihoods: if at least one likelihood is positive, than the event is classified as signal • A consequence of this is that the TCA efficiency is not a crucial issue

17. Likelihood on data • The data histogram has been fitted with the sum of the two dashed histograms corresponding to the likelihoods found on the control samples; the stars are the result of the fit.

18. Conclusions • the likelihood method seems to be very effective in separating pions from electrons in the momentum range 300-500 MeV • no attempt has been made in fitting a specific function for the muons; given the expected cross section, then the angular cut on the pions and the cut on the track mass are enough to neglect their contribution • the efficiency of TCA, for the moment taken from MC, can be simply evaluated from data by requesting an association on one track and by looking at the other one.