0 v 1 2 8 Ja n 20 02 Tadpole diagrams due to KK modes of graviton and radion do not contribute to the ρ parameter

In this brief report we show that tadpole diagrams due to KK modes of the graviton and radion do not contribute to the vectorial isospin breaking ρ parameter. Our result is fairly general and it holds both for ADD and RS type scenarios. It shows that the difference between the results of different publications on this subject is not due to some of them not having considered tadpole diagrams in estimating the contribution to the ρ parameter. E-mail: [email protected] E-mail:[email protected] 1 Recently there has been a lot of activity in putting bounds on the unknown parameters of models of extra dimensions [[1], [2]]. The oblique electrweak (EW) parameters S, T and U in particular have been used to put bounds on the unknown parameters [[3], [4], [5]] of the model. However the analysis of these papers differ considerably among themselves and so also their result. For example in Ref. 3 the tadpole diagrams due to Kaluza-Klein (KK) modes of the graviton and the radion were considered in estimating the contribution of sub-millimeter size extra dimensions to the ρ parameter. However no such tadpole diagrams were considered in Ref. 4 to estimate the ρ parameter in the same model. The controversy between the two papers is particularly serious because of two reasons: i) firstly tadpole diagrams are sometimes necessary to rastore gauge invariance of the final result and ii) secondly the bounds given in Ref. 3 are much stronger than those of Ref. 4. Further in a footnote of Ref. 3 it has been mentioned that the results of Ref. 4 should not be trusted since the authors of that paper do not consider the contribution of tadpole diagrams to the ρ parameter. It is therefore crucial to find out if the difference between the results of Refs. 3 and 4 really originates from tadpole diagrams. In this brief report we shall explicitly show that the tadpole diagrams due to KK modes of graviton and radion do not contribute to the ρ parameter. Our result implies that tadpole diagrams are SU(2)v symmetric. It also shows that the difference between the results of Ref. 3 and Ref. 4 does not originate from tadpole diagrams but from somewhere else e.g. in the treatment of infrared divergences. Let us first consider the contribution of a KK graviton tadpole to the ρ parameter. Let ∆μν,αβ(k = 0) denote the propagator for the KK graviton shown in Fig1. We then have [6]