Brane World Phenomenology

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Brane World Phenomenology
Brane World Phenomenology
Sreerup Raychaudhuri IIT Kanpur

• Sreerup Raychaudhuri
• IIT Kanpur

Sreerup Raychaudhuri IIT Kanpur
From Strings to the LHC Goa, January 2007
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New Physics at a TeV

• Hierarchy Problem to stabilize Higgs boson
  mass
• Grand Unification to bend running coupling
  graphs
• Neutrino Masses a large mass for seesaw

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It is entirely possible that physics at new and
even smaller length scales will be of a
completely unimagined nature, and will require a
much deeper insight into the nature of the
physical world, just as the quark model might
have appeared in the days of Dalton or even of
Thomson and Rutherford
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Brane Worlds the idea
An entire new world is just waiting be revealed
at a (few) TeV

• extra dimensions
• strong quantum gravity
• grand unification
• strings and stringy excitations
• laboratory black holes
• new spacetime structures?

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Brane World Phenomenology the idea
Cis-Planckian phenomenology
We should be able to detect effects of the
low-energy effective theory at (few) 100 GeV
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Trans-Planckian phenomenology
We should be able to see strong gravity effects,
(e.g. black holes, stringy excitations) around or
above the (TeV-order) Planck scale
The LHC stands at the junction of these two
regimes
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Requirements for a New Physics Discovery, esp.
Brane Worlds

• Model(s) with clear and unambiguous numerical
  predictions
• Clever strategies to isolate the signals from
  the backgrounds
• A lot of luck

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Brane World Models
Large (Flat) Extra Dimensions ADD Model
Extensions mainly missing energy signals
Warped Compactification RS Model
Extensions signals for WIMPs
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Both paradigms work if there is a mechanism to
confine the experiment(alist) within the four
Minkowski dimensions i.e. the extra dimensions
are seen by gravity alone
Graviton detection experiments
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ADD Model Gravitational lines of force are
dispersed in the large extra dimensional bulk and
only a small number are observed in
four-dimensional experiments gravitational
force is weakened in proportion - N.
Arkani-Hamed, S. Dimopoulos and G. Dvali
(1998)
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FLAT GEOMETRY
Open strings ? Gauge fields Closed strings ?
MasslessGravitons
3-brane
R
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RS Model Gravity is strong in some other region
of spacetime, and rapidly loses strength as it
shines on our four-dimensional spacetime
force is weakened exponentially according to
distance - L. Randall and R. Sundrum
(1999)
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WARPED GEOMETRY
R
Planck brane
TeV brane
AdS5 throat
Metric contracts exponentially along AdS5
throat ? Gravitons acquire TeV masses
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Phenomenology of the ADD model
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Einstein-Hilbert action in 4d dimensions
Integrate over bulk for large objects
Cis-Planckian regime
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Eöt-Wash experiment
2003 data
For ?1
? lt 150 ?m
Eventually
? lt 60 ?m
Compare with
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Bulk scale versus Planck scale
on a d-torus
Eöt-Wash experiment
Possible to have TeV effects if d gt 2
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Kaluza-Klein decomposition
Massless bulk graviton
T. Kaluza
Fourier series on a d-torus
Massive gravitons on the brane
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Graviton mass is just the momentum component in
the extra dimensions
? creation of a massive graviton is equivalent to
momentum going into the extra dimensions.
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On the brane
Tower of Kaluza-Klein states
Spacing between states
No of contributing states
A massless bulk graviton is like a huge swarm of
massive graviton fields on the brane
quasicontinuum
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Position of the brane is at
Standard Model fields live only on the brane
Interaction with single bulk graviton field is
the same as interaction with a swarm of massive
graviton fields on the brane
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Feynman Rules for the ADD model
all scalars
Han, Lykken and Zhang, Phys Rev D59, 105006
all gauge bosons
all fermions
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Collider physics with gravitons/dilatons

• Graviton tower couples to every
  particle-antiparticle pair
• Blind to all quantum numbers except
  energy-momentum
• Each Kaluza-Klein mode couples equally, with
  strength ?
• Tower of Kaluza-Klein modes builds up
  collectively to an observable effect
• Individual graviton modes escape detection ?
  missing

