  We carry out high-precision calculation of parity violation in cesium atom,
reducing theoretical uncertainty by a factor of two compared to previous
evaluations. We combine previous measurements with our calculations and extract
the weak charge of the 133Cs nucleus, Q_W = -73.16(29)_exp(20)_th. The result
is in agreement with the Standard Model (SM) of elementary particles. This is
the most accurate to-date test of the low-energy electroweak sector of the SM.
In combination with the results of high-energy collider experiments, we confirm
the energy-dependence (or "running") of the electroweak force over an energy
range spanning four orders of magnitude (from ~10 MeV to ~100 GeV).
Additionally, our result places constraints on a variety of new physics
scenarios beyond the SM. In particular, we increase the lower limit on the
masses of extra $Z$-bosons predicted by models of grand unification and string
theories.
