Additional clock transitions in neutral ytterbium bring new possibilities for testing physics beyond the Standard Model

We study the prospects of using transitions from the ytterbium ground state to metastable states $^3{\rm P}^{\rm o}_2$ at $E=19\,710.388~$cm$^{-1}$ and $4f^{13}5d6s^2\,(J=2)$ at $E=23\,188.518~$cm$^{-1}$ as clock transitions in an optical lattice clock. Having more than one clock transition in Yb could benefit the search for new physics beyond the Standard Model via studying the non-linearity of King's plot or the time-variation of the ratio of the frequencies of two clock transitions. We calculate the lifetime of the states, relevant transition amplitudes, systematic shifts, and the sensitivities of the clock transitions to a variation of the fine structure constant and to the gravitational potential. We find that both transitions can probably support ultra-high accuracy, similar to what is already achieved for the $^1$S$_0$ - $^3$P$^{\rm o}_0$ clock transition.