Low-energy interactions of Nambu-Goldstone bosons with $D$ mesons in covariant chiral perturbation theory

We calculate the scattering lengths of Nambu-Goldstone bosons interacting with $D$ mesons in a covariant formulation of chiral perturbation theory, which satisfies heavy-quark spin symmetry and analytical properties of loop amplitudes. We compare our results with previous studies performed using heavy-meson chiral perturbation theory and show that recoil corrections are sizable in most cases.

Figure 1

Tree-level contributions at LO [(a), (b), (c)], NLO (d), and NNLO (e).

Figure 2

NNLO loop contributions that survive in the infinite heavy-meson mass ($m_H\to \infty$) limit.

Figure 3

NNLO loop contributions that vanish in the $m_H\to \infty$ limit. Their crossed counterparts are not shown here but are included in the calculation.