XIII International Workshop on Hadron Physics - XIII Hadron Physics

Calculating the $\mathcal{D^*}$ off-shell case of $g_{\eta_c \mathcal{D}^* \mathcal{D}}$ using the QCD sum rules approach.

Not scheduled

3h 30m

Hotel do Bosque

Poster Hadronic structure - reactions, production and decays

Speaker

Dr Bruno Osorio Rodrigues (CBPF)

Description

In the past few decades, the QCD sum rules (QCDSR) community, has been working actively in the calculation of strong coupling constants of a large variety of interaction vertices between mesons. Particularly, our QCDSR group has been working extensively in the charm sector, with the calculation of a vast number of coupling constants as the $D^{ * } D \pi$, $D^{( * )} D^{( * )} \rho$, $J/\psi D^{( * )} D^{( * )}$ and more recently, the $J/\psi D_s D_s$ and $J/\psi D^{ * }_s D_s$. Continuing this line of research, we started the study of charmed vertices that include the pseudo-scalar meson $\eta_c$. The $\eta_c D^{ * } D$ is one of these vertices. It is related to physical problems of current interest, as the $\eta_c$ decay in two light vector mesons ($\eta_c \to VV$). Experimental data indicates that this type of decay, as the $\eta_c \to \rho \rho$ and $\eta_c \to K^{ * }(892) \bar{K}^{ * }(892)$, is among the most contributing decay channels for the $\eta_c$, with branching ratios of $(1.8 \pm 0.5)\times 10^{-2}$ and $(6.8 \pm 1.3)\times 10^{-3}$ respectively for the mentioned channels. However, these decays should be suppressed by the helicity selection rule (HSR). This is an intriguing problem that shares some similarities with the notorious $\rho \pi$ puzzle, in which the decay $J/\psi \to \rho \pi$ also presents a branching ratio of the order $10^{-2}$ even though being a suppressed decay according to the OZI rule. One way to circumvent the HSR suppression is to consider the $\eta_c \to VV$ decay with an intermediate step through the mesons $D$ and $D^{ * }$, i.e. $\eta_c \to D \bar{D}^{ * } \to VV$. In this picture, the coupling constant $g_{\eta_c D^{ * } D}$ will be necessary to the calculation of these decay amplitudes, making it necessary to have a good estimate for this coupling constant. In this work, we will calculate the $g_{\eta_c D^{ * } D}$ coupling constant using the QCDSR technique for the case where the $D^{ * }$ mesons is considered off-shell. We will take advantage of the similarities between the mesons $D^{( * )}$ and $D_s^{( * )}$ in order to also calculate the $g_{\eta_c D_s^{ * } D_s}$ coupling constant for the $D_s^{ * }$ off-shell case and we will compare both of them according to the SU(4) symmetry.