October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Top Quark Mass Measurements Using Neural Networks Suman B. Beri, Rajwant Kaur Panjab University, India Pushpalatha Bhat Fermilab Harrison B. Prosper Florida State University

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Outline Introduction Neural Networks Event Simulation Preliminary Studies Summary

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Introduction Run I, 1995, March 2: Discovery m t = 176 ± 17 GeV/c 2 (CDF) m t = 199 ± 30 GeV/c 2 (DØ) 1999, Combined Mass m t = 174 ± 5 GeV/c 2 (CDF+ DØ) Run II, (2001…) ? m t = 174 ± ? GeV/c 2

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Why Measure The Top Mass? from which we can infer something about the Higgs mass According to the Standard Model quantum corrections to the W and Z boson masses induce a relationship Corrections to W and Z mass

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Measuring the Top Mass 100 In Run II we expect about 100 times more data than was collected in Run I. reduce systematic errors The main task is to reduce systematic errors so that we can benefit from the reduction in statistical errors Goal to determine m t as accurately as possible by making optimal use of information using as many decay modes as possible several methods using several methods to cross-check the results exploring different methods which may yield smaller systematic errors.

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Feed-Forward Neural Networks x1x1 x2x2 x3x3 x4x4 Use non-linear transfer function (e.g., sigmoid)

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Training simply means minimizing the error function Training Neural Networks n(x i,  ) = network function x i = feature vector for pattern i, where i = 1,…N patterns  = weights d k = desired output for pattern i, where k =1,.. M classes

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri P(k)Prior probability P(k) = Prior probability Pr(x|k)Likelihood Pr(x|k) = Likelihood ( Probability to get x given that x belongs to k) P(k|x)Posterior probability P(k|x) = Posterior probability ( Probability to belong to k given x) A Bit of Bayes!

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri If d k d k = 0 for class k = 1 (e.g., background) d k d k = 1 for class k = 2 (e.g., signal) Then Special Case: Classification Reduces to

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Neural Networks in Run I and II Run I Used by DØ to discriminate signal from background Used in the lepton + jets channel for top quark mass measurement Run II Can they be used to measure masses? Test some ideas using the e-  channel

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri The e-  channel The e-  channel Pbar b b t b b t P

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Branching fractions ee   ee ee  e+ jets  jets  jets 6 jets 44.4% 1.25% 2.5% 14.8% +jets

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Characteristics of e-  Events Signature Two isolated, high p T leptons Significant missing transverse energy 2 jets from b quarks Branching fraction ~ 2.4 %

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Event Simulation Tools Tools : Pythia to generate events SHW 2.3 to model detector (John Conway) MLPfit 1.4 to train networks Python interface to above toolsSignal Top events (100 to 250 GeV in steps 10 GeV)Backgrounds Z   +  -  e  WW  e 

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Event Variables Variables Variables : x 1 = f(e,b 1 ) x 2 = f( ,b 2 ) x 3 = f(e,b 2 ) x 4 = f( ,b 1 ) where End-point occurs at the top mass if b quark and the lepton are correctly paired End-point occurs at the top mass if b quark and the lepton are correctly paired

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Distributions: Correct/Wrong Pairing blue Parton-level (blue) distributions compared to distributions at the red reconstruction-level (red). We see that these variables are insensitive to jet energy scale uncertainties and fragmentation Also, note the sharp end-point when the b and lepton are correctly paired.

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Distributions: Reconstruction Level We have not yet devised a method to pair the lepton and b quark with high probability. For now we take all pairings of leptons and b quarks.

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Combining Variables using NN Use NN to create a single mass-dependent variable y from the variables x 1 to x 4 Training Training: 500 events/top mass (100 to 250 in steps of 10) Target output d k = top quark mass 200 epochs

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Neural Network Output Distributions 160 GeV 169 ± GeV 175 ± GeV 181 ± GeV 186 ± 25 GeV

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Mean NN output vs Top Mass The distortions are caused by edge effects, that is, restriction to a finite range. Need to deal with this.

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Some thoughts about how to proceed Let y = be the NN output. Let P(y|m t ) denote the probability to get y given the true top mass m t. Use Bayes’ theorem to invert probability: Use position of max[P(m t |y] as top mass estimate

October 19, 2000ACAT 2000, Fermilab, Suman B. Beri Summary The challenge in Run II will be to reduce substantially the systematic uncertainties. We are conducting a systematic study of neural network based methods of mass measurement. This is just the beginning. From our success in Run I we are hopeful that our current efforts will be fruitful.