Why X(3915) is so narrow as a ${\chi }_{c0}(2P)$ state

Abstract

New resonance X(3915) was identified as the charmonium ${\chi }_{c0}(2P)$ by BABAR Collaboration, but there seems still open question of this assignment: why its full width is so narrow? To answer this question, we calculate the Okubo-Zweig-Iizuka (OZI) allowed strong decays $X(3915)\to D\bar{D}$, where X(3915) is assigned as a ${\chi }_{c0}(2P)$ state, and estimate its full width in the cooperating framework of ${}^3/!P_0^{}$ model and the Bethe-Salpeter (BS) method using the Mandelstam Formalism, during which non-perturbative QCD effects of the hadronic matrix elements are well considered by overlapping integral over the relativistic Salpeter wave functions of the initial and finial states. We find the node structure of ${\chi }_{c0}(2P)$ wave function resulting in the narrow width of X(3915) and show the dependence of the decay width on the variation of the initial mass of X(3915). We point out that the rate of $\frac{\Gamma (X(3915)\to D^{+}{D}^{-})}{\Gamma (X(3915)\to D^0{\bar{D}}^0)}$ is crucial to confirm whether X(3915) is the ${\chi }_{c0}(2P)$ state or not.

12 pages, 4 figures

References in corpus (10)

• Light Flavour and Heavy Quark Spin Symmetry in Heavy Meson Molecules
• $D_{sJ}(2860)$ and $D_{sJ}(2715)$
• Where is the χ_{c0}(2P)?
• Study of X(3915) --> J/ψω in two-photon collisions
• B_{s1}(5830) and B_{s2}^*(5840)
• Newly observed D_{sJ}(3040) and the radial excitations of P-wave charmed-strange mesons
• Spectrum for Heavy Quankonia and Mixture of the Relevant Wave Functions within the Framework of Bethe-Salpeter Equation
• Decay constants of $P$-wave mesons
• Radiative E1 decays of X(3872)
• Annihilation Rate of Heavy 0^{++} P-wave Quarkonium in Relativistic Salpeter Method

Cited by in corpus (5)

• The hidden-charm pentaquark and tetraquark states
• Strong decays of higher charmonium states into open-charm meson pairs
• Mass spectra for $qc\bar{q}\bar{c}$, $sc\bar{s}\bar{c}$, $qb\bar{q}\bar{b}$, $sb\bar{s}\bar{b}$ tetraquark states with $J^{PC}=0^{++}$ and $2^{++}$
• The Strong Decays of X(3940) and X(4160)
• A quark model study of strong decays of $X\left(3915\right)$