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ACAT05 May 22 - 27, 2005 DESY, Zeuthen, Germany Search for the Higgs boson at LHC by using Genetic Algorithms Mostafa MJAHED Ecole Royale de l’Air, Mathematics and Systems Dept. Marrakech, Morocco

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Introduction Introduction Genetic Algorithms Genetic Algorithms Search for the Higgs boson at LHC by using Genetic Algorithms Search for the Higgs boson at LHC by using Genetic Algorithms Optimization of discriminant functions Optimization of discriminant functions Optimization of Neural weights Optimization of Neural weights Hyperplans search Hyperplans search Hypersurfaces search Hypersurfaces search Conclusion Conclusion Search for the Higgs boson at LHC by using Genetic Algorithms M. Mjahed ACAT 05, DESY, Zeuthen, 26/05/2005 2

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Introduction Introduction Introduction Introduction

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Introduction Higgs production at LHC Several mechanisms contribute to the production of SM Higgs boson in proton collisions The dominant mechanism is the gluon fusion process, gg H

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Introduction Decay Modes decay into quarks: H bb and H cc leptonic decay: H + - gluonic decay: H g g decay into virtual W boson pair: H W + W -

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Introduction Main discovery modes M H < 2M Z : H bb+X H W + W - l l H ZZ 4l H

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The decay channel chosen: H W + W - e + -, + e -, e + e -, + -. Signature: Two charged oppositely leptons with large transverse momentum P T Two energetic jets in the forward detectors. Large missing transverse momentum P’ T Main background: tt production: with tt WbWb l j l j QCD W + W - +jets production Electroweak WWjj H W + W - ll (1) M. Mjahed ACAT 05, DESY, Zeuthen, 26/05/2005 7

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ll, ll : the pseudo-rapidity and the azimuthal angle differences between the two leptons jj, jj : the pseudo-rapidity and the azimuthal angle differences between the two jets M ll, M jj : the invariant mass of the two leptons and jets, M nm (n,m = 1,2,3) some rapidity weighted transverse momentum n, m = 1, 2,3, … i rapidity of the leptons or jets, p iT their transverse momentums. H W + W - ll (2) Main Variables M. Mjahed ACAT 05, DESY, Zeuthen, 26/05/2005 8

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Genetic Algorithms Genetic Algorithms Genetic Algorithms Genetic Algorithms

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Pattern Recognition Measurement Feature Decision Feature Extraction/ Feature Selection Classification M. Mjahed ACAT 05, DESY, Zeuthen, 26/05/2005 10

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Pattern Recognition Methods Pattern Recognition Methods Fuzzy Logic Neural Networks Neural Networks Genetic Algorithms Genetic Algorithms Pattern Recognition Methods Statistical Methods Statistical Methods Connectionist Methods Connectionist Methods Others Methods Others Methods Wavelets PCA Decision Trees Discriminant Analysis Discriminant Analysis Clustering

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Genetic Algorithms Based on Darwin’s theory of ”survival of the fittest”: Living organisms reproduce, individuals evolve/ mutate, individuals survive or die based on fitness The input is an initial set of possible solutions The output of a genetic algorithm is the set of ”fittest solutions” that will survive in a particular environment The process Produce the next generation (by a cross-over function) Evolve solutions (by a mutation function) Discard weak solutions (based on a fitness function) M. Mjahed ACAT 05, DESY, Zeuthen, 26/05/2005 12

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Genetic Algorithms Preparation: Define an encoding to represent solutions (i. e., use a character sequence to represent a classe) Create possible initial solutions (and encode them as strings) Perform the 3 genetic functions: Crossover, Mutate, Fitness Test Why Genetic Algorithms (GAs) ? Many real life problems cannot be solved in polynomial amount of time using deterministic algorithm Sometimes near optimal solutions that can be generated quickly are more desirable than optimal solutions which require huge amount of time Problems can be modeled as an optimization one M. Mjahed ACAT 05, DESY, Zeuthen, 26/05/2005 13

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Crossover 1 0 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 1 11 0 1 0 1 1 1 10 1 0 Mutation 1 0 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1 1 2 2 3 3 4 4 2 2 1 1 2 2 4 4 Spin Roulette Wheel Selection Genetic Functions

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GA Process Initialize Population Terminate? Yes Output solution Output solution No Evaluate Fitness Perform selection, crossover and mutation Perform selection, crossover and mutation Evaluate Fitness M. Mjahed ACAT 05, DESY, Zeuthen, 26/05/2005 15

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O O ptimization of discriminant functions O Optimization of Neural weights H Hyperplans search H Hypersurfaces search GAs for Pattern Classification GAs for Pattern Classification Efficiency and Purity of Classification Validation Test Events Classification C1C1 C2C2 C 1 : N 1 N 11 N 12 C 2 : N 2 N 21 N 22 TotalM1M1 M2M2 Efficiency for C i classification Purity for C i events Misclassification rate for C i or Error

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Search for the Higgs boson at LHC by using Genetic Algorithms

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pp HX W + W - X l + l - X Signal pp ttX WbWbX l j l jX pp qqX W + W - X Search for the Higgs boson at LHC by using Genetic Algorithms Events generated by the LUND MC PYTHIA 6.1 at s = 14 TeV M H = 115 - 150 GeV/c 2 10000 Higgs events and 10000 Background events are used Background Research of discriminating variables M. Mjahed ACAT 05, DESY, Zeuthen, 26/05/2005 18

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Variables ll, ll : the pseudo-rapidity and the azimuthal angle differences between the two leptons jj, jj : the pseudo-rapidity and the azimuthal angle differences between the two jets M ll : the invariant mass of the two leptons Rapidity-impulsion weighted Moments M nm : (n=1, …,6) i rapidity: M jj : the invariant mass of the two jets ll, ll, jj, jj, M ll, M jj, M 11, M 21, M 31, M 41

