Elastic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mtext>−</mml:mtext><mml:mmultiscripts><mml:mi mathvariant="normal">C</mml:mi><mml:mprescripts/><mml:none/><mml:mn>12</mml:mn></mml:mmultiscripts></mml:mrow></mml:math> scattering at low energies with the bound states of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">O</mml:mi><mml:mprescripts/><mml:none/><mml:mn>16</mml:mn></mml:mmultiscripts></mml:math> in effective field theory

The elastic $\ensuremath{\alpha}\text{\ensuremath{-}}^{12}\mathrm{C}$ scattering for $l=0,1,2,3$ channels at low energies is studied, including the energies of excited bound states of $^{16}\mathrm{O}$, in effective field theory. A new renormalization method is introduced due to the large suppression factor produced by the Coulomb interaction when the effective range parameters are fitted to the phase sift data. After fitting the parameters, the asymptotic normalization constants of the ${0}_{2}^{+},\phantom{\rule{0.16em}{0ex}}{1}_{1}^{\ensuremath{-}},\phantom{\rule{0.16em}{0ex}}{2}_{1}^{+},\phantom{\rule{0.16em}{0ex}}{3}_{1}^{\ensuremath{-}}$ states of $^{16}\mathrm{O}$ are calculated. The uncertainties when the amplitudes are interpolated to the stellar energy region of the $^{12}\mathrm{C}(\ensuremath{\alpha},\ensuremath{\gamma})^{16}\mathrm{O}$ reaction are also discussed.

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