Bunichev Viacheslav

1. Testing extra dimensions below the production threshold of Kaluza-Klein excitations Bunichev Viacheslav In collaboration withE.Boos, I.VolobuevandM.Smolyakov V. Bunichev IHEP 2008

2. Motivationofusingadditionalspace-time dimensions • Grand unification. Superstring theory. • Hierarchy problem • Dark matter candidate V. Bunichev IHEP 2008

3. Effective action of theories with compact extra dimensions Where: MN (M, N = 0, 1, 2, 3, …, 3+d, sign  = +, -, … , -)- background metricin 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 pointis that the induced metric on the brane is flat, i.e. the coordinates {xμ} are Galileanon the brane V. Bunichev IHEP 2008

4. It is a common knowledge that the bulk field can be expanded in Kaluza-Klein modes with definite masses (n)(x)and their wave functionsin the space of extra dimension (n)(y). Substituting this representation into action and integrating over the coordinates of extra dimensions, we get the reduced four-dimensional action где Lint ( (m))stands for the self-interaction Lagrangian of the modes, { yb } denotesthe coordinates of the brane in the space of extra dimensions V. Bunichev IHEP 2008

5. Effectivecontactinteractionof KKmodeswithSM fields Now if we consider the theorywith action for the energy or momentum transfer much smaller, than the masses of theKK-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 Md/2, and the coupling constant can be represented as V. Bunichev IHEP 2008

6. 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 thismodel is the presence of a massive scalarmode, – the radion. • Stabilization - the brane separation distance has defined value • Radion massis definedby the brane separation distance. • Theweakness of the gravitationalinteraction is defined by the warp factor in the metric. V. Bunichev IHEP 2008

7. Effectivecontactinteractionof KKmodeswithSM fieldsin the frame of the Stabilized Randall-Sundrum (RS1) model. Inthe 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 ofSM withspin 2 КК modes The sum over the tensor modes can be expressedthrough constant and the mass of the first mode (E. Boos, V.Bunichev, M.Smolyakov, I.Volobuev, arXiv:0710.3100v1 [hep-ph]) Interraction ofSM withspin 0 КК modes V. Bunichev IHEP 2008

8. 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 V. Bunichev IHEP 2008

9. Processes ggZ0Z0 withspin 2 and spin 0 KK states: Total and differential cross sections for the process V. Bunichev IHEP 2008

10. Numericalresults Numerical computations, MC generators and demonstration plots have been performed by means of the CompHEP package Dilepton invariant mass distributionforparameter x(1TeV )4=0.0014(dash-dotted line), 0.0046 (dashed line), 0.01(dotted line) for the LHC V. Bunichev IHEP 2008

11. Collider potential, LHC Estimation of experimental 95% CL limit for the couplingparameter that may be reached at the LHC(L = 100fb-1) Estimationof the lowest value for the fundamental scale parameter from a requirement that the widthofthe first resonance be smaller than its mass: 1< m1/ξ, where ξ > 1. V. Bunichev IHEP 2008

12. Collider potential, TEVATRON Estimation of experimental 95% CL limit for the couplingparameter that may be reached at the TEVATRON (L = 10fb-1) Estimationof the lowest value for the fundamental scale parameter from a requirement that the widthofthe first resonance be smaller than its mass: 1< m1/ξ, where ξ > 1. V. Bunichev IHEP 2008

13. Total sum of KK modesand first КК resonance m1~Ecm m1<Ecm One of the effects in searches for KK resonances below the production threshold of thefirst state is an enhancement of the effective coupling due to KK summation in comparisonto the firstmode contribution below the threshold only. For the considered case of thestabilized 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 adestructiveinterference between the first KKresonance and the remaining KK towercontribution. Thislocal minimum takes place at the value of invariant mass Mmin ≈ 1.5 m1. V. Bunichev IHEP 2008

14. Plans: • Studying spin correlations • Studyinginterferencebetween KK and SMprocesses • MC Generators for processes: • pp → Z0Z0, pp → tt ,pp → +− forTEVATRON, • pp → +−, pp → tt , pp → Z0Z0for LHC, • e+e-→ qq , e+e-→ gg, e+e-→ +− for ILC V. Bunichev IHEP 2008