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• Gravitonic signals will show
• excess over Standard Model cross-sections
• detectable if the excess is larger than the
  experimental errors in measuring the
  cross-section crucially dependent on machine
  luminosity and time of running.
• different distributions due to spin-2 nature
• detectable if the signal is large enough and
  the SM signal shows some characteristics of spin
  0 or spin 1 exchanges
• energy and momentum imbalance
• collective effect of escaping gravitons

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REAL GRAVITONS
Incoherent sum
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VIRTUAL GRAVITONS
Coherent sum
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Sum over KK states can be done using the
quasi-continuum approach
Sum over propagators
reduces to a contact interaction
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Important processes at colliders
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Important issues in ADD phenomenology
1. Find out if there are signals for KK towers of
gravitons - large-pT excess, missing
energy, etc. 2. Determine whether the signals are
indeed due to brane-world gravitons and not some
other new physics - gravitons would be
blind to all SM quantum numbers 3. Identify
these particles (if seen) as graviton modes
- spin-2 nature is a dead giveaway
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• 4. Find out the no of large extra dimensions -
  features in density-of-states function
• 5. Find out the radius of compactification RC,
  or equivalently, the bulk Planck scale (string
  scale MS) - controls the coupling strength
• 6. Find out the geometry of the extra dimensions
  - gravity experiments, stringy excitations?
• 7. Find out dynamics which makes some dimensions
  large some small - underlying string theory

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CMS Detector
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Must have concrete numerical predictions

• Cross-section calculations
• Determination of kinematic cuts
• Choice of kinematic variables
• Monte Carlo simulations
• Detector simulations

Must be comparable with the data eventually
available
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Real Gravitons Single Photon Signal
Mirabelli, Peskin, Perelstein (1998)
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Giudice, Rattazzi, Wells (1999)
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a ? hard truncation b ? no truncation
Giudice, Rattazzi, Wells (1999)
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Real Gravitons Monojet Signal
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a ? hard truncation b ? no truncation
Giudice, Rattazzi, Wells (1999)
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Laboratory Bounds on String Scale
D0 monojet CDF single photon ADLO
single photon (Giudice Strumia 2003)
Abazov, et al., (2003)
Completely cis-Planckian
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Comparative experimental bounds on string scale
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Realistic Simulation
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Virtual Gravitons Drell-Yan Leptons
Sum over propagators diverges cutoff
Hard truncation again
Effectively like a contact interaction
? will not be subject to s-channel suppression
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Virtual Gravitons Drell-Yan Leptons
2.5
4.0
MS
SM
Bin integrated dilepton invariant mass
distribution for Drell-Yan production (MS 2.5
and 4.0 TeV at LHC)
95 C.L. search reach for MS as a function of
the integrated luminosity at LHC
J.L. Hewett (1999)
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Virtual Gravitons Diphotons
ATLAS
MS 4 TeV
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Angular Distribution Diphotons
Central peaking is not characteristic enough
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Angular Distribution in C-o-M Frame
graviton
Godbole Rai SR
Choudhury Rai SR
Spin-2 nature
Requires event-by-event reconstruction of C-o-M
frame
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TransPlanckian phenomenon Laboratory Black Holes
S.B. Giddings, S. Thomas, PRL 65 (2002) 056010
S. Dimopoulos, G. Landsberg, PRL 87 (2001)
161602
Hawking radiation
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Only semi-classical treatment possible
About 107 BHs per year _at_LHC
Rapid evaporation by Hawking radiation
CATFISH generator (2006)
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Simulation of a micro black hole production and
decay event at the LHC (de Roeck 2003)
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Phenomenology of the RS model
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Kaluza-Klein modes of the RS bulk graviton field
Small fluctuations around vacuum metric
Goldberger and Wise (1999) Davoudiasl, Hewett
and Rizzo
Equation of motion
Fourier expansion of graviton field
Warped harmonics
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Conformal coordinates
Eigenvalue equation
Bessel equation of order 2
Warped harmonics
Require harmonics to be continuous at the
orbifold fixed points
?
Electroweak scale
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Graviton interaction with matter
Zero (massless) mode gives usual Einstein gravity
Massive (attenuated) modes have electroweak
strength couplings
RS Gravitons are like WIMPs masses and
couplings both resemble electroweak particles
Feynman rules same as in ADD model apart from
warp-up factor
Two free parameters
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RS graviton phenomenology

• Seek to produce the massive RS graviton modes
  on-shell basically search for resonances
  Cross-section driven by coupling c0 and width ?
• RS graviton width grows rapidly with graviton
  mass
• Only first three modes can form narrow resonances
• For large part of parameter space only first
  resonance is viable
• RS gravitons decay to all particle pairs
  Maximum BR is to jets sizeable width to WW and
  ZZ Cleanest modes at LHC are ee- and ??

