Main Issues in ADD phenomenology

1. Main Issues in ADD phenomenology • Find out of there are signals for Kaluza-Klein towers of gravitons ─ large-pT 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 Rc, or equivalently, the bulk Planck scale (string scale Ms) • Find out the geometry of the extra dimensions • Find out dynamics which makes some dimensions large & some small LHC LHC LHC

2. 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

3. Real Gravitons: each ADD graviton couples as (MP)-1 • escapes detection missingE, psignals • 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+ Gn 2 Sn * Incoherent sum e- 

4. 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/0101339) • Confirmatory process I: e+e-  m+m- G • Eboli, Magro, Mathews, Mercadante (PRD. hep-ph/0103053) • 2  3 process; 14 Feynman diagrams • Confirmatory process II: e+e-  e+e- G • S.Dutta, P.Konar, B.Mukhopadhyaya, SR (PRD, hep-ph/0307117) • 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

5. Dutta, Konar, Mukhopadhyaya, SR

6. Virtual gravitons can produce any pair of SM particles: e+ e- , m+m- , t+t- , q q , g g , 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) e+ 2 Sn Coherent sum Gn e- At low energies MS»slooks like a contact interaction

7. Q. How to distinguish these from other kinds of new physics? • Spin-2 nature of graviton is the giveaway 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- m+m-cross-section etc. 4. Osland, Pankov, Paver (2003)different asymmetries Critical study required!

8. RS Metric: Free parameters: Masses of gravitons m0 ~ 100 GeV (electroweak scale) Coupling of gravitons ~ c0= K / MP ~ few %

9. 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 J1 • 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 LHC LHC LHC

10. 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 than210 GeV • Tevatron Drell-Yan data show no deviations either  lightest RS graviton is heavier than ~ 480 GeV • LC: smaller s but clean final states: • graviton resonances in Bhabha scattering ande+e- +-

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

12. 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:s  1 + cos2 q peaks along beam pipe • Tensor exchange:s  1 - 3cos2 q + 4cos4 qalso transverse peak • Complementary process: Single photon signals for RS gravitons • S.K.Rai and SR (JHEP, hep-ph/0307096) • Process is e+e-  • Single photon recoils against massive graviton modes • Photon spectrum shows peaks corresponding to graviton masses • For largeK /MP resonances broaden into continuous spectrum — difficult to distinguish between ADD/RS • Can distinguish between ADD and RS by comparing e+e- m+m- • Both 2  2 in ADD, single photon is 2  3 in RS

13. Photon Energy Distribution would show multiple resonances

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

15. What is to be done? • 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