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Randall-Sundrum GravitonsRandall-Sundrum Gravitons

with 1 fbwith 1 fb-1-1 of Data of Data

Amitabha DasAmitabha Das

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February 6, 2007 Amitabha Das 2

Theory

Detector

Analysis

Result

OUTLINEOUTLINE



Standard Model

d

u

s

c

b

t

e

e

Quarks

Leptons

Gluon - Mediator of strong force

Photon - Mediator of electromagnetic force

W and Z0 – Mediators of weak force



NOT a complete theory.. Higgs field is needed to generate mass

Higgs mass ~ W mass.

Try to include gravity – Drives up the higgs mass

Gravitational force much weaker than other forcesin nature.

“ Hierarchy Problem ”



Solution ??

New mechanism where the higgs mass doesn’t go up in Planck scale

OR

The fundamental Plack scale is not so big.

Theories based on the idea of extra dimension tryto look into the second possibility.



One extra dimension in addition to the (1+3)-dimensional space-time.

There are two branes embedded in this five-dimensional bulk.

Visible brane : Contains the Standard model fields Invisible brane : Only gravitational field can propagate to this brane.

Randall-Sundrum Model

Lisa Randall and Raman Sundrum, Phys. Rev. Lett. 83, 3370 (1999)



Visible braneContain SM field.

Gravity is weak.

Invisible braneGravity is strong.

Fundamentally gravitational force is strong.

Wave function exponentially suppressed away from the invisible (Planck) brane.

Exponentially suppressed



Phenomenology How we search for gravitons

Graviton – Mediator of gravitational force.

Theory predicts graviton decays to fermion or boson pair

We look for excited graviton through the final states :

GeeG &



Free Parameters

In RS Model there are two free parameters :

1. Mass of the excited state of Graviton M1

2. Coupling to standard model field k√8/MPl - 0.01 to 0.1



DO Detectorat

Fermilab



Calorimeters Tracker

Muon System

Beamline Shielding

Electronics

protons

20 m

TrackerCalorimeter

Anti-proton



Tracking System

Track reconstruction of

the charged particles.

Silicon Tracker

Fiber Tracker

Calculates the

momentum of the

charged particle.

Solenoidal magnetic

field



Silicon Microstrip Tracker (SMT) and

Central Fiber Tracker (CFT)

CFT together with SMT enables track

reconstruction of the charged particles.

Whole tracker inside a 2T magnetic field .

Measure the momentum from the curvature

of the charged particle.



Calorimeter

Measurement of particle energy and particle Identification.



D0 Trigger System


D0 Trigger System

Silicon Track Trigger Silicon Track Trigger (STT)(STT)

No STT triggerused in this

analysis.


Idea behind STT

Main Goal – Fast selection of events with ‘b’ quarks.

Selecting tracks with large Impact Parameter.


STT Conceptual Schematic

Cluster

CFT Data

SMT Data

FiberRoadCard

SiliconTrigger

Card

Hits

Track Fit CardRoad

Silicon Trigger Card (STC) Makes clusters using the SMT. Using “road” data get the clusters within road : Hits.

To L2

Ro

ad


STT Crate LayoutSTT Crate Layout


STT Mother BoardSTT Mother Board


Six STT Sector Crates


Performance of STT

STT trigger included in the D0 trigger list since Summer 2005.

Efficiency

How well STT tracks match with offline reconstructed tracks.

(The D0 Run II Impact Parameter Trigger, physics/0701195)


DefinitionsDefinitions


0 1

2

p p

]2

ln[tan

5.2

Y

Z

X

Pseudo-rapidity


22yxT ppp

Transverse Momentum


Integrated Luminosity Instantaneous luminosity : Number of interaction per unit cross-section, per unit time

Integrated luminosity : Integrate over a period of time

t

InstIntegrated LdtL0

.)(

Unit : 1/cross-section

Lintegrated x Cross-section = Number of events



Object Object IdentificationIdentification


Electron and Photon IdentificationElectron and Photon Identification

Electrons and photons deposit most of their energyin the electromagnetic (EM) calorimeter

1. Identify a region in the EM calorimeter with high energy deposition

2. Several variables to characterize a shower originating from an electron or photon



Some of the variables …

1. What fraction of the total energy is deposited in the electromagnetic calorimeter region.

2. In an event with electron or photon as final state, they should be isolated from other particles, a measure of, by how much the electrons or photons are isolated. 3. Shower shape : A shower originating from electrons or photons is narrow and does NOT penetrate deep in the calorimeter compared to a shower originating from other particles.


Analysis



Data :

Data used for this analysis was taken between Oct. 2002 and Feb. 2006.

Monte Carlo (Simulation) :

Simulated events were used for background prediction and signal efficiency.

