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Asymptotic normalization coefficients (ANCs) of the $0_1^+$, $0_2^+$,$1_1^-$, $2_1^+$, $3_1^-$ ($l_{i th}^\pi$) bound states of $^{16}$O are deducedfrom the phase shift data of elastic $\alpha$-$^{12}$C scattering at lowenergies. $S$ matrices of elastic $\alpha$-$^{12}$C scattering are constructedwithin cluster effective field theory (EFT), in which both bound and resonantstates of $^{16}$O are considered. Parameters in the $S$ matrices are fitted tothe precise phase shift data below the $p$-$^{15}$N breakup energy for thepartial waves of $l=0,1,2,3,4,5,6$, and the ANCs are calculated by using thewave function normalization factors of $^{16}$O propagators for $l=0,1,2,3$. Wereview the values of ANCs, which are compared with other results in theliterature, and discuss uncertainties of the ANCs obtained from the elastic$\alpha$-$^{12}$C scattering data in cluster EFT.

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