Collider Signals of Extra Dimension Scenarios Nobuchika Okada (KEK) KEK LC Physics Meeting May 9-12, KEK, Japan

1. Introduction Large extra-dimension (ADD) scenario (Arkani-Hamed-Dimopoulos-Dvali, ’98) Basic picture: dimensional model We are confined on “3-brane” graviton lives in the bulk SM fields graviton compact extra-dimensions ( with common radii r ) “3-brane”

Alternative solution to the gauge hierarchy problem without SUSY, TC, etc. Low scale gravity model Gauss law  We can take with  We can expect collider signal!

2. Theoretical Framework 4D description : graviton in dimensions  Kaluza-Klein (KK) mode decomposition in 4 dimensions + periodic boundary conditions  Infinite tower of KK modes Ex) if 6 dim. 

KK graviton: KK gravi-scalar: KK vectors KK scalars do not couple to SM fields Reduced Planck mass : negligible at high energies Characteristic features: infinite tower of KK gravitons universal couplings

Feynman rules ex) QED + KK graviton

3. Collider signal of large extra dimension Phenomenology of extra-dimension scenario = Phenomenology of graviton Kaluza-Klein modes Detection of Extra-dimension @ future colliders  detection of KK graviton direct  KK graviton emission processes indirect KK graviton mediated processes First detection of spin 2 particle !

II: angular dependence of cross section Important points: I: total cross section 　　　 new physics evidence deviation from the SM collider energy LC < LHC II: angular dependence of cross section 　  effects due to spin 2 particle exchange precise measurements of angular dependence LC > LHC

KK graviton emission process 3-1. direct detection KK graviton emission process Ex) Each process is suppressed by Emitted KK graviton  non-interacting & stable particle  missing energy event is very small  can be sizable 

KK graviton emission process @ linear colliders Giudice, Rattazzi & Wells, NPB 544 (1999) 3 Example: SM background:

Determination of number of extra-dimensions Sreerup Raycahudhuri et al., PRD 50 6872, 1994 Interplay of

KK graviton mediated process 3-2. indirect detection KK graviton mediated process Need regularization * Physical cutoff  brane tension brane with finite width Naïve: Cut Off by

process Example: KK graviton exchange is dominant N. Delerue, K. Fujii & N. Okada hep-ex/0403029, to appear in PRD process KK graviton exchange is dominant SM background free  very interesting if this cross section is large enough Comparable to

Angular dependence of cross section

Qualitative understanding of angular dependence Initial state helicity:  or Final state helicity: 0 Orbital angular momentum is needed to make up spin 2 of intermediate KK gravitons Angular distribution reflects the spin 2 nature of KK gravitons

Monte Carlo Simulation process two pair of b-jets SM background: processes producing two pair of jets

Invariant mass distributions

Invariant mass distributions

Event selection Criteria: More than 25 tracks with an energy > 100 MeV A visible energy larger than 600GeV Transverse momentum larger than 50 GeV More than 4 jets Invariant mass less than 16 GeV away from Higgs mass One of the jets of each Higgs candidate to be b-taged

15/17 Number of remaining evens per 700 Higgs Pair events @ 1TeV LC integrated luminosity 500 Essentially No SM backgrounds!

Reconstruction of Angular Distribution (after selection) integrated luminosity 500

Next example: process SM background KK graviton contribution

Helicity amplitude for KK graviton mediated processes

Spin 2 nature of KK gravitons

Helicity amplitude for SM processes

SM SM+KK SM+KK

SM 100% polarized SM+KK SM+KK

process SM background KK graviton contribution

SM SM+KK SM+KK

Plan Realistic Monte Carlo simulations Is it possible to distinguish final states with different helicity ? Collider energy should be high as possible Ms should be low as possible

4. Warped (small) Extra Dimension Scenario Randall-Sundrum, PRL 83 (1999) 3370 Setup: 5-dimimensional theory 5th dimension is compactified on Identification

``3-brane’’ ``3-brane’’ SM fields

Solving Einstein’s equations with cosmological constants in bulk on branes Metric ansatz 4 dimensional Poincare invariance Others = 0

  IF satisfied  Solution consistent with the orbifold symmetry

4-dim. Effective Planck scale Solution: strongly warped  flat limit

Collider physics KK graviton resonance production, if Model parameters 

KK graviton resonance production @ LC Davoudiasl, Hewett & Rizzo, PRL 84 (2000) 2080 c: calculable numerical factor 1 0.7 0.5 0.3 Width becomes large as k/M4 becomes large 0.2 0.1

4. Summary Large extra dimension Scenario is an interesting candidate for new physics beyond the standard model The existence of extra dimensions may be revealed through processes involving the KK gravitons, KK graviton emission processes KK graviton mediated processes LC has an advantage to measure the angular dependence of the cross section of the KK graviton mediated process, which reflects the spin 2 nature of the intermediate KK gravitons