Testing physics beyond the standard model through additional clock transitions in neutral ytterbium

We study the prospects of using transitions from the ytterbium ground state to metastable states ³P₂ᵒ at E=190.16em0ex710.3884pt0excm^-1 and 4f¹³5d6s²4pt0ex(J=2) at E=230.16em0ex188.5184pt0excm^-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 nonlinearity 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 high accuracy, approaching what is already achieved for the ¹S₀-³P₀ᵒ clock transition.