  Our improved calculation of the nuclear spin-independent parity violating
electric dipole transition amplitude ($E1_{PV}$) for $6s ~ ^2S_{1/2} - 7s ~
^2S_{1/2}$ in $^{133}$Cs in combination with the most accurate (0.3\%)
measurement of this quantity yields a new value for the nuclear weak charge
$Q_W=-73.71(26)_{ex} (23)_{th}$ against the Standard Model (SM) prediction
$Q_W^{\text{SM}}=-73.23(1)$. The advances in our calculation of $E1_{PV}$ have
been achieved by using a variant of the perturbed relativistic coupled-cluster
theory which treats the contributions of the core, valence and excited states
to $E1_{PV}$ on the same footing unlike the previous high precision
calculations. Furthermore, this approach resolves the controversy regarding the
sign of the core correlation effects. We discuss the implications of the
deviation of our result for $Q_W$ from the SM value by considering different
scenarios of new physics.