All the events were generated using PYTHIA



Graviton

Mass

(LO) No. of events

generated

200 GeV 28.7 pb 1000

350 GeV 20.2 pb 1000

500 GeV 0.34 pb 1000

600 GeV 0.12 pb 1000

700 GeV 0.041 pb 1000

800 GeV 0.015 pb 1000

900 GeV 0.005 pb 1000

Invariant

Mass

(LO) No. of events

generated

60-130 GeV 188 pb 109000

130-250 GeV 1.3 pb 27000

250-500 GeV 0.10 pb 27000

>500 GeV 0.004 pb 25000

Invariant

Mass

(LO) No. of events

generated

45-150 GeV 29 pb 50000

150-300 GeV 1.0 pb 5000

300-500 GeV 0.11 pb 2000

>500 GeV 0.01 pb 3000

Monte Carlo (MC) Samples

Signal (graviton) MC

Drell-Yan MC

Direct diphoton MC



DATA Event Selection

Signal + BackgroundEstimate Background

Excess Signal

No Excess

DISCOVERY

Set Upper Limit of cross-section

at 95% confidence level



Event Selection

Final state : e+e- and gamma gamma

Events having two electromagnetic (EM) objects

Both the EM objects should be in the central calorimeter region

< 1.1.

Require both the EM object to have

Transverse momentum : pT > 25 GeV In addition some quality cuts were applied.

||Do not distinguish

betweenelectron and photon


Sources of Background Standard model background :

Drell-Yan

Direct diphoton

Estimate contribution : Use simulated events

Instrumental Background :

Misidentified electromagnetic objects

Estimate contribution : Get sample rich in misidentified

electromagnetic object from data by applying reverse quality cuts



Background Estimation

Step 1 :Fit the invariant mass spectra at low mass region

SMQCDData NWNWN )1(

NSM = Invariant mass spectra from Drell-Yan + Diphoton

NQCD = Invariant mass spectra from instrumental background

Invariant Mass Spectra :

Calculate the invariant mass for the events which pass the

“Event Selection” cuts



Data

=

W + (1-W)

Instrumentalbackground.

Standard Modelbackground.

Get the weight “W” corresponding to the best fit

Fit region



Fit at Low Mass



Step 2 : Apply the weight ‘W’ to the full mass spectra



How a signal would look like …

350 GeV

600 GeV

900 GeV


DATA Event Selection

Signal + BackgroundEstimate Background

Excess Signal

No Excess

DISCOVERY

Set Upper Limit of cross-section

at 95% confidence level



Set 95% Confidence LimitSet 95% Confidence Limit

Total probability of having Total probability of having cross-section < cross-section < UpperUpper is 95% is 95%



Calculating upper limit of Signal cross-section (u ) at 95% confidence

limit

The number of observed events N is given by:

N = b + L b=background=cross-section = efficiencyL = Integrated luminosity

P(A | B) = Probability of proposition A when

proposition B is true.

(x | B) = Probability of the continuous variable

between x and x+dx when proposition B is

true. Probability density.



The upper limit (u ) at 95% CL is defined as:

u

Ikd

0

),|(95.0I – All prior information

k - No. of observed events

If we know (|k,I) then the solution of the

above integration gives the upper limit at 95%

confidence level.



Limit Limit CalculatorCalculator

Data

Background +/- Err

Efficiency +/- Err

Luminosity +/- Err

Upper Limit

Inputs for the limit calculatorInputs for the limit calculator



Calculate Integrated Luminosity

From normalized background spectra -Get number of Drell-Yan events, N = 280162

The drell-yan cross-section is 254 +/- 10 pbR. Hamberg, W. L. Van Neerven, and T. Matsura, Nucl. Phys. B359, 343 (1991)

Get luminosity = 1.1 +/- 0.04 fb-1

YanDrellYanDrell LN _


Mass Window

Get Data and Background

Data: N = No. of events in a mass window Background: B = Total background in same mass window



Signal EfficiencySignal Efficiency

N = Number of RS Graviton Monte Carlo events for a given mass

n = Number of events that pass selection cuts + mass window cut

N

nEff .

UncertaintiesPRL 95, 091801

Uncertainty on background ~ 9%Uncertainty on efficiency ~ 10%



We set upper limit on cross-section for :We set upper limit on cross-section for :

)()( eeGBXGpp

)(2)( eeGBGB It is found :

Quoting limit for : )( eeGB3

UpperCalculatedUpper


N = 0

b = 0.08 +/- 0.007

L = 1.1 fb-1

= 0.338 +/- 0.033

u

Ikd

0

),|(95.0

fbu 7.2

Example: M=900 GeV









Preliminary ResultICHEP 2006

At 95% Confidence LevelAt 95% Confidence Level

Graviton Mass < Graviton Mass < 865 GeV865 GeV excluded for coupling 0.1 excluded for coupling 0.1

Graviton Mass < Graviton Mass < 240 GeV240 GeV excluded for coupling 0.01 excluded for coupling 0.01



Thank YouThank You




Search for Randall-Sundrum Gravitons with 1 fb -1 of Data Amitabha Das.

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