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

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: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

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, TaitDatta, 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 DimensionsRandall, 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 ~ TeVk/MPl ≲ 0.1

5-d curvature:|R5| = 20k2 < M5

2

Davoudiasl, JLH, Rizzohep-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, RizzoPomarol

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– 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

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

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 = 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

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

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 & 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

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!

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 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

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

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??

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

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

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-obliqueparameters

Scale of unitarity violationin WL scattering

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

Collider Constraints

with Run I data

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

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, 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

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

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