Exploring Artificial Neural Networks to discover the Higgs boson at the LHC

1. Exploring Artificial Neural Networks to discover the Higgs boson at the LHC

2. Overview • Introduction • The Standard Model and the mass problem • Higgs search at the LHC (and ANNs) • ttH, H to bb and other channels • Production process • Decay • Experimental signatures • Background processes • ANNs a possible solution (theory) • ANN development issues (on simple 2-D classification problem + results) • ANNs applied to Higgs data (results) • Summary

3. Introduction • Origin of mass is last big unanswered question in the SM. • The Standard Model • To make physical equations in SM gauge invariant we require new terms, these correspond directly to gauge bosons. (eg photon) • Massless particles would preserve SM’s gauge symmetry (easiest, but not the case) • Higgs mechanism allows generation of mass in the SM (by breaking gauge invariance of vacuum) (spontaneous symmetry breaking) • Needs further particle: HIGGS BOSON!! • So search for Higgs is important to our understanding of particle interactions. • It may be that nature has chosen another mass-generating mechanism, but whatever this mechanism is, it should show itself at the LHC.

4. Search at the Large Hadron Collider (LHC) (Higgs discovery one of its main aims) • H mass not predicted by the SM but production and decay rates can be predicted as function of mH. • From LEP: • 114.4GeV < mH (SM) . • The LHC, with its detectors ATLAS and CMS, (due to go online in 2007) will collide p-p at • 14TeV • Higgs mass reach to about 1TeV. • High Luminosity; • But Higgs production v. rare! (1016 proton-proton interactions will occur per year, but less than 100,000 Higgs bosons will be produced) • As well as Higgs, LHC hopes to find evidence for new physics • Supersymmetry (SUSY) (modifies the SM to include a whole new series of particles, supersymmetric partners of all the particles so far known. Has many desirable features, mending some shortcomings of the SM. • If SUSY is the theory, we do not know how many Higgs bosons we would see (minimum 5)

5. ttH, H to bb Channel • H production processes: • Gluon fusion is dominant Higgs production process, gg to H (but difficult to separate signal from large QCD background) • Associated Production! ttH, Lower cross section but has leptonic final states • Dominant decay mode at mH<130GeV is H to bb bb WW ZZ

6. ttH, H to bb could account for half the Higgs discovery potential at ATLAS (Cammin) • Background; • ttjj (most important, 94% after TDR analysis) • Full reconstruction of final state is necessary to minimize combinatorial background and to discriminate signal from large bg. • TDR analysis has 3 steps: • Preselection • -1 isolated lepton, • -At least 6 jets, • -Exactly 4 tagged as b-jets. • Reconstruction • -reconstruction of 2 top quarks, minimise: • Δ2 = (mlvb – mt)2 + (mjjb – mt)2 • Cuts on the reconstructed t and H masses (where ANNs come in) • -Reconstructed top masses must be within 20GeV of mt. • -mbb = mH30GeV

7. After this TDR analysis, significance S/√B = 1.94 (for 120GeV Higgs) • Could increase significance by: • Better jet pairing • Improving ‘final selection’ (after t reconstruction, apply to events in mbb = mH30GeV) Applying ANNs promising as makes use of event topology, not just mass cuts! Ie minimising (Δ2 eqn) does not take into account additional info such as spatial differences between jets! • I looked at final selection! • Used 10 variables generated by Pythia. (which gave separation in signal and background distributions) • Fed variables into a neural network. (to classify event as signal or background)

8. ANNs • Artificial Neural Networks (ANNs) are computational modelling tools • Inspired by biological nervous system • Good at: • generalization, • non-linear, • learn by example. • Want to train network with examples to recognise right data( classification task) and reject rest • (ANNs perform better than cut based in theory because can separate classes in feature space non linearly) • (but training is difficult, optimisation harder than for cut based methods) x1 x2 x1 x2

9. How do ANNs Work? • Response function: oi=g(∑iwijg(∑kwjkxk)) • Which is non-linear so network able to perform non-linear mappings • Architecture and weight settings are what change classification! • We want network to output 1 for signal • and 0 for all background A neural node oi wij hj wjk xk A neural network

10. Weights are changed in proportion to the difference (error) between target output and actual network output for each example. • Minimize summed square error function: E = 1/2 ∑p∑i(oi(p) - ti(p))2 with respect to the weights. • Error is function of all the weights and forms an irregular multidimensional complex hyperplane with many peaks, saddle points and minima. • Error minimized by finding set of weights that correspond to global minimum. (ie get close to 1 for signal and close to 0 for background) • Done with gradient descent method – (weights incrementally updated in proportion to δE/δwij) Error Surface

11. Summary of learning algorithm • Initialize wij and wjk with random values. • Pick pattern p from training set. • Present input and calculate the output from: oi=g(∑iwijg(∑kwjkxk)) • Update weights according to: wij(t + 1) = wij(t) – Δwij wjk(t + 1) = wjk(t) – Δwjk where Δw = -ηδE/δw. (…etc…for extra hidden layers). • When no change (within some accuracy) occurs, the weights are frozen and network is ready to use on data it has never seen.

12. 2-D problem • Initially looked at simple ANN classification problem; • Separate out a single point in a 2-D plane of randomly generated numbers. • Generated 2 sets of random numbers • Fed network (using SNNS)(2 input 1 output) (show diag!!) examples of signal and background data. (desired output 1 and 0 respectively) • Used 300 patterns in both tr. And val sets. • Background to signal ratio was 3 to 1. • Looked at various net architectures. • Results: • Learning shown by error curves • Projections show hyperplanes • 3 hidden nodes solve classification task fully! (effectively 1 hidden node is equiv. of 1 linear hyperplane)

13. Got spiking behaviour of some error curves. • Showed inconsistent learning (updating of weights) • Was solved by adjusting some network params (made learning more stable!!!) • Learning parameter, η. • dmax. • Shuffle option. • To get a deeper understanding of learning, also looked at weight and bias variables.

15. Using ANNs for Higgs search • Worked with data after reconstruction of top quarks. • Variables used; • mbb: the invariant mass of the two b-jets assigned to the Higgs boson, • Δη(tnear, bb): the difference in pseudo rapidity between the bb-system and the reconstructed top quark nearest ΔR. • cosb,b*: the cosine of the decay angle of the two b-jets from the Higgs boson in the rest frame of the bb-system, • Δη(b,b): the difference in pseudo rapidity between the two b-jets from the Higgs boson, • mbb(1): the combination with the smallest invariant mass mbb out of the six combintations which are possible when selecting two b-jets out of four b-jets, • mbb(2): the combination with the second smallest invariant mass mbb out of the six combinations which are possible when selecting two b-jets out of four b-jets, • t1-t2: the difference in phi between the reconstructed top quarks, • pTt1+pTt2: the sum of the transverse momenta of the reconstructed top quarks.

16. Signal is RED

17. (only ttjj background used) • Rescaled data to [0,1] • Separated data into tr and val sets • Used 1:1 for signal to background. • Looked at various archs (1 and 2 hidden layers) • Weak generalization:

18. Output for best architecture (6-20-20-1) gave: Signal is RED

19. Summary • Optimisation difficulties and solutions have been identified in net development • Some classification produced for Higgs data • More work on arch could be needed (more data, lack of generalization) • s/√B as fn. of cut on output.