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Randall-Sundrum GravitonsRandall-Sundrum Gravitons
with 1 fbwith 1 fb-1-1 of Data of Data
Amitabha DasAmitabha Das
February 6, 2007 Amitabha Das 2
Theory
Detector
Analysis
Result
OUTLINEOUTLINE
February 6, 2007 Amitabha Das 3
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
February 6, 2007 Amitabha Das 4
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 ”
February 6, 2007 Amitabha Das 5
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.
February 6, 2007 Amitabha Das 6
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)
February 6, 2007 Amitabha Das 7
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
February 6, 2007 Amitabha Das 8
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 &
February 6, 2007 Amitabha Das 9
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
February 6, 2007 Amitabha Das 10
DO Detectorat
Fermilab
February 6, 2007 Amitabha Das 11
Calorimeters Tracker
Muon System
Beamline Shielding
Electronics
protons
20 m
TrackerCalorimeter
Anti-proton
February 6, 2007 Amitabha Das 12
Tracking System
Track reconstruction of
the charged particles.
Silicon Tracker
Fiber Tracker
Calculates the
momentum of the
charged particle.
Solenoidal magnetic
field
February 6, 2007 Amitabha Das 13
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.
February 6, 2007 Amitabha Das 14
Calorimeter
Measurement of particle energy and particle Identification.
February 6, 2007 Amitabha Das 15
D0 Trigger System
February 6, 2007 Amitabha Das 16
D0 Trigger System
Silicon Track Trigger Silicon Track Trigger (STT)(STT)
No STT triggerused in this
analysis.
February 6, 2007 Amitabha Das 17
Idea behind STT
Main Goal – Fast selection of events with ‘b’ quarks.
Selecting tracks with large Impact Parameter.
February 6, 2007 Amitabha Das 18
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
February 6, 2007 Amitabha Das 19
STT Crate LayoutSTT Crate Layout
February 6, 2007 Amitabha Das 20
STT Mother BoardSTT Mother Board
February 6, 2007 Amitabha Das 21
Six STT Sector Crates
February 6, 2007 Amitabha Das 22
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)
February 6, 2007 Amitabha Das 23
DefinitionsDefinitions
February 6, 2007 Amitabha Das 24
0 1
2
p p
]2
ln[tan
5.2
Y
Z
X
Pseudo-rapidity
February 6, 2007 Amitabha Das 25
22yxT ppp
Transverse Momentum
February 6, 2007 Amitabha Das 26
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
February 6, 2007 Amitabha Das 27
Object Object IdentificationIdentification
February 6, 2007 Amitabha Das 28
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
February 6, 2007 Amitabha Das 29
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.
February 6, 2007 Amitabha Das 31
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
February 6, 2007 Amitabha Das 32
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
February 6, 2007 Amitabha Das 33
DATA Event Selection
Signal + BackgroundEstimate Background
Excess Signal
No Excess
DISCOVERY
Set Upper Limit of cross-section
at 95% confidence level
February 6, 2007 Amitabha Das 34
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
February 6, 2007 Amitabha Das 35
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
February 6, 2007 Amitabha Das 36
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
February 6, 2007 Amitabha Das 37
Data
=
W + (1-W)
Instrumentalbackground.
Standard Modelbackground.
Get the weight “W” corresponding to the best fit
Fit region
February 6, 2007 Amitabha Das 39
Step 2 : Apply the weight ‘W’ to the full mass spectra
February 6, 2007 Amitabha Das 40
How a signal would look like …
350 GeV
600 GeV
900 GeV
February 6, 2007 Amitabha Das 41
DATA Event Selection
Signal + BackgroundEstimate Background
Excess Signal
No Excess
DISCOVERY
Set Upper Limit of cross-section
at 95% confidence level
February 6, 2007 Amitabha Das 42
Set 95% Confidence LimitSet 95% Confidence Limit
Total probability of having Total probability of having cross-section < cross-section < UpperUpper is 95% is 95%
February 6, 2007 Amitabha Das 43
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.
February 6, 2007 Amitabha Das 44
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.
February 6, 2007 Amitabha Das 45
Limit Limit CalculatorCalculator
Data
Background +/- Err
Efficiency +/- Err
Luminosity +/- Err
Upper Limit
Inputs for the limit calculatorInputs for the limit calculator
February 6, 2007 Amitabha Das 46
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 _
February 6, 2007 Amitabha Das 47
Mass Window
Get Data and Background
Data: N = No. of events in a mass window Background: B = Total background in same mass window
February 6, 2007 Amitabha Das 48
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%
February 6, 2007 Amitabha Das 49
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
February 6, 2007 Amitabha Das 50
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
February 6, 2007 Amitabha Das 54
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
February 6, 2007 Amitabha Das 56
February 6, 2007 Amitabha Das 57
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