A recent measurement of $^4$He photodisintegration reactions, $^4$He($gamma$,$p$)$^3$H and $^4$He($gamma$,$n$)$^3$He with laser-Compton photons shows smaller cross sections than those estimated by other previous experiments at $E_gamma lesssim 30$ MeV. We study big-bang nucleosynthesis with the radiative particle decay using the new photodisintegration cross sections of $^4$He as well as previous data. The sensitivity of the yields of all light elements D, T, $^3$He, $^4$He, $^6$Li, $^7$Li and $^7$Be to the cross sections is investigated. The change of the cross sections has an influence on the non-thermal yields of D, $^3$He and $^4$He. On the other hand, the non-thermal $^6$Li production is not sensitive to the change of the cross sections at this low energy, since the non-thermal secondary synthesis of $^6$Li needs energetic photons of $E_gamma gtrsim 50$ MeV. The non-thermal nucleosynthesis triggered by the radiative particle decay is one of candidates of the production mechanism of $^6$Li observed in metal-poor halo stars (MPHSs). In the parameter region of the radiative particle lifetime and the emitted photon energy which satisfies the $^6$Li production above the abundance level observed in MPHSs, the change of the photodisintegration cross sections at $E_gamma lesssim 30$ MeV as measured in the recent experiment leads to $sim 10$% reduction of resulting $^3$He abundance, whereas the $^6$Li abundance does not change for this change of the cross sections of $^4$He($gamma$,$p$)$^3$H and $^4$He($gamma$,$n$)$^3$He. The $^6$Li abundance, however, could show a sizable change and therefore the future precise measurement of the cross sections at high energy $E_gamma gtrsim$ 50 MeV is highly required.
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