bunichev viacheslav

V. Bunichev IHEP 2008

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Bunichev ViacheslavBunichev Viacheslav

Testing extra dimensions below the productionTesting extra dimensions below the productionthreshold of Kaluza-Klein excitationsthreshold of Kaluza-Klein excitations

In collaboration withIn collaboration with EE..BoosBoos, , I.VolobuevI.Volobuev andand M.M. SmolyakovSmolyakov


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MotivationMotivation ofof usingusing additionaladditional space-time dimensionsspace-time dimensions

• Grand unification. Superstring theory.

• Hierarchy problem

• Dark matter candidate


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Effective action Effective action of theories with compact extra dimensionsof theories with compact extra dimensions

Where:MN (M, N = 0, 1, 2, 3, …, 3+d, sign = +, -, … , -) - background metric in the bulk,

- bulk field,

L() - bulk Lagrangian of the field L(SM-) - Lagrangian of the Standard Model fields, which do not propagate in the bulk

JSM* - scalar product of the corresponding current of the Standard Model fields JSM and the

field on the brane, g - four-dimensional coupling constant,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 {xμ} 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 (n)(x) and their wave functions in the space of extra dimension (n)(y).

где Lint ( (m)) stands for the self-interaction Lagrangian of the modes,

{ yb } denotes the coordinates of the brane in the space of extra dimensions

Substituting this representation into action and integrating over the coordinates of extradimensions, we get the reduced four-dimensional action


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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 isof the same order of magnitude, as the inverse size of extra dimensions. Then the massesof the KK excitations are proportional to this energy scale M and the wave functions areproportional to Md/2, and the coupling constant can be represented as

EffectiveEffective contactcontact interactioninteraction of KKof KK modesmodes withwith SM fieldsSM fields


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SStabilized Randall-Sundrumtabilized Randall-Sundrum ( (RS1RS1) ) modelmodel..

• 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.

• 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.

( E. E. Boos, I. P. Volobuev, Y. A. Kubyshin and M. N. Smolyakov, Theor. Math. Phys. 131, 629 (2002) )

( 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) )


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EffectiveEffective contactcontact interactioninteraction of KKof KK modesmodes withwith SM fieldsSM fields in the frame of the in the frame of the SStabilized Randall-Sundrumtabilized Randall-Sundrum ( (RS1RS1) ) modelmodel..

Interraction of SM with spin 2 КК modes

The sum over the tensor modes can be expressed through constant and the mass of the

first mode

)( 32

, ,)(

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1,

02

2

3

TTm

L

ML

n n

neff

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 0 КК modes

(E. Boos, V.Bunichev, M.Smolyakov, I.Volobuev, arXiv:0710.3100v1 [hep-ph])


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Symbolic results:Symbolic results:

Total width for the KK graviton resonance

Symbolic computations have been performed by means of the version of theCompHEP package realized on basis of the FORM symbolic program.


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Processes ggZ0Z0 with spin 2 and spin 0 KK states:

Total and differential cross sections for the process llqq


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NumericalNumerical resultsresults

Numerical computations, MC generators and demonstration plots have been performed by means of the CompHEP package

Dilepton invariant mass distribution for parameter x(1TeV )4=0.0014 (dash-dotted line), 0.0046 (dashed line), 0.01 (dotted line) for the LHC

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2 m

91.0


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Collider potential, LHCCollider potential, LHC

Estimation of experimental 95% CL limit for the coupling parameter that may be reached at the LHC (L = 100fb-1)

][,0014.091.0 4

21

2

TeV

m

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< m1/ξ, where ξ > 1.

][,82.2 41

TeV


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Collider potential, TEVATRONCollider potential, TEVATRON

Estimation of experimental 95% CL limit for the coupling parameter that may be reached at the TEVATRON (L = 10fb-1)

][,66.091.0 4

21

2

TeV

m

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< m1/ξ, where ξ > 1.

][,61.0 41

TeV


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Total sum of KK modesTotal sum of KK modes and firstand first КК КК resonanceresonance

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 rate.

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 Mmin ≈ 1.5 m1.

m1~Ecm m1<Ecm


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Plans:Plans:

• Studying spin correlations

• Studying interference between KK and SM processes

• MC Generators for processes: pp → Z0Z0, pp → tt , pp → +− for TEVATRON, pp → +−, pp → tt , pp → Z0Z0 for LHC, e+e-→ qq , e+e-→ gg, e+e-→ +− for ILC

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