1. Collider Signals From Extra Dimensions Greg Landsberg Berkeley 2000 A Workshop to Study the Physics and Detectors of Future e  e  Colliders March 29-31, 2000

2. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions Outline Basic Phenomenology Graviton Production and Virtual Graviton Exchange LEP2 Searches Run I Tevatron Searches Run II Tevatron and LHC Sensitivity Studies Projections for NLC Conclusions

3. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions Theory of Large Extra Dimensions New idea, inspired by the string theory, with direct connection to the observables! Main goal: to bring the GUT scale to the EW scale in order to solve the infamous hierarchy problem Replace standard RGE equations by the new ones that take into account virtual gravitons from the extra dimensions Dimopoulos, Arkani-Hamed, Dvali, 1998 – found a serious loophole in the current Newton’s law tests: no one looked at gravity below  1mm scale! Therefore, large spatial extra dimensions compactified at sub-millimeter scale are, in principle, allowed! 33 22 11 MZMZ M GUT M Pl RGE evolution MSMS M’ GUT What we think is the Planck scale: M Pl = G N -1/2 is just an effect of the “parallax” due to the modification of the Newton’s law M GUT is also lower due to the “parallax” of the 3+1-dimensional RGE evolution

4. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions Alternative EWSB Mechanism Since large extra dimensions bring the GUT and gravity scales right at the EWSB scale, they solve the hierarchy problem There are multiple mechanisms that allow gauge fields in the bulk to communicate symmetry breaking to our brane A new mechanism, “shining” is a powerful way of introducing a small parameter into the theory, and explain many yet unsolved phenomena, such as CP violation, etc. New framework, possibly explaining neutrino masses, EWSB mechanism, and other puzzling phenomena A significant theoretical interest to the subject ensures rapid development of this field Over 150 theoretical papers on this subject over the past two years – truly a topic du jour SM bulk gauge fields gravity bulk big bang “CP-brane” “shining” SM

5. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions Compactified Extra Dimensions Compactified dimensions offer a way to increase tremendously gravitational interaction due to a large number of available “winding” modes This tower of excitations is known as Kaluza-Klein modes, and such gravitons propagating in the compactified extra dimensions are called Kaluza-Klein gravitons, G KK For M S  1 TeV, n=1 is already excluded from Cavendish-type of experiments For n = 2 minimum allowed scale M S is > 30-100 TeV from SN1987A neutrino flux and distortion of CMB; for n > 3 cosmological limits are weak Since the mass per excitation mode is so small (e.g. 400 eV for n = 3, or 0.2 MeV for n = 4), a very large number of modes can be excited at high energies Compactifie d dimension R G KK Flat dimension M(G KK ) =  P x 2 = 2  k /R

6. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions Examples of Compactified Spatial Dimensions M.C.Escher, Mobius Strip II (1963) M.C.Escher, Relativity (1953)

7. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions Collider Signatures for Extra Dimensions Kaluza-Klein gravitons couple to the momentum tensor, and therefore contribute to most of the SM processes For Feynman rules for G KK see, e.g. [ Han, Lykken, Zhang, PR D59 (1999) 105006 ] Since it is possible for a graviton to propagate into the bulk, energy and momentum are not conserved in the G KK emission from the point of view of our 3+1 space-time Since the spin 2 graviton in generally has a bulk momentum component, its spin from the point of view of our brane can appear as 0, 1, or 2 Depending on whether the G KK leaves our world or remains virtual, the collider signatures include single photons/Z/jets with missing E T or fermion/vector boson pair production Real Graviton Emission Monojets at hadron colliders Single VB at hadron or e + e - colliders Virtual Graviton Emission Fermion or VB pairs at hadron or e + e - colliders

8. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions LEP2 Searches for Direct Graviton Production - I e  e    G Photon + ME T signature “Recycling” of the GMSB analyses ALEPH (2D-fit), DELPHI, L3 (x)  95 = 0.17 pb Theory: [Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version: hep-ph/9811291] Experiment: ALEPH-CONF-2000-005 DELPHI 2000 CONF 344 L3: Phys. Lett. B470, 268 (1999) M S = 1 TeV, n=2 ALEPH, 99 DELPHI, 00 Results: M S > 1.3-0.6 TeV for n=2-6 (DELPHI) ALEPH, L3 – slightly worse

9. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions LEP2 Searches for Direct Graviton Production - II e  e    G Z(jj) + ME T signature “Recycling” of the invisible Higgs analyses ALEPH: Z(jj)G, 184 GeV, total cross section method L3: Z(jj)G, 189 GeV, increased sensitivity via analysis of the visible mass distribution M S > 0.35-0.12 TeV (ALEPH) for n = 2-6 M S > 0.60-0.21 TeV (L3) for n = 2-6 Theory: [Balazs, Dicus, He, Repko, Yuan, Phys. Rev. Lett. 83, 2112 (1999) – width ratio] [Cheung, Keung, Phys. Rev. D60, 112003 (1999) – mass distribution] Experiment: ALEPH-CONF-99-027 L3: Phys. Lett. B470, 281 (1999) M S = 0.5 TeV, n=2  189 GeV

10. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions LEP2 Searches for Virtual Graviton Effects - ff e  e   ff Recycle QED analyses Look at angular and energy dependences Bhabha scattering is the most sensitive channel L3: uses compositeness framework by Hewett with the G KK coupling given by /M S 4, with O(1) constant =  1 [L3, PL B464, 135 (1999)] A lot of confusion about the sign of the interference term; published L3 papers are internally inconsistent ALEPH: uses GRW framework, but uses two signs of  T. Apart from Bhabha, L3 and ALEPH limits are related by: M S (L3)+- = 0.89  T (ALEPH)-+ DELPHI, OPAL: use Hewett’s convention N.B. This is identical to Hewett’s notation, but the sign of is flipped! N.B. This is identical to Rizzo’s notation; results of GRW differ slightly L3: e  e   ff  Drell-Yan production L3: e  e   e  e   Bhabha scattering Theory: [Hewett, Phys. Rev. Lett. 82, 4765 (1999) - DY] [Giudice, Rattazzi, Wells Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291 – DY, Bhabha] [Rizzo, Phys. Rev. D59, 115010 (1999) - Bhabha]

11. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions LEP2 Searches for Virtual Graviton Effects - ff Had L3 really reversed the sign? – Doubtful! ALEPH CONF 99-027 PL B470, 281 (1999) L3 Note 2516 (2000) DELPHI CONF 355 (2000) OPAL CERN-EP/99-097 189 GeV 192-202 GeV  189 GeV  202 GeV  189 GeV   ee PL B470, 281 (1999) M S >0.8- 1.0 TeV

12. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions LEP2 Searches for Virtual Graviton Effects - VV e  e    ALEPH: GRW convention [ALEPH CONF 2000-005] DELPHI: GRW convention w/ errors [DELPHI CONF 324 (1999)] L3: AD convention [Phys. Lett. B464, 135 (1999)] OPAL: based on old GRW w/ wrong direct term [Phys. Lett. B465, 303 (1999)] Theory: [Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291] [Agashe, Deshpande, Phys. Lett. B456, 60 (1999)] AD convention: GRW convention: AD convention is equivalent to Hewett’s with a flipped sign of

13. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions LEP2 Searches for Virtual Graviton Effects - VV e  e    Recycle anomalous Z  couplings analyses Look at angular dependence of the diphoton production M S >0.7- 0.8 TeV N.B. DELPHI and OPAL results are likely to have problems ALEPH CONF 2000-005 189-202 GeV PL B470, 281 (1999) DELPHI CONF 363 (2000) OPAL PN 420 (1999) 202 GeV 200 GeV 189-200 GeV  189 GeV

14. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions LEP2 Searches for Virtual Graviton Effects - VV e  e   WW/ZZ Recycle WW cross section and anomalous ZZ  couplings analyses L3 used angular distributions (WW) and mass variables (ZZ) to set limits Theory: [Agashe, Deshpande, Phys. Lett. B456, 60 (1999)] AD convention is equivalent to Hewett’s with a flipped sign of M S > 520-650 GeV (WW); M S > 460-470 GeV (ZZ) PL B470, 281 (1999)  189 GeV Also: ZZ  qqqq ZZ  qq ZZ  ll ZZ  llll

15. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions LEP2 Lower 95% CL M S (Hewett) Limits (TeV) Experiment eeee   qqf  WWZZ Combined ALEPH (  T ) 0.80 1.03 0.63 0.68 0.57 0.59 0.66/0.61 0.55/0.55 (bb) 0.82 1.04 0.91 0.92 0.84/1.12 ( 0.75/1.00 DELPHI 0.59 0.73 0.56 0.65 0.60 0.76 0.69 0.71 0.60/0.76 (ff) (<202) M S for  is wrong? L3 (???) 0.91 0.99 0.56 0.69 0.58 0.540.49 0.84 1.00 0.80 0.79 0.68 0.79 0.76 0.77 0.87/1.07 (<189) ??? 0.82/0.89 (VV) OPAL 0.63 0.60 0.50 0.63 0.61 0.68 0.63 0.64 0.61/0.68 (ff) (<189) M S for  is wrong? ee  Gee  Ge  e   ZG Experiment n=2n=3n=4n=5n=6n=2n=3n=4n=5n=6 ALEPH 1.100.860.700.600.520.350.220.170.140.12 DELPHI 1.250.970.790.680.59 L3 1.020.810.670.580.510.600.380.290.240.21 OPAL Color coding  184 GeV  189 GeV  202 GeV =-1 =+1 GL Virtual Graviton Exchange

16. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions Virtual graviton Drell-Yan and diphoton production Mass spectrum has been looked at [Gupta, Mondal, Raychaudhuri, hep-ph/9904234, Cheung, Phys. Rev. D61, 015005 (2000), Phys. Lett. B460, 383 (1999),…] Key improvement [Cheung, GL, hep-ph/9909218]: simultaneous analysis of the mass and angular distributions, as a spin 2 graviton would result in different angular distributions compared to the SM backgrounds There are three terms: SM, interference, and graviton contribution Tevatron Search for Virtual Graviton Effects Note that the term in [ ] is a full square! SM interference term G KK terms After [Han, Lykken, Zhang, Phys. Rev. D59, 105006 (1999)] (explicit n-dependence of the virtual graviton exchange) DY: Diphotons:

17. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions Two-Dimensional Analysis Parameterize cross section as a bilinear form in scale  Use Bayesian fit to the data (real one or MC one) to get the best estimate of  For sensitivity studies, repeat the MC gedankenexperiment many times and use the median of the resulting to obtain the sensitivity Note the asymmetry of the interference term,  4, for ll production Sensitivity is 20-30% (in terms of  Ldt) higher than for 1-dimensional analysis  ll SM  4 ll  8 ll   SM  4   8  [Cheung, GL – hep-ph/9909218]

18. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions Search for Extra Dimensions in the di-EM channel at DØ Basic idea: combine dielectron and diphoton channels to increase efficiency, and hence, sensitivity: 2 EM clusters w/ E T > 45 GeV, |  |<1.1 or 1.5<|  |<2.5   80%  Ldt = 127 pb  1 – entire Run I statistics Adding theoretical cross sections is OK, since at LO the relative contribution of each channel is known precisely NLO corrections are modeled via a constant K-factor of 1.3 ± 0.1

19. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions DØ Results

20. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions DØ Limits on Large Extra Dimensions Comparison w/ Hewett’s and GRW frameworks: M(  ) = 574 GeV cos  * = 0.86 M S > 1.1 TeV  T > 1.2 TeV

21. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions Tevatron: Real Graviton Emission qq  gG (dominant channel) jets + ME T final state Z( )+jet irreducible background Important instrumental backgrounds from jet mismeasurement, cosmics, etc. Both CDF and DØ are pursuing this search Theory: [Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291] [Mirabelli, Perelstein, Peskin, PRL 82, 2236 (1999)] nM S reach, Run I M S reach, Run II 21100 GeV1400 GeV 3950 GeV1150 GeV 4850 GeV1000 GeV 5700 GeV900 GeV Note that non- perturbative effects could become important at high n Note that this sensitivity estimate is probably optimistic, as it does not take into account copious instrumental backgrounds [M.Spiropulu] Tevatron Run I/II reach, CDF+DØ [Giudice et al.]

22. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions DØ Run I (preliminary): 1.0-1.3 TeV Dependence on the cut-off scale  = cM S : n=3 n=5 n=7 n=3 n=5 n=7 n=3 n=5 n=7 c=O(1) is natural in string theory (from exponential suppression of the G KK couplings [ Antoniadis et al, hep-ph/9904232 ] or from the brane tension [ Bando et al, hep-ph/9906549 ]) Virtual exchange: expected sensitivity @95% CL: Run II and LHC Reach in Virtual Graviton Exchange

23. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions LHC Reach in Direct Graviton Production qg  qG and qq   G reach at the LHC  s = 2000 GeV [Giudice, Rattazzi, Wells, NP B544, 3 (1999)] qG E T min spectrum qG cross section  G cross section  G E T min spectrum Caveat: instrumental backgrounds are ignored Note that non-perturbative effects could become important at high n nM S reach Perturbativity 28.5 TeV3.8 TeV 36.8 TeV4.3 TeV 45.8 TeV4.8 TeV 55.0 TeV5.4 TeV LHC reach in j+ME T channel for  Ldt = 100 fb  1

24. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions Real Graviton Emission at the NLC e  e    G/ZG Similar to LEP2 Studies Polarization helps to reduce SM backgrounds Low background gives an edge above LHC Giudice, Rattazzi, Wells, NP B544, 3 (1999) Mirabelli, Perelstein, Peskin, PRL 82, 2236 (1999) Cheung, Keung, PR D60, 112003 (1999) Many others… M S reach 200 fb -1 Giudice M S reach ? fb -1 Mirabelli M S reach 50 fb -1 Cheung n 1 TeV, P = 90%,  G 1 TeV, P=0,  G/ZG 27.7 TeV5.7 TeV4.5 TeV 3.2-4.2 TeV 34.0 TeV 44.5 TeV3.0 TeV 52.4 TeV 63.1 TeV [Giudice et al., NP B544, 3 (1999)] [Cheung et al., PR D60, 11203 (1999)] GG GG ZG E T min spectrum M S dependence s-dependence

25. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions Virtual Graviton Effects at the NLC e  e    ff, WW, ZZ, etc. Similar to LEP2 Studies Polarization helps to reduce SM backgrounds Sensitivity comparable to that at the LHC Hewett, Phys. Rev. Lett. 82, 4765 (1999) Giudice, Rattazzi, Wells, NP B544, 3 (1999) Rizzo, Phys. Rev. D59, 115010 (1999) Cheung, Phys.Rev. D61, 015005 (2000) Davoudiasl, Phys.Rev. D61, 044018 (2000) Many others… HewettGiudiceRizzoCheungDavoudiasl Luminosity200 fb -1 ? fb -1 100-500 fb -1 10 fb -1 200 fb -1  3.8 TeV3.5-4.0 TeV ff6.0-7.0 TeV6.0-7.5 TeV   ff 3.5-4.5 TeV Compton  6 TeV [Cheung, PR D61, 015005 (1999)]

26. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions NLC Reach for Large Extra Dimensions If LED do exist, LHC is likely to discover them For real graviton emission NLC has an edge for low number of extra dimensions Phenomenology of LED could be very rich, and some effects (e.g., s-channel Kaluza-Klein resonances) could be studied only at NLC Polarized beams, a unique NLC capability, could be very helpful in studying the virtual graviton effects, and to suppress SM backgrounds to direct graviton emission [M.Spiropulu] Run I LEP2 LHC Run II NLC n=4,  G (ee), gG (pp) Note that LHC reach exceeds that for NLC for n = 6, 7

27. NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions Conclusion: WWW Search for Extra Dimensions Stay tuned – next generation of colliders has a good chance to solve the mystery of large extra dimensions! http://www.extradimensions.com Extra Dimensions TV Show On 2/15/00 patent 6,025,810 was issued to David Strom for a "hyper-light-speed antenna." The concept is deceptively simple: "The present invention takes a transmission of energy, and instead of sending it through normal time and space, it pokes a small hole into another dimension, thus sending the energy through a place which allows transmission of energy to exceed the speed of light." According to the patent, this portal "allows energy from another dimension to accelerate plant growth." - from APS “What’s New”, 3/17/00 Carolina’s Extra Dimensions