Testing extra dimensions below the production threshold of Kaluza-Klein excitations

We consider a stabilized Randall Sundrum 1 model in the energy range below the direct production of Kaluza-Klein (KK) states. In this range, we work out the effective Lagrangian due to exchange of heavy KK tensor graviton and scalar radion states and compute explicitly the corresponding effective coupling constants. As an example, the Drell-Yan lepton pair production at the Tevatron and the LHC is analyzed in two situations, when the first KK resonance is too heavy to be directly detected at the colliders, and when the first KK resonance is visible, but other states are still too heavy. It is shown that in both cases the contribution from the KK invisible tower leads to a modification of final particles distributions. In particular, for the second case a nontrivial interference between the first KK mode and the rest KK tower takes place. Expected 95% C.L. limits for model parameters for the Tevatron and the LHC are given. In the Appendix, useful formulas for the cross sections and distributions of various new 2→2 processes via heavy KK tower exchange are presented, the new formulas containing nonzero particle masses for final state fermions and bosons. The formulas and numerical results are obtained by means of the CompHEP code, in which all new effective interactions are implemented providing a tool for simulation of corresponding events and a more detailed analysis.