Calculation of higher-order corrections to the light shift of the $5s^2{}^1\text{\hspace{0.17em}⁣}{S}_0$--$5s5p{}^3\text{\hspace{0.17em}⁣}{P}_0^o$ clock transition in Cd

In the recent work [A.~Yamaguchi et. al, Phys. Rev. Lett. {\bf 123}, 113201 (2019)] Cd has been identified as an excellent candidate for a lattice clock. Here, we carried out computations needed for further clock development and made an assessment of the higher-order corrections to the light shift of the $5s^2, ^1!S_0$--$5s5p, ^3!P_0^o$ clock transition. We carried out calculations of the magnetic dipole and electric quadrupole polarizabilities and linear and circular hyperpolarizabilities of the $5s^2{}^1\text{\hspace{0.17em}⁣}{S}_0$ and $5s5p{}^3\text{\hspace{0.17em}⁣}{P}_0^o$ clock states at the magic wavelength and estimated uncertainties of these quantities. We also evaluated the second-order Zeeman clock transition frequency shift.