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

2. 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”

3. 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!

4. 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. 

5. 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

6. Feynman rules
ex) QED + KK graviton

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

8. 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

9. 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 

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

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

12. 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

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

14. Angular dependence of cross section

15. 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

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

17. Invariant mass distributions

18. Invariant mass distributions

19. 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

20. 15/17
Number of remaining evens per
700 Higgs Pair 1TeV LC
integrated luminosity 500
Essentially No SM backgrounds!

21. Reconstruction of Angular Distribution
(after selection)
integrated luminosity 500

22. Next example:
process
SM background
KK graviton contribution

23. Helicity amplitude for KK graviton mediated processes

24. Spin 2 nature of KK gravitons

25. Helicity amplitude for SM processes

26. SM
SM+KK
SM+KK

27. SM
100% polarized
SM+KK
SM+KK

28. process
SM background
KK graviton contribution

29. SM
SM+KK
SM+KK

30. 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

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

32. ``3-brane’’
``3-brane’’
SM fields

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

34.   IF
satisfied
 Solution consistent with the orbifold symmetry

35. 4-dim. Effective Planck scale
Solution:
strongly warped 
flat limit

36. Collider physics KK graviton resonance production, if
Model parameters 

37. 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

38. 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