Main Issues in ADD phenomenology Find out of there are signals for Kaluza-Klein towers of gravitons ─ large-p T excess, missing energy, etc. Determine whether the signals are indeed due to brane-world gravitons and not some other new physics ─ gravitons would be blind to all SM quantum numbers Identify these particles as graviton modes ─ spin-2 nature is a dead giveaway Find out the number of large extra dimensions Find out the radius of compactification R c, or equivalently, the bulk Planck scale (string scale M s ) Find out the geometry of the extra dimensions Find out dynamics which makes some dimensions large & some small LHC

ADD phenomenology at e + e - colliders: Virtual process Excess in pair-production of SM particles Variation in angular distribution of final states Real process Radiation off a SM particle Missing energy from radiated graviton

Real Gravitons: each ADD graviton couples as (M P ) -1 escapes detection  missing E, p signals Most important process for real gravitons is e+ e-   *   G Single-photon + missing energy signals (Peskin et al) Worked out in LEP context: extended to LC e+ e-e- **  GnGn nn Incoherent sum 2

Need to distinguish from all sorts of other new physics e.g. extra neutrinos, neutralinos, gravitinos, etc. Focus on angular distribution of single photon Gopalakrishna, Perelstein, Wells (Snowmass, hep-ph/ ) Confirmatory process I: e+e-   +  - G Eboli, Magro, Mathews, Mercadante (PRD. hep-ph/ ) – 2  3 process; 14 Feynman diagrams Confirmatory process II: e+e-  e+e- G S.Dutta, P.Konar, B.Mukhopadhyaya, SR (PRD, hep-ph/ ) – 2  3 process; 28 Feynman diagrams (add t-channel) – Predict significant deviations from Standard Model Total cross-section Kinematic distributions – Results of single photon process and this one will be correlated – Can determine the number of extra dimensions

Dutta, Konar, Mukhopadhyaya, SR

e+ e-e- nn Coherent sum GnGn Virtual gravitons can produce any pair of SM particles: e + e -,  +  -,  +  -, q q, g g, , Z Z, W + W - Giudice, Rattazzi, Wells (1998), Han, Lykken, Zhang (1998) Hewett & Rizzo (1998 – 2003), Kingman Cheung (1998, 2001) Agashe, Deshpande (1999) At low energies M S »  s looks like a contact interaction 2

How to utilise this best? 1. K.Y.Lee, H.S.Song, J.H.Song, C.Yu (1999) spin correlations of top quarks 2. Poulose (2001) forward-backward asymmetry e + e -  W + W - 3. Rizzo (2002) multipole moments of e + e -   +  - cross-section etc. 4. Osland, Pankov, Paver (2003) different asymmetries Critical study required! Q. How to distinguish these from other kinds of new physics? A.Spin-2 nature of graviton is the giveaway

RS Metric: Free parameters: Masses of gravitons m 0 ~ 100 GeV (electroweak scale) Coupling of gravitons ~ c 0 = K / M P ~ few %

Main Issues in RS phenomenology Find out of there are signals for graviton resonances ─ bump hunting… Determine whether the resonances are indeed RS gravitons and not some other new physics ─ RS graviton masses are spaced like zeros of Bessel function J 1 Identify these resonances as graviton modes ─ spin-2 nature is a dead giveaway Find out if there are signals for radions ─ very similar to Higgs search Find out the mass and coupling parameters ─ mass and width measurements (like W,Z at Tevatron) If the resonances are broad distinguish between RS and ADD models Distinguish the radion from a Higgs scalar LHC

RS graviton phenomenology: RS graviton width grows rapidly with graviton mass –Only first three modes can form narrow resonances –For large part of parameter space only first resonance is viable RS gravitons decay to all particle pairs –Maximum BR is to jets; sizeable width to WW and ZZ No deviations from SM at LEP-2  lightest RS graviton is heavier than 210 GeV Tevatron Drell-Yan data show no deviations either  lightest RS graviton is heavier than ~ 480 GeV LC: smaller  but clean final states: –graviton resonances in Bhabha scattering and e+e-   +  -

Graviton resonances in e+e-   +  - Hewett & Rizzo (2002) K / M P varies between 0.01 and 0.1

Final states will have angular distributions carrying signatures of spin- 2 nature of RS gravitons –E.g. e+e-   +  - (e.g. LHC:Allanach, Odagiri, Parker, Webber, JHEP) –Vector exchange:  cos 2  peaks along beam pipe –Tensor exchange:  cos 2  cos 4  also transverse peak Complementary process: Single photon signals for RS gravitons –S.K.Rai and SR (JHEP, hep-ph/ ) –Process is e + e -   –Single photon recoils against massive graviton modes –Photon spectrum shows peaks corresponding to graviton masses –For large K / M P resonances broaden into continuous spectrum — difficult to distinguish between ADD/RS –Can distinguish between ADD and RS by comparing e + e -      –Both 2  2 in ADD, single photon is 2  3 in RS

Photon Energy Distribution would show multiple resonances

Correlation plot between e + e -   E and e + e -   +  - Rai and SR SM

Prepare consolidated list of formulae for all cross- sections, both for real and virtual gravitons. Use the same parameterizations, same set of conventions Keep helicity states of e + e - to take care of beam polarization Incorporate in an event generator which is standard, user-friendly, flexible Include ISR and beamstrahlung effects Construct asymmetries, multipole moments etc. Detector simulation What is to be done?