Transcript Document
Testing extra dimensions below the production threshold of Kaluza-Klein excitations
Bunichev Viacheslav
In collaboration with E.Boos, I.Volobuev and M. Smolyakov
V. Bunichev IHEP 2008
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Motivation of using additional space-time dimensions
•
Grand unification. Superstring theory.
•
Hierarchy problem
•
Dark matter candidate
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Effective action of theories with compact extra dimensions
Where:
MN (M, N = 0, 1, 2, 3, …, 3+d, sign
L(
) - bulk field, - bulk Lagrangian of the field
= +, -, … , -) - background metric in the bulk, L (SM-
) - Lagrangian of the Standard Model fields, which do not propagate in the bulk J SM*
- scalar product of the corresponding current of the Standard Model fields J SM field
on the brane, g - four-dimensional coupling constant, and the M - fundamental energy scale of the (4+d)-dimensional theory defined by the gravitational interaction, An important point is that the induced metric on the brane is flat, i.e. the coordinates {x μ } are Galilean on the brane
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It is a common knowledge that the bulk field can be expanded in Kaluza-Klein modes with definite masses in the space of extra dimension
(n) (y) .
(n) (x) and their wave functions Substituting this representation into action and integrating over the coordinates of extra dimensions, we get the reduced four-dimensional action где L int (
(m) ) stands for the self-interaction Lagrangian of the modes, { y b } denotes the coordinates of the brane in the space of extra dimensions
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Effective contact interaction of KK modes with SM fields
Now if we consider the theory with action for the energy or momentum transfer much smaller, than the masses of the KK-excitations
(n) , n
0
,
we can pass to the effective ”low-energy” theory, which can be obtained by the standard procedure. We have to drop the momentum dependence in the propagators of the heavy modes and to integrate them out in the functional integral. The action of the resulting theory looks like: We assume that the fundamental energy scale of the (4 + d)-dimensional theory M is of the same order of magnitude, as the inverse size of extra dimensions. Then the masses of the KK excitations are proportional to this energy scale M and the wave functions are proportional to M d/2 , and the coupling constant can be represented as
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Stabilized Randall-Sundrum (RS1) model.
( L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999) ) ( O. DeWolfe, D. Z. Freedman, S. S. Gubser and A. Karch, Phys. Rev. D 62 (2000) ) ( E. E. Boos, I. P. Volobuev, Y. A. Kubyshin and M. N. Smolyakov, Theor. Math. Phys. 131, 629 (2002) ) •
Multidimensional Planck mass and other model parameters are in the TeV energy range.
• • • •
5-dimensional space-time.
Two branes.
Our world is located on the negative tension brane.
A flaw of this model is the presence of a massive scalar mode, – the radion.
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Stabilization - the brane separation distance has defined value
• •
Radion mass is defined by the brane separation distance.
The weakness of the gravitational interaction is defined by the warp factor in the metric.
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Effective contact interaction of KK modes with SM fields in the frame of the Stabilized Randall-Sundrum (RS1) model.
In the case, where the center of mass energy is below the threshold of the excitations production, the Lagrangian of interaction sum of KK modes with matter describes contact interactions of a current x current type.
Interraction of SM with spin 2 КК modes L eff
1 16
M
3
n
0 2
n m n
2 (
L
)
T
,
T
, , ( 3 2 )
The sum over the tensor modes can be expressed through constant
first mode and the mass of the
(E. Boos, V.Bunichev, M.Smolyakov, I.Volobuev, arXiv:0710.3100v1 [hep-ph])
Interraction of SM with spin 0 КК modes
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Symbolic results:
Symbolic computations have been performed by means of the version of the CompHEP package realized on basis of the FORM symbolic program.
Total width for the KK graviton resonance
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Processes gg
Z 0 Z 0 with spin 2 and spin 0 KK states: Total and differential cross sections for the process q q
l
l
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Numerical results
Numerical computations, MC generators and demonstration plots have been performed by means of the CompHEP package Dilepton invariant mass distribution for parameter
0 .
91
2
m 2 1
x(1TeV ) 4 =0.0014 (dash dotted line), 0.0046 (dashed line), 0.01
(dotted line) for the LHC
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Collider potential, LHC
Estimation of experimental 95% CL limit for the coupling parameter that may be reached at the LHC (L = 100fb -1 )
0 .
91 2
m
1 2 0 .
0014 , [
TeV
4 ]
Estimation of the lowest value for the fundamental scale parameter from a requirement that the width of the first resonance be smaller than its mass:
1 < m 1 /ξ, where ξ > 1.
2 .
82 1 4 , [
TeV
]
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Collider potential, TEVATRON
Estimation of experimental 95% CL limit for the coupling parameter that may be reached at the TEVATRON (L = 10fb -1 )
0 .
91 2
m
1 2 0 .
66 , [
TeV
4 ]
Estimation of the lowest value for the fundamental scale parameter from a requirement that the width of the first resonance be smaller than its mass:
1 < m 1 /ξ, where ξ > 1.
0 .
61 1 4 , [
TeV
]
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Total sum of KK modes and first КК resonance
rate.
m 1 ~E cm
One of the effects in searches for KK resonances below the production threshold of the first state is an enhancement of the effective coupling due to KK summation in comparison to the first mode contribution below the threshold only. For the considered case of the stabilized RS model this leads to an increase by 3.3 times in the production
m 1 Another effect: in addition to the resonance pike there is an area with a minimum due to a destructive interference between the first KK resonance and the remaining KK tower contribution. This local minimum takes place at the value of invariant mass M 1.5 m 1 . min ≈ 13 V. Bunichev IHEP 2008 • Studying spin correlations • Studying interference between KK and SM processes • MC Generators for processes: pp → Z 0 Z 0 , pp → t , pp → p e + e → q q t p → + − , p p → t t , p + − , e + e → gg , e + e → + − for TEVATRON, p → Z 0 Z 0 for LHC, for ILC V. Bunichev IHEP 2008 14Plans: