modeling fake missing transverse energy with bayesian neural networks

Silvia TentindoFlorida State University

ACAT 11, Brunel University, UK

Outline

Motivation

Modeling Missing Transverse Energy

Results

Summary and Conclusions

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Missing Transverse Energy @ the LHC Missing Transverse Energy (MET) is an important

observable in many analyses at the LHC: ElectroWeak,

Top, SUSY, Exotica, Higgs, …

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SM Higgs : Production and Decay yields

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Higgs production Total Cross SectionAt LHC (7 TeV)Gluon Gluon ~ 10pb@MH=150GeV

Higgs branching ratios: H->ZZ, H->WWAnd H->bb are dominant at MH=150GeV

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:

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H → V V → 2l,2ν V =Z,W

SM Higgs Production and Decay

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gluon gluon fusion vector boson fusion

dominant Higgs production mechanism

Higgs decay modes to di-leptons:

H W W -> (l,v),(l,v)

H ->Z Z -> (l,l) (v,v)

MET

H

W

W H

Z

Z

H → ZZ /WW → 2l,2ν

Di-Muon Event Observed by CMS

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muon

MET

pp → H → ZZ→ 2μ,2νA Higgs candidate event:

muon

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transverse plane view

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)

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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

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Missing ET – definition and measurement

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Definition:

Measurement:

MET true

H Z Z (l, l) (v, v)

MAIN BACKGROUNDSIGNAL q q Z (l,l) + Jets

MET fake

€

/ r E = /

r E real + /

r E fake

€

/ r E = − r p Ti

i∑

Fake Missing Et in a typical background event

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p p --> Z (l l) + jets

Monte Carlo simulation of Missing ET

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Missing Et from simulation and data

The present simulation of missing Et is satisfactory,but future conditions from the machine (increasedluminosity, pile up effects, and increased energy) motivate exploringdata driven modeling of missing Et

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

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Pavlunin arXiv:0906.5016v1

a typical Photon + Jet event

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q q Photon + Jets

MET

fake

Photon + jets events are kinematically and topologically similar to Z + jets events

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transverse plane view

a typical Photon + Jet event

Modeling Fake Missing ET

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photon

jets

MET

MET

The Photon pT and the Fake Missing Et (MET) are related

DeltaPHI (Photon, jets) DeltaPHI(MET, jets)

Modeling Fake Missing ET

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photon

jets

METMET

Fake Missing Et vsPt of Photon

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

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€

p(MET) = p(MET | pT ) pZ (pT ) dpT∫

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)

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bnn(MET , pT ) =p(MET, pT )

p(MET, pT )+U(MET)p(pT )

METpT

bnn(MET, pT)

Modeling Fake Missing ET with BNN

5 – Then the desired density can be written as:

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p(MET | pT ) =U(MET)bνν(MET, pT )

1−bνν(MET, pT )⎡⎣⎢

⎤⎦⎥

METpT

bnn(MET, pT)

Results of BNN Training

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MET distributions for a fixed bin in photon pT

Results of BNN Training – Closure Test

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MET distribution integrated over photon pT spectrum

Preliminary results of closure test look promising €

p(MET) = p(MET | pT ) pγ (pT ) dpT∫

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.

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Bayesian Neural Networks

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= =

++=

H

j

P

iiijjj xuavbwxf

1 1

tanh),(

y(x,w)

x1

x2

)],(exp[11),(

wxfwxy

+=

bnn(x) =1N

y(x,wi)i=1

N

∑The weights are sampled from aprobability density function defined onthe neural network parameter space

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

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Modeling Fake Missing ET

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pp → γ + jet

pp → Z /W + jet

Basic Idea: extract fake missing ET distribution from:

Fake Missing ET

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Courtesy ATLAS+CMS

pp → Z+ jetsZ + jets

Fake missing ET (MET) largely due to jetmismeasurements

Z

jet

Expect MET to be aligned or anti-aligned with jet