Search for “Large” Spatial Extra Dimensions at the Tevatron Tom Ferbel University of Rochester Cairo January 9-14 This was stolen from Greg by Tom, and edited for a 25 minute talk at Cairo

Is There Life Beyond the Standard Model ? The Standard Model is recognized as a low-energy approximation to a more complete theory This new theory supposedly takes over at some scale , comparable to the Higgs mass, i.e.,   1 TeV At one time, there were two serious candidates for such a theory: SUSY Strong Dynamics But more recently, it has been suggested that there may be no other scale, and that the SM model is fine up to some effective “Planck” scale of ~ 1 TeV [ Arkani-Hamed, Dimopoulos, Dvali (1998) ]

How Does This Work? Change in Newton’s law: Ruled out for huge extra dimensions, but not for sufficiently small n compactified extra dimensions of size R: = the effective Planck Scale, M S

Effectively Makes Gravity Strong G’ N = 1/M S 2  G F  M S  1 TeV More precisely, from Gauss’s Law: There are very few tests of Newton’s Law at distances smaller than  1 mm Consequently, large spatial extra dimensions compactified at sub- millimeter scales cannot be excluded!

Kaluza-Klein Gravitons Compactified dimensions greatly increase the strength of gravitational interactions through Kaluza-Klein “winding” modes or G KK gravitons From the point of view of a (3+1) space-time, the Kaluza-Klein graviton modes are massive, with the mass excitation spaced  1/R Because the mass per excitation mode is 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 Compactified dimension R G KK Flat dimension Each Kaluza-Klein graviton mode couples with gravitational strength For the large number of modes, accessible at high energies, gravitational coupling is therefore greatly enhanced Low energy precision measurements are not sensitive to ADD effects

Signatures for Large Extra Dimensions at the Tevatron Kaluza-Klein gravitons couple to the energy- momentum tensor, and therefore contribute to most SM processes Since gravitons can propagate in the bulk, from our perspective in (3+1) space-time, energy and momentum will appear not to be conserved in G KK emission Since the spin-2 graviton, in general, has a momentum component in the bulk, its spin from the point of view of our brane can appear to be 0, 1, or 2 Depending on whether the G KK leaves our brane or remains virtual, collider signatures can include single photons/Zs/jets with missing E T,, or pair produced objects Real Gravitons Monojets at hadron colliders G KK g q q g g g Single VB at hadron or e + e - colliders G KK V V V V Virtual Gravitons Fermion or VB pairs at hadron or e + e - colliders V V G KK f f f f

Virtual Gravitons For the case of pair production, amplitude for gravity contribution interferes with the SM (e.g., l + l - production): Production cross section has three terms: SM, interference, and direct gravity The sum in KK states is divergent in the effective theory, so calculation of cross sections, requires explicit cutoff Expected value of the cutoff is  M S (the scale at which effective theory breaks down, and string theory must be used) Three different conventions used for writing an effective Lagrangian: Hewett, Phys. Rev. Lett. 82, 4765 (1999) Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999); revised version, hep- ph/ Han, Lykken, Zhang, Phys. Rev. D59, (1999); revised version, hep-ph/ All are completely equivalent, and only the definitions of M S differ:

Hewett, GRW, and HLZ Formalisms Hewett: neither sign of the interference nor the dependence on the number of extra dimensions is specified; hence, for the interference term use ~ /M S 4 (Hewett), where is of order 1, and ±1 GRW: sign of the interference is fixed, but the dependence on number of extra dimensions not specified; therefore, interference term is ~  /  T 4 (where  T is notation for M S ) HLZ: sign of interference and the n-dependence calculated in effective theory; with interference term ~ F /M S 4 (HLZ), and F containing explicit dependence on n: Correspondence between formalisms: Rule of thumb:

Dilepton and diphoton production via virtual graviton Mass spectrum has been looked at [Gupta, Mondal, Raychaudhuri, hep-ph/ ; Cheung, Phys. Rev. D61, (2000), Phys. Lett. B460, 383 (1999),…] Improvement [Cheung, Landsberg, PRD 62, (2000)]: simultaneous analysis of mass and angular distributions (J=2 graviton different angular distributions from SM ) There are three terms: SM, interference, and direct graviton contribution Use Han/Lykken/Zhang formalism: Virtual Graviton Exchange at the Tevatron Dileptons: Diphotons: G KK term SM interference term G KK term NLO corrections accounted for via a constant K-factor

Search at DØ First search for large extra dimensions at Tevatron Based on Cheung/Landsberg, with following modifications: DØ detector does not have a central magnetic field, hence cannot measure electric charge of electrons  use |cos  * | Dimuon mass resolution at high mass is poor  do not use dimuons Dielectron and diphoton efficiencies are only moderate (~50%) due to tracking inefficiency (for electrons) and conversions or overlap of photons with random tracks  maximize DØ discovery potential by combining dielectrons and diphotons (essentially ignore tracking information), i.e., use di-EM signature! Instrumental background is not expected to be important at high mass, hence,  release strict EM-ID requirements to maximize efficiency

Mulitjet and Direct Photon Background SM  vs. instrumental backgrounds [Landsberg & Matchev, PRD 62, (2000)]

