The s-wave πd scattering length from the πd atom in an effective field theory approach

The π−d atom strong energy‐level shift in the 1s state is derived by using effective field theory. We have considered the deuteron as a particle described by a vector field. The pion is described by a scalar field. To obtain the nonrelativistic Hamiltonian for the πd system a Foldy‐Wouthuysen transformation has been derived for the vector field. The strong interaction between pion and deuteron has been taken at the zero‐range approach. We have found a Deser‐type formula for the relation between the strong energy‐level shift and the s‐wave πd scattering length.

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