# Presentation: 071077

## 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. Hewett

- Mini-BSM Workshop

## Universal Extra Dimensions

## 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:_
- KK excitations only produced in pairs
- Relaxation of collider & precision EW constraints
-      Rc-1 ≥ 300 GeV
- Lightest KK particle is stable (LKP) and is Dark Matter candidate
- Boundary terms separate masses and give SUSY-like spectrum

- Appelquist, Cheng, Dobrescu

## 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!

## 1st Excitation Quark Production @ Tevatron

- Production Processes

- ii, v, iii

- i, iv

- Rizzo, hep-ph/0106336

## 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, Tait
- Datta, Kong, Matchev

## 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

## 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

## Warped Extra Dimensions

## Localized Gravity:  Warped Extra Dimensions

- Randall, Sundrum

- Bulk = Slice of AdS5
- 5 = -24M53k2
- k = curvature scale

- Naturally stablized via Goldberger-Wise

- Hierarchy is generated by exponential!

##     4-d Effective Theory

- Phenomenology governed by two parameters:
-  or m1 ~ TeV
- k/MPl ≲ 0.1

- 5-d curvature:
- |R5| = 20k2 < M52

- Davoudiasl, JLH, Rizzo
- hep-ph/9909255

- KK Graviton Wavefunction & Interactions:

## 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

**-**

## Tevatron limits on RS Gravitons

- CDF Drell-Yan spectrum

## 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, Rizzo
- Pomarol

- Fix 1:  Enlarge EW gauge group to SU(2)L x SU(2)R , preserves
-            custodial symmetry

- Agashe, Sundrum

## Fix 2:  Add Fermions in the Bulk

- Introduces new parameter, related to fermion Yukawa
- mfbulk = 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, Pomarol
- Davoudiasl, JLH, Rizzo

- LHC

- Tevatron

- k/MPl = 1, 0.1, 0.01

## Graviton Branching Fractions

**B******** = 2B****ll**

- dijets

- tops

- leptons

- Higgs

- gluons

- WW

- ZZ/

**m****1**** = 1 TeV**

- Fermions on TeV brane                       Fermions in bulk

- Davoudiasl, JLH, Rizzo, hep-ph/0006041

- _Phenomenology Summary for Bulk Fermions_

- Davoudiasl, JLH, Rizzo, hep-ph/0006041

- Precision EW

## 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 = M53/4  d4x rcd (-G) {R(5) + (2/krc)[0() + (-)]R(4)}
- SGauge = ∫ d5x [-FMNFMN/(4g52) - (x5) FF/(4ga2)]
-                                           0,  are free parameters

- Dvali etal

- Georgi etal

## 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

- 2
- 3
- ...

- 0 = 0

-  = 1, -1, -2, -10

##   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!

## BKT’s modify KK spectra – masses & couplings

- Randall-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

## Extend Manifold:  AdS5 x S

- e+e- +-   ( = 1)

- Drell-Yan (LHC)

- Davoudiasl, JLH, Rizzo
- hep-ph/0211377

- Gives a forest of KK graviton resonances!

- Drastically modifies Graviton KK spectrum!

## Higgsless EWSB

## 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!

## 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

## 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 KK

- Orbifold 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

## A(y) ~ n an cos(mny) + bn sin(mny)

∂5A(y) ~ mnn (-an sin(mny) + bn cos(mny)

BC’s:     A(y=0) = 0       an = 0
           ∂5A(y=R) = 0    cos(mnR) = 0  

- ∂5A(y) ~ mnn (-an sin(mny) + bn cos(mny)
- BC’s:     A(y=0) = 0       an = 0
-            ∂5A(y=R) = 0    cos(mnR) = 0

- ∂5A=0

- A=0

- 1st KK

- 0-mode

- A cannot be flat with these
- boundary conditions!

- mn = (n + 1⁄2)/R

- The zero mode is massive!
- A5 acts as a Goldstone
- U(1) is broken

- Orbifold Boundary Conditions:
-               ∂5A  = 0
-                   A5 = 0

## Exchange gauge 
KK towers:

- KK towers:

- Conditions on KK masses & couplings:
- (g1111)2 = k (g11k)2
- 4(g1111)2 M12 = k (g11k)2 Mk2

- 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??

## Realistic Framework:

- SU(2)L x SU(2)R x U(1)B-L  in 5-d Warped bulk

- Agashe etal hep-ph/0308036
- Csaki etal hep-ph/0308038

- Planck
- brane

- 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 Symmetry
- is preserved!

- WR, ZR get Planck
- scale 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

## Gauge KK Spectrum

- Effects of Brane terms

-  = 1

- Schematic KK Spectra

- Every other neutral gauge KK
- level is degenerate!

- Brane terms split this degeneracy
- And give lighter KK states

- Masses are fixed by model
- parameters

- n ~ z[an J1(mnz) + bn Y1(mnz)],  z=eky/k

- Davoudiasl, JLH, Lillie, Rizzo
- hep-ph/0312193,0403300

## 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?

## Precision EW pseudo-oblique

- parameters

- Scale of unitarity violation
- in WL scattering

- Davoudiasl, JLH, Lillie, Rizzo hep-ph/0312193,0403300

## Collider Constraints

- _Collider Constraints_

- with Run I data

## Monte Carlo Exploration of Parameter space

- Over 3M points scanned

- Points which pass all constraints except PUV:  (none pass PUV!)

- Prefers light Z’ with small couplings
- Perfect for the Tevatron Run II !!
- Realistic models put fermions in the bulk

- JLH, Lillie, Rizzo
- hep-ph/0407059

## Truly Exotic

## 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, Moroto
- hep-ph/0405286
- Creminelli, 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

## Production processes:
gg  g, qq  g, , qg  q
Monojet/photon + missing ET  

- gg  g, qq  g, , qg  q
- Monojet/photon + missing ET

- -

- Run I

- Run II `Projections”

- N=1

- 200 pb-1

- D0 Monojet data
- CDF single photon data

## There are numerous discovery opportunities for the Tevatron for the remainder of Run II !