  We present a new theoretical analysis of the strongly suppressed F- and
M-dependent Stark shifts of the Cs ground state hyperfine structure. Our
treatment uses third order perturbation theory including off-diagonal hyperfine
interactions not considered in earlier treatments. A numerical evaluation of
the perturbation sum using bound states up to n=200 yields ground state tensor
polarizabilities which are in good agreement with experimental values, thereby
bridging the 40-year-old gap between experiments and theory. We have further
found that the tensor polarizabilities of the two ground state hyperfine
manifolds have opposite signs, in disagreement with an earlier derivation. This
sign error has a direct implication for the precise evaluation of the blackbody
radiation shift in primary frequency standards.
