# XIII International Workshop on Hadron Physics - XIII Hadron Physics

22-27 March 2015
Hotel do Bosque
Brazil/East timezone

## 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

#### Hotel do Bosque

Rodovia Mário Covas (Rio-Santos) BR - 101 Sul, Km 533, Angra dos Reis, RJ, Brazil
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.

### Co-authors

Prof. Carina Zanetti (UERJ) Prof. Mirian bracco (UERJ)

### Presentation Materials

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