Identifying the structure of near-threshold states from the line shapeSupported by National Natural Science Foundation of China (11147022, 11035006, 11305137), Chinese Academy of Sciences (KJCX2-EW-N01), Ministry of Science and Technology of China (2009CB825200), DFG and NSFC (11261130311) through funds provided to the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD”, and Doctor Foundation of Xinjiang University (BS110104)

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*0D̅0 invariant mass spectrum in B→D*0D̅0K and determine a nonvanishing value of Z. It suggests that the X(3872) as a candidate of the D*0D̅0 molecule may still contain a small cc̄ core. This elementary component, on the one hand, explains its production in the B meson decay via a short-distance mechanism, and on the other hand, is correlated with the D*0D̅0 threshold enhancement observed in the D*0D̅0 invariant mass distributions. Meanwhile, we also show that if Z is non-zero, the near-threshold enhancement of the D*0D̅0 mass spectrum in the B decay will be driven by the short-distance production mechanism