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 (42)

• Observation of a narrow charmonium-like state in exclusive B+ -> K+ pi+pi- J/psi decays
• Observation of a New Narrow Charmonium State in Exclusive B+-->K+ pi+pi- J/psi Decays
• Heavy quarkonium: progress, puzzles, and opportunities
• Observation of a charged charmoniumlike structure in e+e- to pi+pi-J/psi at \sqrt{s}=4.26 GeV
• A New Expansion for Nucleon-Nucleon Interactions
• Study of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ and Observation of a Charged Charmonium-like State at Belle
• Two-Nucleon Systems from Effective Field Theory
• Observation of two charged bottomonium-like resonances in Y(5S) decays
• Isospin breaking of the narrow charmonium state of Belle at 3872 MeV as a deuson
• Observation of a charged charmoniumlike structure Z_c(4020) and search for the Z_c(3900) in e+e- to pi+pi-h_c
• Short Range Structure in the X(3872)
• Evidence that the a0(980) and f0(980) are not elementary particles
• Observation of the Charged Hadron $Z_c^{\pm }(3900)$ and Evidence for the Neutral $Z_c^0(3900)$ in $e^{+}{e}^{-}\to \pi \pi J/\psi$ at $\sqrt{s}=4170$ MeV
• The D*0 D0bar threshold resonance
• Observation of a charged (DD*bar)- mass peak in e+e- --> pi+ (DD*bar)- at Ecm=4.26 GeV
• Decoding the riddle of Y(4260) and $Z_c(3900)$
• Low-energy Universality and the New Charmonium Resonance at 3870 MeV
• Interference and binding effects in decays of possible molecular component of X(3872)
• The X(3872) boson: Molecule or charmonium
• Molecular States of Heavy Quark Mesons
• Pion Interactions in the X(3872)
• Is the X(3872) Production Cross Section at Tevatron Compatible with a Hadron Molecule Interpretation?
• Coupled-channel dynamics in the reactions piN --> piN, etaN, KLambda, KSigma
• Diagnostic Decays of the X(3872)
• Reconciling the X(3872) with the near-threshold enhancement in the D^0\bar{D}^{*0} final state
• Evidence for the decay $X(3872)\to \psi (2S)\gamma$
• Study of Resonances in Exclusive B Decays to Dbar(*)D(*)K
• Bound state nature of the exotic Z_b states
• 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
• Study of the $B\to X(3872)(\to D^{\ast 0}{\bar{D}}^0)K$ decay
• A study of B->X(3872) K, with X(3872)->J/Psi pi+ pi-
• Confirming the molecular nature of the $Z_b(10610)$ and the $Z_b(10650)$
• Dynamical origin and the pole structure of X(3872)
• J/psi gamma and psi(2S) gamma decay modes of the X(3872)
• Nature of X(3872) from data
• Ambiversion of X(3872)
• Analysis of J/psi pi+ pi- and D0 D0-bar pi0 Decays of the X(3872)
• Quark mass dependence of the X(3872) binding energy
• $B\to {\chi }_{c1}(1P,2P)K$ decays in QCD factorization and X(3872)
• 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