$K^{*}_3[1780]$ Two Body Decay Vertices(8)

There are 8 vertices in this part

Vertex 9: $\overline{K^0}({p_3})~-f_2[1270]^{0}_{\beta ,\gamma }~({p_2})~- K^{*}_3[1780]_{\mu ,\nu ,\alpha }~({p_1})~$

$$\begin{eqnarray*} &V_{9}=-\epsilon_{{p_1},{p_2},\mu ,\beta }gi~({p_1}_\gamma {p_2}_\nu {p_2}_ \alpha f_{192}+{p_2}_\nu g_{\alpha ,\gamma }f_{191}) \end{eqnarray*}$$

Vertex 10: $\overline{K^{*}_3[1780]}_{\mu ,\nu ,\alpha }~({p_1})~- f_2[1270]^{0}_{\beta ,\gamma }~({p_2})~-K^0({p_3})~$

$$\begin{eqnarray*} &V_{10}=-\epsilon_{{p_1},{p_2},\mu ,\beta }gi~({p_1}_\gamma {... ..._\nu {p_2}_ \alpha f_{192}+{p_2}_\nu g_{\alpha ,\gamma }f_{191}) \end{eqnarray*}$$

Vertex 11: $\gamma^{0}_{\gamma }~({p_3})~-\overline{K^{*}[892]^0}_{\beta }~( {p_2})~-K^{*}_3[1780]_{\mu ,\nu ,\alpha }~({p_1})~$

$$\begin{eqnarray*} &V_{11}={\displaystyle{g \over 2}}~(-{p_1}^2{p_3}_\nu {p_3}_\... ... &+2{p_3}_\nu {p_3}_\alpha {p_3}_\beta g_{\mu , \gamma }f_{185}) \end{eqnarray*}$$

Vertex 12: $\overline{K^{*}_3[1780]}_{\mu ,\nu ,\alpha }~({p_1})~- K^{*}[892]^0_{\beta }~({p_2})~-\gamma^{0}_{\gamma }~({p_3})~$

$$\begin{eqnarray*} &V_{12}={\displaystyle{g \over 2}}~({p_1}^2{p_3}_\nu {p_3}_\a... ... &-2{p_3}_\nu {p_3}_\alpha {p_3}_\beta g_{\mu , \gamma }f_{185}) \end{eqnarray*}$$

Vertex 13: $\gamma^{0}_{\gamma }~({p_3})~-\overline{K^{*}[1680]}_{\beta }~( {p_2})~-K^{*}_3[1780]_{\mu ,\nu ,\alpha }~({p_1})~$

$$\begin{eqnarray*} &V_{13}={\displaystyle{g \over 2}}~(-{p_1}^2{p_3}_\nu {p_3}_\... ... &+2{p_3}_\nu {p_3}_\alpha {p_3}_\beta g_{\mu , \gamma }f_{182}) \end{eqnarray*}$$

Vertex 14: $\overline{K^{*}_3[1780]}_{\mu ,\nu ,\alpha }~({p_1})~-K^{*}[1680] _{\beta }~({p_2})~-\gamma^{0}_{\gamma }~({p_3})~$

$$\begin{eqnarray*} &V_{14}={\displaystyle{g \over 2}}~({p_1}^2{p_3}_\nu {p_3}_\a... ... &-2{p_3}_\nu {p_3}_\alpha {p_3}_\beta g_{\mu , \gamma }f_{182}) \end{eqnarray*}$$

Vertex 15: $\overline{K^0}({p_3})~-\gamma^{0}_{\beta }~({p_2})~-K^{*}_3[1780] _{\mu ,\nu ,\alpha }~({p_1})~$

$$\begin{eqnarray*} &V_{15}=\epsilon_{{p_1},{p_2},\mu ,\beta }f_{159}gi~{p_2}_\nu {p_2}_\alpha \end{eqnarray*}$$

Vertex 16: $\overline{K^{*}_3[1780]}_{\mu ,\nu ,\alpha }~({p_1})~-\gamma^{0} _{\beta }~({p_2})~-K^0({p_3})~$

$$\begin{eqnarray*} &V_{16}=-\epsilon_{{p_1},{p_2},\mu ,\beta }f_{159}gi~{p_2}_\nu {p_2}_\alpha \end{eqnarray*}$$