Readdressing the hierarchy problem in a Randall-Sundrum scenario with bulk Kalb-Ramond background

We re-examine the fine tuning problem of the Higgs mass, when an antisymmetric two form Kalb-Ramond(KR) field is present in the bulk of a Randall Sundrum (RS) braneworld. Taking into account the back-reaction of the KR field, we obtain the exact correction to the RS metric, and show that the modified metric puts a stringent condition on the Kalb-Ramond energy density, if the Higgs mass is to be warped from the Planck scale to the Tev scale. This condition, which requires that the KR field energy density must be heavily suppressed on the observable three brane, remarkably matches with a previously obtained result where the massless mode of the KR field was shown to have an exponential suppression in a RS braneworld. This result is particularly relevant for certain string based models where the KR field is unavoidably present in the bulk. We further show that such a bulk antisymmetric KR field along with gravity fails to stabilize the braneworld.