Constraining the Randall-Sundrum modulus in the light of recent PVLAS data

Recent PVLAS data put stringent constraints on the measurement of birefringence and dichroism of electromagnetic waves travelling in the constant and homogeneous magnetic field. There have been theoretical predictions in favor of such phenomena when appropriate axion-electromagnetic coupling is assumed. Origin of such a coupling can be traced in a low energy string action from the requirement of quantum consistency. The resulting couplings in such models are an artifact of the compactification of the extra dimensions present inevitably in a string scenario. The moduli parameters which encode the compact manifold therefore play a crucial role in determining the axion-photon coupling. In this work we examine the possible bounds on the value of compact modulus that emerge from the experimental limits on the coupling obtained from the PVLAS data. In particular we focus into the Randall-Sundrum (RS) type of warped geometry model whose modulus parameter is already restricted from the requirement of the resolution of the gauge hierarchy problem in connection with the mass of the Higgs. We explore the bound on the modulus for a wide range of the axion mass for both the birefringence and the dichroism data in PVLAS. We show that the proposed value of the modulus in the RS scenario can only be accommodated for axion mass greater than or similar to 0.3 eV.