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Extra Dimensions with Many Inverse Femptobarns at the
Tevatron
• Universal Extra Dimensions• Warped Extra Dimensions – Beyond RS1
- SM in the bulk– Brane Kinetic Terms– Extended Manifolds– Higgsless Models of EWSB
• Truly Exotic– Branon Production
J. HewettMini-BSM Workshop
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Universal Extra Dimensions
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Universal Extra Dimensions
• All SM fields in TeV-1, 5d, S1/Z2 bulk• No branes! translational invariance is preserved tree-level conservation of p5
• KK number conserved at tree-level • broken at higher order by boundary terms
• KK parity conserved to all orders, (-1)n
Consequences:1. KK excitations only produced in pairs
Relaxation of collider & precision EW constraints Rc
-1 ≥ 300 GeV
2. Lightest KK particle is stable (LKP) and is Dark Matter candidate
3. Boundary terms separate masses and give SUSY-like spectrum
Appelquist, Cheng, Dobrescu
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Universal Extra Dimensions: Bosonic SUSY
Phenomenology looks like Supersymmetry:
Heavier particles cascade down to LKP
LKP: Photon KK state appears as missing ET
SUSY-like Spectroscopy
Confusion with SUSY if discovered @ LHC !
Chang, Matchev,Schmaltz
Spectrum looks like SUSY !
No Tevatron exp’t limits to date!
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1st Excitation Quark Production @ Tevatron
Production Processes
ii, v, iii
i, iv
Rizzo, hep-ph/0106336
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How to distinguish SUSY from UED I:
Observe KK states in e+e- annihilation
Measure their spin via:
•Threshold production, s-wave vs p-wave•Distribution of decay products
•However, could require CLIC energies...
JLH, Rizzo, TaitDatta, Kong, Matchev
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How to distinguish SUSY from UED II:
Observe higher level (n = 2) KK states:
– Pair production of q2q2, q2g2, V2 V2
– Single production of V2 via (1) small KK number breaking couplings and (2) from cascade decays of q2
Discovery reach @ Tevatron/LHC
Datta, Kong, Matchev
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How to distinguish SUSY from UED III:
Measure the spins of the KK states – Difficult!Decay chains in SUSY and UED:
Form charge asymmetry:
Works for some, but not all, regions of parameter space
Smillie, Webber
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Warped Extra Dimensions
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Localized Gravity: Warped Extra DimensionsRandall, Sundrum
Bulk = Slice of AdS5
5 = -24M53k2
k = curvature scale
Naturally stablized via Goldberger-Wise
Hierarchy is generated by exponential!
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4-d Effective Theory
Phenomenology governed by two parameters: or m1 ~ TeVk/MPl ≲ 0.1
5-d curvature:|R5| = 20k2 < M5
2
Davoudiasl, JLH, Rizzohep-ph/9909255
KK Graviton Wavefunction & Interactions:
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Drell-Yan Production: Randall-Sundrum Graviton Resonances
Tevatron: pp G(1) ℓ+ℓ- 1st & 2nd KK cross sections
Davoudiasl, JLH, Rizzo
Different curves for k/MPl = 0.1 – 1.0
-
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Tevatron limits on RS Gravitons
CDF Drell-Yan spectrum
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Peeling the Standard Model off the Brane
• Model building scenarios require SM bulk fields– Gauge coupling unification– Supersymmetry breaking mass generation– Fermion mass hierarchy– ….
SM gauge fields alone in the bulk violate custodial symmetry!
Gauge boson KK towers have coupling gKK = 8.4gSM !!
Precision EW Data Constrains: m1A > 25 TeV > 100
TeV!Davoudiasl, JLH, RizzoPomarol
Fix 1: Enlarge EW gauge group to SU(2)L x SU(2)R , preserves custodial symmetry Agashe, Sundrum
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Fix 2: Add Fermions in the Bulk
• Introduces new parameter, related to fermion Yukawa– mf
bulk = k, with ~ O(1) and determines location in bulk
• Zero-mode fermions couple weaker to gauge KK states than brane fermions
Precision EW & collider constraints on mass of 1st gauge KK state
towards Planck brane towards TeV brane
Ghergetta, PomarolDavoudiasl, JLH, Rizzo
LHC
Tevatron
k/MPl = 1, 0.1, 0.01
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Graviton Branching Fractions
B = 2Bℓℓ
dijets
tops
leptons
Higgs
gluons
WWZZ/
m1 = 1 TeV
Fermions on TeV brane Fermions in bulk
Davoudiasl, JLH, Rizzo, hep-ph/0006041
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Phenomenology Summary for Bulk Fermions
Davoudiasl, JLH, Rizzo, hep-ph/0006041
Precision EW
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Fix 3: Brane Kinetic Terms• Originally introduced to allow infinite 5th dimension recover 4-d
behavior at short distances • Generated at loop-order from brane quantum effects of
orbifold and/or matter fields on brane• Required as brane counter terms for bulk quantum effects
Brane kinetic terms are naturally present!! Their size is determined by the full UV theory
Appears in the action for bulk fields:SGravity = M5
3/4 d4x rcd (-G) {R(5) + (2/krc)[0() + (-)]R(4)}
SGauge = ∫ d5x [-FMNFMN/(4g52) - (x5) FF/(4ga
2)]
0, are free parameters
Dvali etal
Georgi etal
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BKT’s modify KK spectra – masses & couplings
Randall-Sundrum model: graviton fields in the bulk
KK coupling strength
Davoudiasl, JLH, Rizzo, hep-ph/0305086
e+e- +-
n=1
23…
0 = 0
= 1, -1, -2, -10
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Tevatron Search Reach: RS Gravitons with BKTs
1st Excitation search reach
Davoudiasl, JLH, Rizzo, hep-ph/0305086
Run I Run II, 5 fb-1
Curvature parameter is varied
0 = 0
Allows for very light Gravitons!
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BKT’s modify KK spectra – masses & couplingsRandall-Sundrum model: gauge fields in the bulk
KK coupling strength Precision EW bound on 1st KK state
Davoudiasl, JLH, Rizzo, hep-ph/0212279 See also Carena etal, hep-ph/0212307
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Extend Manifold: AdS5 x S
e+e- +- ( = 1) Drell-Yan (LHC)
Davoudiasl, JLH, Rizzohep-ph/0211377
Gives a forest of KK graviton resonances!
Drastically modifies Graviton KK spectrum!
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Higgsless EWSB
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What good is a Higgs anyway??
• Generates W,Z Masses• Generates fermion Masses
• Unitarizes scattering amplitudes (WLWL WLW L )
Do we really need a Higgs? And get everything we know right….
Our laboratory: Standard Model in 1 extra warped dimension Minimal Particle Content!
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Generating Masses
Consider a massless 5-d field
∂2 = (∂∂ - ∂52 ) = 0
looks like (∂∂ - m2 ) = 0 (KK tower)
The curvature of the 5-d wavefunction is related to its mass
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Toy Example: Flat space with U(1) gauge field in bulk with S1/Z2 Orbifold
A(y) ~ cos (ny/R) A5(y) ~ sin (ny/R)
0 R
0-mode
1st KKOrbifold Boundary Conditions:
∂5A = 0 A5 = 0
0-mode is flat & y independent
m0 = 0
If The Same boundary conditions are applied at both boundaries,0-mode is massless and U(1) remains unbroken
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A(y) ~ n an cos(mny) + bn sin(mny)
∂5A(y) ~ mnn (-an sin(mny) + bn cos(mny)
BC’s: A(y=0) = 0 an = 0
∂5A(y=R) = 0 cos(mnR) = 0
∂5A=0 A=0
1st KK
0-mode
A cannot be flat with theseboundary conditions!
mn = (n + ½)/RThe zero mode is massive!A5 acts as a GoldstoneU(1) is broken
Orbifold Boundary Conditions:
∂5A = 0 A5 = 0
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Exchange gauge KK towers:
Conditions on KK masses & couplings:
(g1111)2 = k (g11k)2
4(g1111)2 M12 = k (g11k)2 Mk
2
Necessary, but not sufficient, to guarantee perturbative unitarity!
Csaki etal, hep-ph/0305237
Unitarity in Gauge Boson Scattering•SM without Higgs violates perturbative unitarity in WLWL WLWL at s ~ 1.7 TeV
•Higgs restores unitarity if mH < TeV What do we do without a Higgs??
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Realistic Framework:
SU(2)L x SU(2)R x U(1)B-L in 5-d Warped bulk
Agashe etal hep-ph/0308036Csaki etal hep-ph/0308038
Planckbrane TeV-brane
SU(2)R x U(1)B-L
U(1)Y
SU(2)L x SU(2)R
SU(2)D
SU(2) Custodial Symmetryis preserved!
WR, ZR get
Planckscale masses
W, Z get TeV scale masses left massless!
BC’s restricted by variation of the action at boundary
Parameters: = g5R/g5L (restricted range) L,Y,B,D brane kinetic terms g5L fixed by GF , = g5B/g5L fixed by MZ
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Gauge KK Spectrum
Effects of Brane terms = 1
Schematic KK Spectra
Every other neutral gauge KKlevel is degenerate!
Brane terms split this degeneracyAnd give lighter KK states
Masses are fixed by modelparameters
n ~ z[an J1(mnz) + bn Y1(mnz)], z=eky/k
Davoudiasl, JLH, Lillie, Rizzohep-ph/0312193,0403300
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What are the preferred gauge KK masses?
Tension Headache:
Colliders
PUV in WW scattering
Precision EW
needs light KK’s
needs heavier KK’s
Important direct constraints
Is there a consistent region of parameter space?
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Precision EW pseudo-obliqueparameters
Scale of unitarity violationin WL scattering
Davoudiasl, JLH, Lillie, Rizzo hep-ph/0312193,0403300
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Collider Constraints
with Run I data
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Monte Carlo Exploration of Parameter space
Over 3M points scannedPoints which pass all constraints except PUV: (none pass PUV!)
Prefers light Z’ with small couplingsPerfect for the Tevatron Run II !!Realistic models put fermions in the bulk
JLH, Lillie, Rizzohep-ph/0407059
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Truly Exotic
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Branon Production
Branon - fields associated with brane fluctuations along extra dimensions. Pseudo-goldstone bosons from spontaneous breaking of translational invariance. Are expected to be light.
Cembranos, Dobado, Morotohep-ph/0405286Creminelli, Strumia, hep-ph/0007267
Interact with SM fields via T
Parameters: N = # of Branons f = Brane tension scale M = Branon mass
•Parity requires branons to be produced in pairs•Branons couple ~ f-1 are weakly interacting, Dark Matter candidates•Appear as missing ET in detector
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Production processes:– gg g, qq g, , qg q– Monojet/photon + missing ET
-
Run I Run II `Projections”N=1
200 pb-1D0 Monojet dataCDF single photon data
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There are numerous discovery opportunities for the Tevatron for the remainder of Run II !