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Residue theorem and summing over Kaluza-Klein excitations
Applying the equations of motion together with corresponding boundary
conditions of bulk profiles at infrared and ultraviolet branes, we verify some
lemmas on the eigenvalues of Kaluze-Klein modes in framework of warped extra
dimension with the custodial symmetry . Using the lemmas and performing properly
analytic extensions of bulk profiles, we present the sufficient condition for a
convergent series of Kaluze-Klein excitations and sum over the series through
the residue theorem. The method can also be applied to sum over the infinite
series of Kaluze-Klein excitations in unified extra dimension. Additional, we
analyze the possible connection between the propagators in five dimensional
full theory and the product of bulk profiles with corresponding propagators of
exciting Kaluze-Klein modes in four dimensional effective theory, and recover
some relations presented in literature for warped and unified extra dimensions
respectively. As an example, we demonstrate that the corrections from neutral
Higgs to the Wilson coefficients of relevant operators for contain the suppression factor comparing
with that from other sectors, thus can be neglected safely.Comment: 44 pages, no figur
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