Extra Dimensions and Exotica at a Linear e

+

e

-

Collider Indian Contributions

Sreerup Raychaudhuri I.I.T. Kanpur

6 th ACFA Meeting on Linear Collider

TIFR, Mumbai December 15-17, 2003

Advantages

• Clean environment

• less hadronic activity

• Lab frame is CM frame

•  s is sharply defined

• Very high luminosities

• 100 – 1000 fb -1

• Beam polarization

• 80% for electron, 60% for positron

• Different modes: • e+e- , e-e- , e



,



Extra Dimensions

Origins

Kaluza (1921), Klein (1926):

unification of electromagnetism with gravity in a 1+4 dimensional world 1 extra dimension compactified on a circle Superstring theory: 1+9 dimensions 6 extra dimensions compactified to Planck length 10 -33 cm

Revived to solve hierarchy problem (1998): –N.

A

rkani-Hamed, S.

D

impoulos, G.

D

vali

–

ADD model

•SM fields confined to brane; not more than 10 -17 cm thick Brane 1 + 3 Bulk 4 + d

Large Extra Dimensions

•Gravity propagates in bulk •Brane catches only small part of graviton wave function •Bulk size can be 0.02 cm; brane-to-bulk ratio is tiny •Gravity very weak on brane; strong in bulk •Planck scale at 1 TeV •No hierarchy of scales!

•Observable consequences at laboratory energies: • Graviton lives in the bulk – extra degrees of freedom E 2 = p 2 = (- p 0 2 + p 2 )+ p 2  When projected on the brane, these extra degrees of freedom appear as a tower of  closely-spaced

massive

graviton states SM fields live on the brane: can see only this tower   Each graviton in the tower couples as (M P ) -1 Spacing between graviton states is as low as 0.001 eV    At linear collider energies, there are ~10 16-17 of these graviton modes Collective interaction builds up to near-electroweak strength Detection of gravitational effects is possible!

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

• Each ADD graviton couples as (M P ) -1 • escapes detection  missing E, p signals •

Most important process

for real gravitons is e+ e   *   G e+ G n S n  * e  Incoherent sum Single-photon + missing energy signals

(Peskin

et al

)

Worked out in LEP context: extended to LC

• LEP bounds on M S

1.6

1.4

1.2

1 0.8

0.6

0.4

0.2

0 2 4

•Supernova bounds on M S d = 2: M S > 30 – 130 TeV

6 ALEPH DLPHI L3 OPAL

Single photons LHC, LC M S upto few TeV d = 3: M S > 4 TeV d = 4: M S > 1 TeV

•Need to distinguish from all sorts of other new physics •E.g. extra neutrinos, neutralinos, gravitinos, etc.

•Gopalakrishna, Perelstein, Wells (Snowmass, hep-ph/0101339) •Focus on angular distribution of single photon •

Indian contributions:

•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

ILCWG

–S.Dutta, P.Konar, B.Mukhopadhyaya, SR ( PRD, hep-ph/0307117) –2  3 process; 28 Feynman diagrams (add

t

-channel) –Calculation is long and messy –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

Virtual gravitons can produce any pair of SM particles: e + e , m + m , t + t , q q , g g ,   , Z Z , W + W -, , HH Giudice, Rattazzi, Wells (1998), Han, Lykken, Zhang (1998) Hewett & Rizzo (1998 – 2003), Kingman Cheung (1998, 2001) Agashe, Deshpande (1999) e+ S n e G n Coherent sum At low energies Japanese group: M S »  s looks like a contact interaction Okada et al  concentrate on HH

Q. How to distinguish these from other kinds of new physics?

A. 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!

What is to be done?

•Prepare consolidated list of formula for all cross sections, both for real and virtual gravitons

• Keep helicity states of e

+

e

-

to take care of beam polarization •

Incorporate in an event generator

• Include ISR and beamstrahlung effects •

Construct asymmetries, multipole moments etc.

•

Detector simulation

 Cosmological constant

Warped gravity models:

R

andall and

S

undrum (1999) Planck Brane AdS 5 negative in bulk & TeV brane; positive on Planck brane  Fine-tuning of cosmo logical constants  ‘Warped’ solution of Einstein equations Bulk  Gravity strong (~ ew) on invisible brane TeV Brane  Graviton wavefunction falls exponentially across bulk  Natural solution to hierarchy problem Created to solve hierarchy problem without large dimensions –Model has one extra dimension: orbifolded

S

1 /

Z

2 (small) –Two branes at each end: visible(TeV) & invisible (Planck)

• Observable consequences at laboratory energies: – Again there is a tower of massive graviton states – Graviton masses are

~

electroweak scale K e p K R – Each graviton couples with electroweak strength K / M P  Each graviton behaves like a WIMP  Expect multiple resonances • Require a bulk scalar field to hold branes at correct distance apart – Leads to light residual scalar on visible brane – This is dubbed the ‘ radion ’ – Radion has Higgs-like couplings with SM fields

RS graviton phenomenology at e

+

e

-

colliders:

• 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 • Smaller s but clean final states: – graviton resonances in Bhabha scattering and e+e  m + m • • 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

Graviton resonances in e+e  m + m 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  m + m (e.g.

LHC: Allanach, Odagiri, Parker, Webber , JHEP) – Vector exchange: – Tensor exchange: s  1 + cos 2 q s  1 - 3 cos 2 q + 4 cos 4 q peaks along beam pipe also transverse peak •

Indian Contribution: ILCWG

• 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 / M P 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

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

Radion signals in e

+

e

-

collisions

• • Radion phenomenology is rather similar to Higgs phenomenology for tree-level processes – Possibility of Higgs-radion mixing (Mukhopadhyaya’s talk) – At one-loop, effect of kinetic terms in radion-fermion couplings becomes important – (Das, Mahanta , SR, in preparation )

Indian Contribution: ILCWG

• ‘Radion’strahlung process … – Das, Choudhury, Majhi (in preparation) – Just like Higgs-strahlung: worked out cross-sections etc.

– Next step: Try to identify radion by its slightly different decay widths to gluons (one-loop) i.e. dijet decay mode – Problem is difficult!

Exotic modes of the linear collider e e , e ±  ,   •RS graviton exchange in e-e colliders –Ghosh and SR (PLB, hep-ph/0007354) •ADD gravitons in e  colliders –Davoudiasl (PRD, hep-ph/9907347) –Ghosh, Poulose, Mathews, Sridhar (MPLA, hep-ph/9909377) •RS gravitons in e  colliders –Choudhury, Cornell, Joshi (PRD, hep-ph/0105002) •ADD gravitons & dijets in  colliders –Ghosh, Mathews, Sridhar (JHEP, hep-ph/9909567) • RS graviton exchange in  –Choudhury, Cornell, Joshi colliders –one-loop processes in SM (box diagrams); tree-level in RS model – –   –       with graviton exchange with radion exchange (PLB, hep-ph/0007043) (PLB, hep-ph/0012043) ZZ with graviton & radion exchange (PLB, hep-ph/0202272)

Outlook

• Even if LHC discovers extra dimensions, LC will tell us about the geometry, dynamics • A lot of work has been/is being done in India • Need to consolidate these efforts • Theorists must work with experimentalists

THANK YOU