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

Abstract

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 $B\to D^{\ast 0}{\bar{D}}^{0}K$ 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. 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 $D^{\ast 0}{\bar{D}}^0$ threshold enhancement observed in the $D^{\ast 0}{\bar{D}}^0$ invariant mass distributions. Meanwhile, we also show that if $Z$ is non-zero, the near-threshold enhancement of the $D^{\ast 0}{\bar{D}}^0$ mass spectrum in the $B$ decay will be driven by the short-distance production mechanism. This conclusion is still true even if the long-distance production is enhanced by some unexpected mechanism.

version to be published in Chinese Physics C

References in corpus (16)

• Heavy quarkonium: progress, puzzles, and opportunities
• Study of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ and Observation of a Charged Charmonium-like State at Belle
• Observation of a charged charmoniumlike structure Z_c(4020) and search for the Z_c(3900) in e+e- to pi+pi-h_c
• Observation of a charged (DD*bar)- mass peak in e+e- --> pi+ (DD*bar)- at Ecm=4.26 GeV
• Pion Interactions in the X(3872)
• Is the X(3872) Production Cross Section at Tevatron Compatible with a Hadron Molecule Interpretation?
• Reconciling the X(3872) with the near-threshold enhancement in the D^0\bar{D}^{*0} final state
• Evidence for the decay $X(3872)\to \psi (2S)\gamma$
• Evidence for X(3872) from DD* scattering on the lattice
• Line Shapes of the X(3872)
• Production of the X(3872) in charmonia radiative decays
• Confirming the molecular nature of the $Z_b(10610)$ and the $Z_b(10650)$
• Nature of X(3872) from data
• Ambiversion of X(3872)
• Quark mass dependence of the X(3872) binding energy
• Light quark mass dependence of the X(3872) in XEFT

Cited by in corpus (18)

• Hadronic molecules
• The hidden-charm pentaquark and tetraquark states
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Different pole structures in line shapes of the $X(3872)$
• Structure of near-threshold quasi-bound states
• From the lineshape of the $X(3872)$ to its structure
• Strong decays of higher charmonium states into open-charm meson pairs
• Heavy Flavour Physics and CP Violation at LHCb: a Ten-Year Review
• $X(3872)$, $X_b$, and the ${\chi }_{b1}(3P)$ state
• Compositeness of $T_{cc}$ and $X(3872)$ by considering decay and coupled-channels effects
• Decipher the short-distance component of $X(3872)$ in $B_c$ decays
• The nature of $Z_b$ states from a combined analysis of ${\rm Y}(5S)\to h_b(mP){\pi }^{+}{\pi }^{-}$ and ${\rm Y}(5S)\to B^{(\ast )}{\bar{B}}^{(\ast )}\pi$
• Compositeness of hadrons, nuclei, and atomic systems
• The effects of charmonium on the properties of the $1^{++}$ hidden charm poles in effective field theory
• The general propagator for S-wave threshold states
• Compositeness of Hadrons and Near-Threshold Dynamics
• Exotic hadrons associated with $b$-quark
• Structure of $X_b$ from line shape analysis