Speaker
Description
Whether the X(3872) is a compact tetraquark or a loosely bound $D\bar{D}^*$
molecule remains one of the central open questions in exotic hadron
spectroscopy. In this talk we argue that the answer is encoded in the
particle's lineshape, but only if the data are analysed within the right
effective theory. The Flattè distribution ($f_-$) routinely used to fit
experimental lineshapes is derived from a Lagrangian in which $X$, $D$ and
$\bar{D}^*$ all appear as elementary fields; a good Flattè fit therefore
tests the compact hypothesis, not the
molecular one, and applying the Weinberg compositeness criterion to such a
fit becomes circular. A genuinely molecular $X$ must instead be described by
an effective theory in which the $X$ field is absent, or introduced only as
an auxiliary, unphysical field. Remarkably, the resulting lineshape $f_+$
differs from the Flattè one by a single sign, that of the kinetic term
of the $X$ field ($\sigma=-1$ for the molecular case versus $\sigma=+1$ for
the elementary one). We validate this construction on the
analogous nucleon--deuteron system, where the coupling between the bound
state and its constituents is not free but fixed model-independently by the
Landau coupling, $g_B^2 = \frac{2\pi}{m}\sqrt{\frac{2B}{m}}$. With this input the
framework reproduces the $np \to \text{deuteron} \to np$ scattering data and
the measured deuteron effective range. Then we present
a Monte Carlo study showing that refitting the X(3872) lineshape with the
same parametrization, and with a coupling compatible with the Landau coupling,
provides a genuine, non-circular test of its molecular interpretation.