Quark model description of $\psi$(4260)

From lattice indications we follow a Born-Oppenheimer approximation to build a quark-antiquark static potential for $J^{PC}=1^{--}$ charmonium states below their first $S$-wave meson-meson threshold. We show that a good description of the mass and decay properties of the experimentally well established $\psi \left(4260\right)$ resonance is feasible.

Figure 1

Representation of the static potential $V_C\left(r\right)$ with $\sigma =850$ MeV/fm and $\zeta =100$ MeV fm.

Figure 2

Representation of the $0^{+}\left(1^{++}\right)c\overline{c}$ static potential $V_{\left[0,m_{D\overline{D^{*}}}\right]}\left(r\right)$ with $m_c=1348.6$ MeV, $\sigma =850$ MeV/fm, $\zeta =100$ MeV fm, and $m_{D\overline{D^{*}}}=3872$ MeV.

Figure 3

Radial wave functions $R\left(r\right)$ (in units of ${\text{fm}}^{-\frac{3}{2}})$ for the $1^{++}\left(2p_{\left[0,m_{D\overline{D^{*}}}\right]}\right)$ state (thick line) and the $1^{++}\left(2p\right)$ state (thin line).

Figure 4

Representation of the $0^{-}\left(1^{--}\right)c\overline{c}$ static potential $V_{\left[0,m_{D\overline{D_1}}\right]}\left(r\right)$ with $m_c=1348.6$ MeV, $\sigma =850$ MeV/fm, $\zeta =100$ MeV fm, $m_{D\overline{D_1}}=4287$ MeV, $\mathrm{\Delta }=60$ MeV, and $s=12.97$ MeV/fm.

Figure 5

Radial wave functions $R\left(r\right)$ (in units of ${\text{fm}}^{-\frac{3}{2}})$ for the $1^{--}\left(4s_{\left[0,m_{D\overline{D_1}}\right]}\right)$ state (thick line) and the $1^{--}\left(4s\right)$ state (thin line).