Binding energy of the $X(3872)$ at unphysical pion masses

Understand

Chiral extrapolation of the $X(3872)$ binding energy is investigated using the modified Weinberg formulation of chiral effective field theory for the $D \bar{D}^*$ scattering.

• Given its explicit renormalisability, this approach is particularly useful to explore the interplay of the long- and short-range $D \bar{D}^*$ forces in the $X(3872)$ from studying the light-quark (pion) mass dependence of its binding energy.
• In particular, the parameter-free leading-order calculation shows that the $X$-pole disappears for unphysical large pion masses.
• On the other hand, without contradicting the naive dimensional analysis, the higher-order pion-mass-dependent contact interaction can change the slope of the binding energy at the physical point yielding the opposite scenario of a stronger bound $X$ at pion masses larger than its physical value.