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We have calculated static and dynamic electric dipole (E1) polarizabilities($\alpha_F$) of the hyperfine levels of the clock transition precisely in$^{133}$Cs. The scalar, vector, and tensor components of $\alpha_F$ areestimated by expressing as sum of valence, core, core-core, core-valence, andvalence-core contributions that are arising from the virtual and coreintermediate states. The dominant valence contributions are estimated bycombining a large number of matrix elements of the E1 and magnetic dipolehyperfine interaction operators from the relativistic coupled-cluster methodand measurements. For an insightful understanding of their accuratedetermination, we explicitly give intermediate contributions in different formsto the above quantities. Very good agreement of the static values for thescalar and tensor components with their experimental results suggest that ourestimated dynamic $\alpha_F$ values can be used reliably to estimate the Starkshifts while conducting high-precision measurements at the respective laserfrequency using the clock states of $^{133}$Cs.

High-precision Electric Dipole Polarizabilities of the Clock States in $^{133}$Cs