msc thesis

A Study of Missing Transverse Energy in Minimum Bias Events with In-time Pile-up at The Large Hadron Collider using√s=7 TeV data

A Study of Missing Transverse Energy inMinimum Bias Events with In-time Pile-up at

The Large Hadron Collider using√s=7 TeV data

Kuhan Wang

Supervisor: Richard KeelerCommittee Members: Michel Lefebvre, Rob McPherson

External Examiner: Michel C. Vetterli

July 1st, 2011

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Outline

Outline

1 Introduction

2 The Standard Model

3 Minimum Bias

4 The Large Hadron Collider

5 ATLAS

6 Pile-up

7 Missing Transverse Energy

8 Data Selection and Monte Carlo

9 Analysis

10 Conclusions

11 Backup

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Introduction

IntroductionWe examined approximately

∫L dt = 3668 nb−1 of data

taken at the LHC at√s =7 TeV during 2010

Minimum bias events are selected using a “single arm” MBTStriggerWe examine the Missing Transverse Energy (MET) ofminimum bias events after selection for run, timing, jet andtrack qualityThe events are sorted by the number of primary vertices so asto study the effects of in-time pile-upWe compare and contrast the resolution, mean andasymmetry of the MET with respects to global calibrationschemes and Monte Carlo resultsThe resolution of minimum bias events parametrized in

∑ET

does not vary with respects to in-time pile-up, up to at least 4vertices

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The Standard Model

I

The Standard Model

SM is the current theory ofparticle physics

3 forces mediated byBosons, 3 generations ofFermions

Fermions: Quarks andLeptons

Quarks and Gluons carrycolor charge

Quarks are color confinedand must exist in a colorneutral combination

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Minimum Bias

I

Minimum Bias

The term “minimum bias events“ refers to selecting collisionevents using an inclusive as possible trigger, with the leastamount of selection, kinematic or topological

Define the minimum bias cross section σMB ,

σMB = σSD + σDD + σND + σCD . (1)

Minimum bias events are typically soft hadronic processescharacterized by low momentum transfer between theinteracting particles.

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The Large Hadron Collider

I


Most powerful particleaccelerator built to date

Located near Geneva,Switzerland. Built by CERN.

26.7 km circumferencesynchrotron accelerator

Peak performance - 14 TeV√s, 1034 cm−2s−1

luminosity

Probe of new physics andprecision studies of the SM

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II


Define the luminosity,

L =N2bnbfrevγr4πεnβ∗

F [1

cm2s]. (2)

The average number of interactions per bunch crossing isgiven by,

Nc =LσeventRC

. (3)

For 2010, assuming an inelastic p-p cross section of 57.2± 6.3this is,

Nc '5.1

NB. (4)

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ATLAS

I

ATLAS

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ATLAS

II

ATLAS

A Toroidal LHC ApparatuS, One of four major detectorexperiments at the LHC

Approximately 7000 tonnes, 25 m x 44 m length by width

Inner Detector - Tracking, momentum and vertexmeasurements and electron identification

Calorimetry - energy measurements of particles exceptneutrinos and muons

Muon Spectrometer - tracks charged particles that exit thecalorimeter, measures their momentum

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ATLAS

III

ATLASMinimum Bias Trigger Scintillator (MBTS) is the primarydevice for observing minimum bias events in ATLASDedicated machine for observing minimum bias eventsMounted on the A and C sides of the detector

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Pile-up

I

In-time Pile-up is the phenomena of multiple proton-protoncollisions occuring in one bunch crossing

This is estimated by the number of primary vertices in the event.

The probability of in-time pile-up is governed by Poisson statistics

The probability P(n) for n independent events occuring in onebunch crossing is given by,

P(n) = Ae−λλn

n!. (5)

The number spectrum, λ, is a function of the luminosity, L, bunchseparation, Tc and cross section for the interaction, σpp,

λ = LTcσpp. (6)

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Missing Transverse Energy

I


EMissX = −

N∑i=1

Ei sin θi cosφi , EMissY = −

N∑i=1

Ei sin θi sinφi . (7)

EMissT =

√(EMiss

X )2 + (EMissY )2, (8)

φX ,Y = arctan(EMissY

EMissX

). (9)

The missing transverse energy per event is the negative of the vector sum of theenergy deposited into the calorimeter in an event

Closely related to this concept is the scalar sum given by,

∑ET =

N∑i

Ei sin θi . (10)

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II


EMissX ,Y are constructed as,

EMissX ,Y = EMiss,calo

X ,Y + EMiss,cryoX ,Y + EMiss,muon

X ,Y . (11)

In the case of refined calibrations, EMiss,caloX ,Y is constructed such

that,

EMiss,caloX ,Y = EMiss,e

X ,Y +EMiss,γX ,Y +EMiss,τ

X ,Y +EMiss,jetsX ,Y +EMiss,µ

X ,Y +EMiss,CellOutX ,Y .

(12)

Constructing the MET as seen above will give the measurement atelectromagnetic energy scale

There are two global calibration schemes

Global Cell energy-density Weighting (GCW)

Local Cluster Weighting (LCW)

These correct for dead and malfunctioning cells and correct forhadronic energy signals in the calorimeter

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Data Selection and Monte Carlo

I

Data Selection and Monte Carlo

Our data selection criteria is as follows -

Trigger: L1 MBTS 1

GRL

Timing- LAr Calorimeters- MBTS

Bad jets- HEC Spike- e/m Coherent Noise- Beam Background

Ugly Jets

Track Quality- ≥ 1 Primary vertex, > 5 Tracks, Pt > 150 MeV

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Analysis

Selection I

AnalysisSelection histograms, electromagnetic energy scale

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Analysis

Selection II

AnalysisSelection histograms, GCW energy scale

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Analysis

Selection III

AnalysisSelection histograms, LCW energy scale

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Analysis

Pile-up I

Analysis

Distribution of vertices per event, Data (left) and Monte Carlo (right).

