Modeling Fake Missing Transverse Energy with Bayesian Neural NetwoRkS

1. Silvia Tentindo Florida State University ACAT 11, Brunel University, UK Modeling Fake Missing Transverse Energy with Bayesian Neural NetwoRkS

2. Outline • Motivation • Modeling Missing Transverse Energy • Results • Summary and Conclusions Silvia Tentindo ACAT 11

3. Motivation – PHysics

4. Missing Transverse Energy @ the LHC • Missing Transverse Energy (MET) is an important observable in many analyses at the LHC: ElectroWeak, Top, SUSY, Exotica, Higgs, … Silvia Tentindo ACAT 11

5. SM Higgs : Production and Decay yields Higgs production Total Cross Section At LHC (7 TeV) Gluon Gluon ~ 10pb@MH=150GeV Higgs branching ratios: H->ZZ, H->WW And H->bb are dominant at MH=150GeV Silvia Tentindo ACAT 11

6. Missing Transverse Energy @ the LHC • In particular, it is important in searches for the Standard Model (SM) Higgs boson in the channels: H  W,W  (l,ν),(l,ν) H  Z, Z  (l,l) (ν,ν) H  Z, Z  (l,l) (b,b); (l,l) (j,j) H  Z, Z  τ,τ • We will focus here on the following channels: Silvia Tentindo ACAT 11

7. SM Higgs Production and Decay dominant Higgs production mechanism gluon gluon fusion vector boson fusion Higgs decay modes to di-leptons: HH l H  W W -> (l,v),(l,v) Z l W v l v H H ->Z Z -> (l,l) (v,v) Z v H W l v MET Silvia Tentindo ACAT 11

8. Di-Muon Event Observed by CMS A Higgs candidate event: muon muon MET Silvia Tentindo ACAT 11

9. transverse plane view Silvia Tentindo ACAT 11

10. MODELING MISSING ET

11. Monte Carlo Simulation of Variables • Detector simulations at the LHC are able to describe accurately most of the variables that characterize an event • For example: Pt transverse momentum simulated vs measured (ATLAS) Silvia Tentindo ACAT 11

12. Monte Carlo Simulation of Missing Et • Missing transverse energy is a complex observable. The quality of its measurement depends on: • the hermeticity and granularity of the detector, • pile up effects, • jet multiplicity, etc. • Missing transverse energy comprises both real missing ET from escaping weakly interacting particles as well as fake missing ET Silvia Tentindo ACAT 11

13. Missing ET – definition and measurement Definition: Measurement: METfake MET true H Z Z  (l, l) (v, v) SIGNAL q q  Z (l,l) + Jets MAIN BACKGROUND Silvia Tentindo ACAT 11

14. Fake Missing Et in a typical background event p p --> Z (l l) + jets Silvia Tentindo ACAT 11

15. Monte Carlo simulation of Missing ET Missing Et from simulation and data The present simulation of missing Et is satisfactory, but future conditions from the machine (increased luminosity, pile up effects, and increased energy) motivate exploring data driven modeling of missing Et Silvia Tentindo ACAT 11

16. Modeling Fake Missing Et • Use photon + Jets data to model fake missing Et: --- Photon + jets events are kinematically and topologically similar to Z + jets events --- The cross section for photon + jets >> cross section for Z + jets --- The energy of the photon is very well measured C : Use fake missing Et distribution in photon + jets data to model the fake missing Et in Z + jets events Pavlunin arXiv:0906.5016v1 Silvia Tentindo ACAT 11

17. a typical Photon + Jet event Photon + jets events are kinematically and topologically similar to Z + jets events METfake Silvia Tentindo ACAT 11 q q  Photon + Jets

18. a typical Photon + Jet event transverse plane view Silvia Tentindo ACAT 11

19. Modeling Fake Missing ET The Photon pT and the Fake Missing Et (MET) are related DeltaPHI (Photon, jets) DeltaPHI(MET, jets) photon MET jets MET Silvia Tentindo ACAT 11

20. Modeling Fake Missing ET Fake Missing Et vs Pt of Photon photon MET jets MET Silvia Tentindo ACAT 11

21. Modeling Fake Missing Et by BNN 1 – The Z pt (Photon pt ) and the fake missing Et (MET) are related: p(MET | pT, …). Moreover, the MET could be related to other observables. 2 – The density p(MET | pT) should be the same for Z + jets and for Photon + jets 3 – Given pZ(pT) of Z , model the fake MET in Z + jets events using Silvia Tentindo ACAT 11

22. Modeling Fake Missing ET with BNN 4 – Use a Bayesian neural network (BNN) to approximate where U(MET) is a known density (e.g., a uniform). (MC) training data: MET, pT from photon + jets (target = 1) MET from U(MET) and pT from photon + jets (target = 0) MET pT bnn(MET, pT) Silvia Tentindo ACAT 11

23. Modeling Fake Missing ET with BNN 5 – Then the desired density can be written as: MET pT bnn(MET, pT) Silvia Tentindo ACAT 11

24. RESULTS

25. Results of BNN Training MET distributions for a fixed bin in photon pT Silvia Tentindo ACAT 11

26. Results of BNN Training – Closure Test MET distribution integrated over photon pT spectrum Preliminary results of closure test look promising Silvia Tentindo ACAT 11

27. Summary and Conclusions • As the LHC luminosity increases (and the energy), we expect that the simulation of MET could become harder • We proposed a method to extract the Fake Missing Et spectrum from photon + jets data and approximate it with a Bayesian neural network. • The method could be useful in modeling the Fake Missing Et for Z + jets events, which are the dominant background in the Higgs to 2l, 2v channel. Silvia Tentindo ACAT 11

28. Backup slides

29. x1 y(x,w) x2 Bayesian Neural Networks The weights are sampled from a probability density function defined on the neural network parameter space Silvia Tentindo ACAT 11

30. BNN details • Use ~ 15,000 simulated photon + jets events • Use neural networks (NNs) with 2 inputs and 15 hidden nodes • Generate ensemble of NNs with Flexible Bayesian Modeling (FBM) package by Radford Neal • Average over 100 independent NNs Silvia Tentindo ACAT 11

31. Modeling Fake Missing ET Basic Idea: extract fake missing ET distribution from: Silvia Tentindo ACAT 11

32. Fake Missing ET Z + jets Fake missing ET (MET) largely due to jet mismeasurements jet Z Courtesy ATLAS+CMS Expect MET to be aligned or anti-aligned with jet Silvia Tentindo ACAT 11