ANCs of the bound states of ${}^{16}$O deduced from elastic $\alpha$-${}^{12}$C scattering data

Asymptotic normalization coefficients (ANCs) of the $0_1^{+}$, $0_2^{+}$, $1_1^{-}$, $2_1^{+}$, $3_1^{-}$ ($l_{ith}^{\pi }$) bound states of ${}^{16}$O are deduced from the phase shift data of elastic $\alpha$-${}^{12}$C scattering at low energies. $S$ matrices of elastic $\alpha$-${}^{12}$C scattering are constructed within cluster effective field theory (EFT), in which both bound and resonant states of ${}^{16}$O are considered. Parameters in the $S$ matrices are fitted to the precise phase shift data below the $p$-${}^{15}$N breakup energy for the partial waves of $l=0,1,2,3,4,5,6$, and the ANCs are calculated by using the wave function normalization factors of ${}^{16}$O propagators for $l=0,1,2,3$. We review the values of ANCs, which are compared with other results in the literature, and discuss uncertainties of the ANCs obtained from the elastic $\alpha$-${}^{12}$C scattering data in cluster EFT.