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Analysis

Pile-up II

AnalysisEMissT ,

∑ET , EMiss

X and EMissY . Data (crosses) and Monte Carlo (bars). Electromagnetic energy scale.

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Analysis

Pile-up III

AnalysisEMissT ,

∑ET , EMiss

X and EMissY . Data (crosses) and Monte Carlo (bars). GCW energy scale.

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Analysis

Pile-up IV

AnalysisEMissT ,

∑ET , EMiss

X and EMissY . Data (crosses) and Monte Carlo (bars). LCW energy scale.

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Analysis

Pile-up V

AnalysisAverage

∑ET as a function of the number of primary vertices per event.

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Analysis

Resolution I

Analysis

Let’s quantify the resolution

Parametrize EMissX and EMiss

Y in∑

ET

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Analysis

Resolution II

AnalysisSlice the result in vertical segments of

∑ET .

Each slice is Gaussian distributed in EMissX and EMiss

Y .

If you did this for EMissT , the slices would be Rayleigh distributed.

Add the histograms of EMissX versus

∑ET and EMiss

Y versus∑

ET together- This assumes that σX = σY .Fit each slice of this new 2D histogram to a gaussian function,

f (x) = 1√2πσ2

e−(x−µ)2/2σ2

Plot the values of the fitted σ as a function of the∑

ET , do this for 1 vertexevents, 2 vertex events...so forth

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Analysis

Resolution III

Analysis

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Analysis

Resolution IV

Analysis

Since σX = σY , σT for EMissT goes as,

(∆EMissT )2 = (

∂EMissT

∂EMissX

∆EMissX )2 + (

∂EMissT

∂EMissY

∆EMissY )2 (13)

=(EMiss

X ∆EMissX )2 + (EMiss

Y ∆EMissY )2

(EMissT )2

(14)

∆EMissX = ∆EMiss

Y

= ((EMiss

X )2 + (EMissY )2

(EMissT )2

)(∆EMissX ,Y )2 = (∆EMiss

X ,Y )2 (15)

Thus, if σX = σY , the resolution of EMissX ,Y is the resolution of EMiss

T .

Assumption: EMissX and EMiss

Y are uncorrelated.

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Analysis

Resolution V

Analysis

We quantify the resolution with respect to the∑

ET as,

σX ,Y =√A∑

ET ⊕√B∑

ET , (16)

We are interested in how the behaviour of the resolutionparametrized in

∑ET changes as a function of the number of

primary vertices in events, i.e. in-time pile-up

Qualitatively, from the plots shown above, they don’t really change.

NOTE TO SELF THIS IS: σX ,Y =√

A∑

ET + B(∑

ET )2

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Analysis

Resolution VIII

AnalysisFit Parameters with respect to the resolution for data (left) and Monte Carlo (right).

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Conclusions

I

Conclusions

We analyzed the MET in minimum bias events in the contextof in-time pile-up

Our primary was goal was to study the MET resolution withrespects to in-time pile-up

We find that the MET resolution parametrized in∑

ET doesnot qualitatively change with regards to the number ofprimary vertices

These results are reproduced in Monte Carlo and at e/m,GCW and LCW calibrated energy scales.

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Backup

I

Backup

In addition to the resolution we examined the bias of theMET parametrized in

∑ET and the asymmetry in the φX ,Y

distribution of EMissT

We find a bias in the mean, µX and µY , that is approximatelylinear with respects to

∑ET

We examine this effect by looking at the asymmetry in theφX ,Y distribution, sorted with respects to the number ofprimary vertices per event

We can approximate the asymmetry using a simple model ofdetector misalignment as shown.

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Backup

Resolution IX

Analysis

Is σX = σY ?

Easy to check in terms of∑

ET

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Backup

Resolution X

Analysis

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Backup

Resolution XI

Analysis

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Backup

Mean I

Analysis

How is the mean, µX ,Y , effected by pile-up?

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Backup

Mean II

Analysis

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Backup

Mean III

Analysis

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Backup

Asymmetry I

Analysis

A good way to understand the mean is to examine the

quantity φX ,Y = arctan(EMissY

EMissX

), this is the azimuthal direction

of the EMissT

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Backup

Asymmetry II

Analysis

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Backup

Asymmetry III

Analysis

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Backup

Asymmetry IV

Analysis

We quantify this as amisalignment of the nominaland real origins of the detector

If we source the MET from theincorrect O’ the azimuthalangle φ′ will be related to φ′

by,

φX ,Y = arctan(k + r sinφ′

h + r cosφ′).

(17)

This gives dNdφ′ ,

dN

dφ′∼ h′ cosφ′ + k ′ sinφ′ + 1

h′2 + k ′2 + 1 + 2(h′ cosφ′ + k ′ sinφ′)(18)

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Backup

Asymmetry V

AnalysisWe can see how well this simple model works by making a fit.1 Vertex events at electromagnetic scale from data

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msc thesis

Documents

minimum bias eventsmounted

tev d pileup iintime

minimum bias cross section

tev d atlas iatlas

n independent events

time pileupwe

standard model3 minimum

jet andtrack qualitythe