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 2-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. The modified metric also warps the Higgs mass from Planck scale ( in higher dimension) to TeV scale ( on the visible brane) for a range of values of kr exceeding the original RS value ( where k = Planck mass and r = size of extra dimension). However, it requires an extraordinary suppression of the KR field density, indicating the re-appearence of the fine-tuning problem in a different guise. The new spacetime also generates a small negative cosmological constant on the visible brane. These results are 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 fails to stabilize the braneworld.