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C C Higgs C Back The most separating discriminant Function F Higgs / Back between the classes C Higgs and C Back is : F Higgs / Back = - 0.02+0.12 ll +0.4 jj +0.35 M ll +0.61 M jj + 0.74M 11 +1.04M 21 The classification of a test event x 0 is then obtained according to the condition: if F Higgs / Back (x o ) 0 then x o C Higgs else x o C Back Optimization of Discriminant Functions (1) Classification of test events 0.610 0.601 Efficiency C Back C Higgs Test events 0.604 0.606 Purity Classification F(x ) = (g signal - g back ) T V -1 x = i x i Discriminant Analysis

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Optimization of Discriminant Functions ( 2) 5i5i 4i4i 2i2i 1i1i 0i0i 6i6i 3i3i II Discriminant Function GA Parameters Number of generations Selection, Crossover, Mutation 0.741.010.40.12-0.020.610.350.395 Fitness GA Code Matlab GA Toolbox Fitness Fn: Misclassification rate M. Mjahed ACAT 05, DESY, Zeuthen, 26/05/2005 21 Test Events Classification Eff.PurityEff C Higgs 0.6010.606 0.60550.3945 C Back 0.6100.604

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Optimization of Discriminant Functions (3) Chromosome 1 ……………… Chromosome N Generation of N solutions Fitness Fn: Initialize Population Terminate? Yes Output solution Output solution No Evaluate Fitness Perform selection, crossover and mutation Perform selection, crossover and mutation Evaluate Fitness Genetic Process 5151 4141 2121 1111 0101 6161 3131 II 5N5N 4N4N 2N2N 1N1N 0N0N 6N6N 3N3N NN Coefficients of F

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Optimization of Discriminant Functions (4) Optimization Results Number of generations =10000 CPU Time: 120 s 0.741.010.40.12-0.020.610.35 Optimal Disc. Fn 0.650 0.649 Purity 0.648 0.652 Eff. Classification 0.65 Eff C Back 0.35 C Higgs Test Events M. Mjahed ACAT 05, DESY, Zeuthen, 26/05/2005 23

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Optimization of Neural Weights (1) Classification of test events Neural Analysis NN Architecture: (10, 10, 10, 1) if O 1 (x) 0.5 then x C Higgs else x C Back Test Evts Classification Eff.Pur.Eff C Higgs 0.6540.663 0.6610.338 C Back 0.6690.659 ll ll jj jj M ll M 0 M 11 M 21 M 31 M 41 O1O1 h1h1 h2h2

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Optimization of Neural Weights (2) Connection Weights + Thresholds GA Parameters Total number of parameters to be optimized : 230 Fitness: Misclassification rate, W ij xh1, i h1 II W ij h1h2, i h2 W ij h2o 100 +10 II 10 Optimization Results Number of generations =1000 CPU Time: 6 mn Test Evts Classification Eff.Pur.Eff C Higgs 0.6910.696 0.6950.305 C Back 0.6990.693

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Hyperplan search (1) Hyperplan H j Genetic Process 0 j 1 j 2 j 3 j 4 j 5 j 6 j 7 j 8 j 9 j 10 j Generation of N hyperplans H j, j=1: N=20 11 parameters to optimize Number of generations =10000 CPU Time: 4 mn H(x) = 0 + i x i = 0, i=1, 10 Classification rule if H(x) 0 then x C Higgs else x C Back Initialize Population Terminate? Yes Output solution Output solution No Evaluate Fitness Perform selection, crossover and mutation Perform selection, crossover and mutation Evaluate Fitness

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Hyperplan search (2) Hyperplan search Results Test Evts Classification Eff.Pur.Eff C Higgs 0.6610.655 0.6560.344 C Back 0.6510.657 Classification of test events Same results than Discriminant functions optimization 0.650 0.649 Pur. 0.648 0.652 Eff. Classification 0.65 Eff C Back 0.35 C Higgs Test Events

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Hypersurface search (1) Hypersurface j Initialize Population Terminate? Yes Output solution No Evaluate Fitness Perform selection, crossover and mutation Evaluate Fitness Genetic Process Generation of N hyperplans S j, j=1: N=20 31 parameters to optimize Number of generations =10000 CPU Time: 6 mn Classification rule if S(x) 0 then x C Higgs else x C Back I j i=0:10 j j i j i=1:10 i j i=1:10

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Hypersurface search Results Test Evts Classification Eff.Pur.Eff C Higgs 0.6890.696 0.6910.309 C Back 0.693 Classification of test events Same results as NN weights optimization Hypersurface search (2) M. Mjahed ACAT 05, DESY, Zeuthen, 26/05/2005 29 0.693 0.696 Pur. 0.699 0.691 Eff. Classification 0.695 Eff C Back 0.305 C Higgs Test Evts

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Conclusion Methods Importance of Pattern Recognition Methods The improvement of an any identification is subjected to the multiplication of multidimensional effect offered by PR methods and the discriminating power of the proposed variables. Genetic Algorithms Method allows to minimize the classification error and to improve efficiencies and purities of classifications. The performances are in average 3 to 5 % higher than those obtained with the other methods. Discriminant Functions Optimization : comparative to hyperplan search approach Neural Weights Optimization : comparative to hypersurface search approach C C C Higgs C Back M. Mjahed ACAT 05, DESY, Zeuthen, 26/05/2005 30

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VV ariables Conclusion (continued) C Characterisation of Higgs Boson events: Other variables should be examined PP hysics Processes Other processes should be considered Detector effects should be added to the simulated events M. Mjahed ACAT 05, DESY, Zeuthen, 26/05/2005 31

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