How to identify the structure of near-threshold states from the line shape

Understand

We revisit the compositeness theorem proposed by Weinberg in an effective field theory (EFT) and explore criteria which are sensitive to the structure of $S$-wave threshold states.

• On a general basis, we show that the wave function renormalization constant $Z$, which is the probability of finding an elementary component in the wave function of a threshold state, can be explicitly introduced in the description of the threshold state.
• As an application of this EFT method, we describe the near-threshold line shape of the $D^{\ast 0}\bar D^0$ invariant mass spectrum in $B\rightarrow D^{\ast 0}\bar D^0 K$ and determine a nonvanishing value of $Z$.
• It suggests that the $X(3872)$ as a candidate of the $D^{\ast 0}\bar D^0$ molecule may still contain a small $c\bar{c}$ core.