The $c\bar{c}$ interaction above threshold and the radiative decay $X(3872)\to J/\psi \gamma$

Abstract

Radiative decays of $X(3872)$ are studied in single-channel approximation (SCA) and in the coupled-channel (CC) approach, where the decay channels $D{\bar{D}}^{\ast }$ are described with the string breaking mechanism. In SCA the transition rate ${\tilde{\Gamma }}_2=\Gamma (2{}^3{P}_1\to \psi \gamma )=71.8$~keV and large ${\tilde{\Gamma }}_1=\Gamma (2{}^3{P}_1\to J/\psi \gamma )=85.4$~keV are obtained, giving for their ratio the value $\widetilde{R_{\psi \gamma }}=\frac{{\tilde{\Gamma }}_2}{{\tilde{\Gamma }}_1}=0.84$. In the CC approach three factors are shown to be equally important. First, the admixture of the $1{}^3{P}_1$ component in the normalized wave function of $X(3872)$ due to the CC effects. Its weight $c_{\mathrm{X}}(E_{\mathrm{R}})=0.200\pm 0.015$ is calculated. Secondly, the use of the multipole function $g(r)$ instead of $r$ in the overlap integrals, determining the partial widths. Thirdly, the choice of the gluon-exchange interaction for $X(3872)$, as well as for other states above threshold. If for $X(3872)$ the gluon-exchange potential is taken the same as for low-lying charmonium states, then in the CC approach ${\Gamma }_1=\Gamma (X(3872)\to J/\psi \gamma )\sim 3$~keV is very small, giving the large ratio $R_{\psi \gamma }=\frac{\mathcal{B}(X(3872)\to \psi (2S)\gamma )}{\mathcal{B}(X(3872)\to J/\psi \gamma )}\gg 1.0$. Arguments are presented why the gluon-exchange interaction may be suppressed for $X(3872)$ and in this case ${\Gamma }_1=42.7$~keV, ${\Gamma }_2=70.5$~keV, and $R_{\psi \gamma }=1.65$ are predicted for the minimal value $c_{\mathrm{X}}(\min )=0.185$, while for the maximal value $c_{\mathrm{X}}=0.215$ we obtained ${\Gamma }_1=30.8$~keV, ${\Gamma }_2=73.2$~keV, and $R_{\psi \gamma }=2.38$, which agrees with the LHCb data.

arXiv comment12 pages, no figures

References in corpus (59)

• 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
• The chiral and deconfinement aspects of the QCD transition
• Higher Charmonia
• Observation of the Narrow State $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ in $\bar{p}p$ Collisions at $\sqrt{s}=1.96 \TeV$
• Observation and Properties of the X(3872) Decaying to J/psi pi+ pi- in p-p(bar) Collisions at sqrt(s) = 1.96 TeV
• Isospin breaking of the narrow charmonium state of Belle at 3872 MeV as a deuson
• Study of the B- --> J/psi K- pi+ pi- Decay and Measurement of the B- --> X(3872) K- Branching Fraction
• Short Range Structure in the X(3872)
• Determination of the X(3872) meson quantum numbers
• Observation of String Breaking in QCD
• The 2009 World Average of ${\alpha }_s$
• The D*0 D0bar threshold resonance
• Higher Charmonia and X,Y,Z states with Screened Potential
• Quarkonia and their transitions
• Charmonium Options for the X(3872)
• Charmonium levels near threshold and the narrow state $X(3872) \to π^{+}π^{-}\jpsi$
• Casimir scaling of SU(3) static potentials
• Field correlators in QCD. Theory and applications
• The X(3872) boson: Molecule or charmonium
• Analysis of the Quantum Numbers $J^{PC}$ of the X(3872) Particle
• Is X(3872) {\sl Really} a Molecular State?
• Diagnostic Decays of the X(3872)
• Evidence for X(3872) --> psi(2S) gamma in B+/- --> X(3872) K+/- decays, and a study of B --> ccbar gamma K
• Observation of X(3872) production in pp collisions at sqrt(s)= 7 TeV
• New states above charm threshold
• Observation of $X(3872)\to J/\psi \gamma$ and search for $X(3872)\to {\psi }^{\prime }\gamma$ in B decays
• Production of the X(3872) in charmonia radiative decays
• Search for B+ --> X(3872) K+, X(3872) --> J/psi gamma
• Charmless Final States and S--D-wave mixing in the ${\psi }^{\prime \prime }$
• Interpretation of the X(3872) as a charmonium state plus an extra component due to the coupling to the meson-meson continuum
• Precision Measurement of the X(3872) Mass in J/psi pi+ pi- Decays
• Dynamical origin and the pole structure of X(3872)
• World Summary of ${\alpha }_s$ (2012)
• Light meson radial Regge trajectories
• Channel coupling in heavy quarkonia: energy levels, mixing, widths and new states
• Determination of the Static Potential with Dynamical Fermions
• Higher excitations of the $D$ and $D_s$ mesons
• Systematics of heavy quarkonia from Regge trajectories on $(n,M^2)$ and $(M^2,J)$ planes
• Radiative E1 decays of X(3872)
• Radiative transitions of heavy quarkonium states
• Exchange Current Operators and Electromagnetic Dipole Transitions in Heavy Quarkonia
• The three-quark static potential in perturbation theory
• The ratio of decay widths of X(3872) to ${\psi }^{\prime }\gamma$ and $J/\psi \gamma$ as a test of the X(3872) dynamical structure
• Dielectron widths of the S-, D-vector bottomonium states
• Asymptotic freedom and IR freezing in QCD: the role of gluon paramagnetism
• String Breaking in Four Dimensional Lattice QCD
• Spin-dependent interactions in quarkonia
• Radiative decay Y(4260) -> X(3872) + gamma involving hadronic molecular and charmonium components
• $X(3872)$, $X_b$, and the ${\chi }_{b1}(3P)$ state
• The Hyperfine Splittings in Bottomonium and the $B_q(q=n,s,c)$ Mesons
• Di-electron and two-photon widths in charmonium
• Relativistic theory of string breaking in QCD
• Recent progress on the study of the charmoniumlike states
• The static force in background perturbation theory
• Static hybrid quarkonium potential with improved staggered quarks
• Microscopic study of the string breaking in QCD
• Radial Regge trajectories for higher $\psi (nS)$ and $\psi (nD)$ states

Cited by in corpus (8)

• Heavy hadronic molecules with pion exchange and quark core couplings: a guide for practitioners
• X(3872) in the molecular model
• $X(3872)$ as virtual companion pole of the charm-anticharm state ${\chi }_{c1}(2P)$
• Dimesonic states with the heavy-light flavour mesons
• The radial Regge trajectories and leptonic widths of the isovector mesons
• Probing the nature of the ${\chi }_{c1}(3872)$ state using radiative decays
• The nature of ${\chi }_{c1}\left(3872\right)$ and $T_{cc}^{+}\left(3875\right)$
• Study of $e^{+}{e}^{-}\to \omega X(3872)$ and $\gamma X(3872)$ from 4.66 to 4.95 GeV