The Born-Oppenheimer approximation in an effective field theory framework

The Born-Oppenheimer approximation is the standard method for the studying atoms and molecules. It is founded on the observation that the energy scale of the electron dynamics in a molecule is larger than that of the nuclei. A very similar physical picture can be used to describe QCD states containing heavy quarks as well as light quarks and gluonic excitations. In this communication I present selected results of a recent work [N. Brambilla, G. Krein, J. Tarrús-Castellà and A. Vairo, Phys. Rev. D 97, 016016 (2018)] in which the Born-Oppenheimer approximation for atomic and hadronic molecular systems emerges as the leading-order approximation of an effective field theory obtained by sequentially integrating out degrees of freedom living at energies above the typical energy scale where the dynamics of the heavy degrees of freedom occurs. As an example, the simple case of a ion molecule formed by two heavy nuclei and one electron is considered.