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

ADD phenomenology at e+ e- colliders:

Virtual process Excess in pair-production of SM particles

Variation in angular distribution of final states

Real processRadiation off a SM particle

Missing energy from radiated graviton

• Real Gravitons: each ADD graviton couples as (MP)-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-

*

Gn

nIncoherent

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/0101339) • Confirmatory process I: e+e- +- 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

Dutta, Konar, Mukhopadhyaya, SR

e+

e-

nCoherent

sum

Gn

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 MS » 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

m0 ~ 100 GeV (electroweak scale)

Coupling of gravitons ~ c0 = K / MP

~ few %

0cKr

n n nM x Ke x m

2

0

0

cm

1( ) 0nJ x

cR2 2 2Kcds e dx dx R d

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

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 /MP 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: cos2 peaks along beam pipe– Tensor exchange: cos2 cos4 also 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 large K /MP 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?