Data Selection and Efficiency Use entire Run-1st luminosity, low-threshold, di-EM triggers:  Ldt = 127  6 pb -1 Offline criteria: Exactly 2 EM clusters, E T >5 GeV, |  |<1.1 or 1.5<|  |<2.5, passing basic EM ID criteria: EMF > 0.95 ISO < 0.10  2 < 100 ME T < 25 GeV No other kinematic restrictions in the analysis, since (M,cos  *) define the process completely Resulting data sample contains 1250 events Efficiency of the ID is determined from Z events obtained with same triggers, but lower E T (EM) threshold Criterion# of events Starting sample87,542 Quality criteria82,947  2 EM =2 EM82,425 E T > 25 GeV36,409 Acceptance30,585 EM ID10,711 ET > 45 GeV1,250 CriterionSignal Efficiency EM ID (87  2)% MET < 25 GeV (98  1)% Event quality (99.8  0.1)% Overall, per event (79  2)%

Monte Carlo for Signal and Background Based on Cheung/Landsberg LO parton level generator that produces weighted events Augmented with fast parametrized DØ detector simulation that models: DØ detector acceptance and resolutions Primary vertex smearing and resolution Effects of additional vertices from multiple interactions in the event Transverse kick of the di-EM system to account for ISR effects Integration over parton distribution functions (CTEQ4LO and other PDFs) K-factor correction to cross sections Both SM and gravity effects

Summary of Backgrounds SM backgrounds in the MC: Drell-Yan (e-pairs)  (gg   is negligible  not included) Other SM backgrounds are mostly at low mass, and negligible: W+j/  < 0.4% WW< 0.1% top< 0.1% Z   < 0.1% Z+  < 0.01% Other< 0.01% Instrumental background from jj/j  “  ” from jet fragmenting to leading  0 Determined from data with single-EM triggers (40 GeV threshold) & applying probability of (0.18  0.04)%, for a jet to mimic photon - independent of (E T,  Instrumental background (mostly jj)~7% Ignore smaller backgrounds , fb/bin M(di-EM), GeV Total SM background qq   gg   At high mass, SM background dominated by qq  

MC Description of Data and Systematics Kinematic distributions are well described by the sum of SM and instrumental backgrounds Following systematic uncertainties on differential cross sections were taken into account: Instrumental background (uncertain to 25%) SourceUncertainty K-factor10% Choice of PDF5%  Ldt 4% Efficiency3% Overall12%

Observe good agreement in Mass cutoffNBP > 100 GeV > 150 GeV > 200 GeV > 250 GeV > 300 GeV > 350 GeV > 400 GeV > 450 GeV > 500 GeV > 550 GeV > 600 GeV0<

Instrumental background

Monte Carlo for Signal and Background SM 44 88 M S = 1 TeV n=4

Fit MC & Data to Extract Effects of Gravity Bin the events in a M  |cos  * | grid (up to 40  10 bins; M  [0,2 TeV], |cos  * |  [0,1]) Parameterize cross section in each bin as simple form in  :  =  SM +  4 +  2  8 Use Bayesian fit with flat prior (in  ) to extract the best value of  and 95% C.L. intervals: Cross-check using maximum likelihood M S extraction input n=4 M S = 1.3 TeV expected limits:  < 0.44 TeV 95% C.L.

DØ Results in Di-EM Channels High mass and small |cos  | are characteristic signatures of LED 2-dimensional analysis resolves LED from high-mass and large |cos  | tail from QCD diphotons No excess seen at high mass and large scattering angles, where LED signal is expected Limit found: 0.46 TeV -4 Expected limit: 0.44 TeV -4

DØ Limits on Large Extra Dimensions For n > 2, M S limits can be obtained directly from limits on  For n = 2, use average s for gravity contribution (  s  = 0.36 TeV 2 ) Translate limits in the Hewett and GRW frameworks for ease of comparison with other experiments: M S (Hewett) > 1.1 TeV and 1.0 TeV (  )  T (GRW) > 1.2 TeV These limits are similar to most recent preliminary results from LEP2 Complementary to those from LEP2, probing different range of energies Looking forward to limits from CDF DY analysis (M S ~ TeV), utilizing the same technique Sensitivity is limited by statistics; reach in terms of M S will double in Run-2a (2 fb -1 ) and triple in Run-2b (20 fb -1 ) ^ ^ hep-ex/ , to appear in PRL

Highest-Mass Candidates Parameters of the two candidate events of highest mass: RunEventZ vtx ME T TypeET1ET1 ET2ET2 11 22 M cos  * N jet P T -kick cm15 GeV  81 GeV GeV GeV cm15 GeVee134 GeV132 GeV GeV GeV Event with highest mass observed in Run-1 M(  ) = 574 GeV cos  * = 0.86

Summary DO has searched for contributions from virtual graviton exchange in a context motivated by the possibility of there being only one scale for particle physics, and “large” extra spatial dimensions. On the basis of the production of massive e-pairs and di-photons, such a scale, must be higher than ~ 1 TeV More studies are being pursued at both DO and CDF, and can be expected to start converging in winter These will be both on virtual-graviton exchange as well as real graviton (mono-jet) production. Run-2 will (eventually) be sensitive to scales of 3-4 TeV The LHC will be able to access effective “Planck” scales of > 10 TeV And now back to musing on Flatland (such stuff as dreams are made on)

Next-to-Leading Order Corrections Angle  * in the parton-level cross section is defined as the angle between the incoming parton from p and the l +, i.e. in the Gottfried- Jackson frame In the presence of ISR this frame is no longer viable, and we use instead the helicity frame, defining  * as angle between the direction of the di-EM system (boost) and the direction of EM object in that frame. ISR-induced “smearing”, i.e. the difference between cos  * in the GJ and helicity frame is small (~0.05) ISR effect is modeled in the signal MC Since NLO corrections for diphoton and dielectron production cross section are close, there is no theoretical “overhead” related to adding two channels; we use K = 1.3 ± 0.1 No FSR for true di-EM final states Boost of EM-pair z ISR helicity angle ** q q EM ** z helicity angle = GJ angle q q EM