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Graviton Branching Ratios
Same for all KK modes
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Virtual Gravitons Sum over propagators
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Graviton resonances
Davoudiasl, Hewett and Rizzo
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• No contributions to oblique parameters at LEP-1
• ? lightest RS graviton is heavier than 140 GeV
• No deviations from SM at LEP-2
• ? lightest RS graviton is heavier than 210 GeV
• Tevatron Drell-Yan data show no deviations
  either
• ? lightest RS graviton is heavier than 850 GeV
• LC smaller ?s but clean final states
• graviton resonances in Bhabha scattering and
  ee- ? ??-

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Combined Bounds on Parameter Space
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LHC
C. Collard (ATLAS) 2004
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C. Collard (ATLAS) 2004
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C. Collard (ATLAS) 2004
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m0 400 GeV
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Comments on Drell-Yan dielectron study
C. Collard (ATLAS) 2004
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Angular Distribution in C-o-M Frame
Resonant production of G1
ATLAS
Allanach et al (2000)
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Modulus stabilization and the radion
Warping is extremely sensitive to RC
Consider the radius of the extra dimension as a
dynamical object
Modulus field
Radion field
Radion is a free field i.e. it can assume any
value ? same for modulus
Need for modulus stabilization
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Goldberger-Wise mechanism
Assume a bulk scalar field
Write down a ?B4 theory in the bulk and on the
two branes
Solving the equation of motion for ?(x) and
integrating over y leads to potential with a
steep minimum at
Can assume the desired value ( 11.6) without
assuming any large/small numbers
Undetermined parameters radion mass
radion vev
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Radion couplings are very Higgs-like
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Radion phenomenology

• Radion phenomenology is rather similar to Higgs
  phenomenology for tree-level processes
• Possibility of Higgs-radion mixing
• Giudice, Rattazzi, Wells (2000)
• Huitu, Datta (2002)
• Radionstrahlung process
• Production is just like Higgs-strahlung
• At one-loop, effect of kinetic terms in
  radion-fermion couplings becomes important
• Try to identify radion by its somewhat different
  decay widths to gluons (one-loop) i.e. dijet
  decay mode

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Radion Branching Ratios
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Light radion decays primarily to gluon jets
light Higgs decays primarily to b-jets Use
b-tagging to compare cross-sections for
and
Ratio shows distinct difference
Das, Rai, SR, PLB 2005
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Radions_at_LHC
Huge QCD backgrounds for jet production
Final state diphoton dijet (b-tagged)
CMS Most promising
Other possibilities
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Main Issues in RS Phenomenology
1. Find out signals for graviton resonances -
bump hunting 2. Determine whether the
resonances are indeed RS gravitons and not some
other new physics - RS graviton masses
are spaced like zeros of Bessel function J1
3. Identify these resonances as graviton modes
- spin-2 nature is a dead giveaway
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4. Find out the mass and coupling parameters -
mass and width measurements (like W,Z at
Tevatron) 5. If the resonances are broad
distinguish between RS and ADD models ILC
study by Rai and SR 6. Find out if there are
signals for radions - very similar to Higgs
search 7. Distinguish the radion from a Higgs
scalar ILC study by Das, Rai and SR
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Thought for the Day
Science can be defined as a method for, and a
body of information obtained by, trying to answer
only questions which can be put in the form If I
do this, what will happen? The technique
fundamentally is Try it and see. Then you put
together a large amount of information from such
experiences.
R.P. Feynman
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Further Thought for the Day
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All eyes are now on the LHC experiments
Startup summer 2007 Commissioning end 2007
? After one year 12 fb-1
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THANK YOU