1. 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

2. Universal Extra Dimensions

3. All SM fields in TeV -1, 5d, S 1 /Z 2 bulk No branes!  translational invariance is preserved  tree-level conservation of p 5 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 R c -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

4. Universal Extra Dimensions: Bosonic SUSY Phenomenology looks like Supersymmetry: Heavier particles cascade down to LKP LKP: Photon KK state appears as missing E T SUSY-like Spectroscopy Confusion with SUSY if discovered @ LHC ! Chang, Matchev,Schmaltz Spectrum looks like SUSY ! No Tevatron exp’t limits to date!

5. 1 st Excitation Quark Production @ Tevatron Production Processes ii, v, iii i, iv Rizzo, hep-ph/0106336

6. 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

7. How to distinguish SUSY from UED II: Observe higher level (n = 2) KK states: –Pair production of q 2 q 2, q 2 g 2, V 2 V 2 –Single production of V 2 via (1) small KK number breaking couplings and (2) from cascade decays of q 2 Discovery reach @ Tevatron/LHC Datta, Kong, Matchev

8. 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

9. Warped Extra Dimensions

10. Localized Gravity: Warped Extra Dimensions Randall, Sundrum Bulk = Slice of AdS 5  5 = -24M 5 3 k 2 k = curvature scale Naturally stablized via Goldberger-Wise Hierarchy is generated by exponential!

11. 4-d Effective Theory Phenomenology governed by two parameters:   or m 1 ~ TeV k/M Pl ≲ 0.1 5-d curvature: |R 5 | = 20k 2 < M 5 2 Davoudiasl, JLH, Rizzo hep-ph/9909255 KK Graviton Wavefunction & Interactions:

12. Drell-Yan Production: Randall-Sundrum Graviton Resonances Tevatron: pp  G (1)  ℓ + ℓ - 1 st & 2 nd KK cross sections Davoudiasl, JLH, Rizzo Different curves for k/M Pl = 0.1 – 1.0 -

13. Tevatron limits on RS Gravitons CDF Drell-Yan spectrum

14. 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 g KK = 8.4g SM !! Precision EW Data Constrains: m 1 A > 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

15. Fix 2: Add Fermions in the Bulk Introduces new parameter, related to fermion Yukawa –m f 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 1 st gauge KK state towards Planck branetowards TeV brane Ghergetta, Pomarol Davoudiasl, JLH, Rizzo LHC Tevatron k/M Pl = 1, 0.1, 0.01

16. 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

17. Phenomenology Summary for Bulk Fermions Davoudiasl, JLH, Rizzo, hep-ph/0006041 Precision EW

18. Fix 3: Brane Kinetic Terms Originally introduced to allow infinite 5 th 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: S Gravity = M 5 3 /4  d 4 x r c d   (-G) {R (5) + (2/kr c )[  0  (  ) +    (  -  )]R (4) } S Gauge = ∫ d 5 x [-F MN F MN /(4g 5 2 ) -  (x 5 ) F  F  /(4g a 2 )]  0,   are free parameters Dvali etal Georgi etal

19. 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-  +-e+e-  +- n=1 23…23…  0 = 0   = 1, -1, -2, -10

20. Tevatron Search Reach: RS Gravitons with BKTs 1 st Excitation search reach Davoudiasl, JLH, Rizzo, hep-ph/0305086 Run IRun II, 5 fb -1 Curvature parameter is varied  0 = 0 Allows for very light Gravitons!

21. BKT’s modify KK spectra – masses & couplings Randall-Sundrum model: gauge fields in the bulk KK coupling strength Precision EW bound on 1 st KK state Davoudiasl, JLH, Rizzo, hep-ph/0212279See also Carena etal, hep-ph/0212307

22. Extend Manifold: AdS 5 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!

23. Higgsless EWSB

24. What good is a Higgs anyway?? Generates W,Z Masses Generates fermion Masses Unitarizes scattering amplitudes (W L W L  W L W 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!

25. Generating Masses Consider a massless 5-d field ∂ 2  = (∂  ∂  - ∂ 5 2 )  = 0 looks like (∂  ∂  - m 2 )  = 0 (KK tower) The curvature of the 5-d wavefunction  is related to its mass

26. Toy Example: Flat space with U(1) gauge field in bulk with S 1 /Z 2 Orbifold A  (y) ~ cos (ny/R) A 5 (y) ~ sin (ny/R) 0 RR 0-mode 1 st KK Orbifold Boundary Conditions: ∂ 5 A  = 0 A 5 = 0 0-mode is flat & y independent  m 0 = 0 If The Same boundary conditions are applied at both boundaries, 0-mode is massless and U(1) remains unbroken

27. A(y) ~  n a n cos(m n y) + b n sin(m n y) ∂ 5 A(y) ~ m n  n (-a n sin(m n y) + b n cos(m n y) BC’s: A(y=0) = 0  a n = 0 ∂ 5 A(y=  R) = 0  cos(m n  R) = 0 ∂ 5 A  =0 A  =0 1 st KK 0-mode A  cannot be flat with these boundary conditions! m n = (n + ½)/R The zero mode is massive! A 5 acts as a Goldstone U(1) is broken Orbifold Boundary Conditions: ∂ 5 A  = 0 A 5 = 0

28. Exchange gauge KK towers: Conditions on KK masses & couplings: (g 1111 ) 2 =  k (g 11k ) 2 4(g 1111 ) 2 M 1 2 =  k (g 11k ) 2 M k 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 W L W L  W L W L at  s ~ 1.7 TeV Higgs restores unitarity if m H < TeV What do we do without a Higgs??

29. 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! W R , Z R get Planck scale masses W , Z get TeV scale masses  left massless! BC’s restricted by variation of the action at boundary Parameters:  = g 5R /g 5L (restricted range)  L,Y,B,D brane kinetic terms g 5L fixed by G F, = g 5B /g 5L fixed by M Z

30. 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[a n J 1 (m n z) + b n Y 1 (m n z)], z=e ky /k Davoudiasl, JLH, Lillie, Rizzo hep-ph/0312193,0403300

31. 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?

32. Precision EW pseudo-oblique parameters Scale of unitarity violation in W L scattering Davoudiasl, JLH, Lillie, Rizzo hep-ph/0312193,0403300

33. Collider Constraints with Run I data

34. 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

35. Truly Exotic

36. 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 E T in detector

37. Production processes: –gg  g , qq  g , , qg  q  –Monojet/photon + missing E T - Run I Run II `Projections” N=1 200 pb -1 D0 Monojet data CDF single photon data

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