The role of the pion in the lineshape of the X(3872)

We determine the contribution of long-range pion interactions to the X(3872) dynamics, assuming it is a loosely bound D0D¯∗0 molecule. Our result is based on the distorted wave Born approximation in non-relativistic quantum mechanics. Despite their long-range nature, we find that pion interactions cannot produce a large and negative effective range. Nonetheless, they introduce imaginary parts. In particular, they contribute to the total decay width of the X(3872) with a term associated with, but not precisely corresponding to, the D∗ width. Our approach can also be applied to the recently discovered T+cc states.