hadronic FCNC processes {#sec:ops}
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The effective weak Hamiltonians relevant to rare hadronic $B$ decays based on the quark transitions $\bar b\to\bar s q\bar q$ or $\bar b\to\bar d q\bar q$ have been discussed extensively in the literature. Here we consider only the first case, adopting the notations of [@Heff]. A similar discussion (with obvious replacements of indices) would apply to the other case. In the SM, the result can be written in the compact form $$\label{Heff}
   {\cal H}_{\rm eff} = \frac{G_F}{\sqrt2}\,\sum_{q=u,c}
   \lambda_q\,\bigg[ \sum_{i=1,2} C_i(\mu)\,Q_i^q(\mu)
   + \sum_{i=3\dots 10} C_i(\mu)\,Q_i(\mu)
   + C_{8g}(\mu)\,Q_{8g}(\mu) \bigg] \,,$$ where $\lambda_q=V_{qb}^* V_{qs}$ are combinations of CKM matrix elements obeying the unitarity relation $\lambda_u+\lambda_c+\lambda_t=0$, and $Q_i$ are local operators containing quark and gluon fields. Specifically, $$\label{curcur}
   Q_1^q = (\bar b_\alpha q_\beta)_{V-A}\,
    (\bar q_\beta s_\alpha)_{V-A} \,, \qquad
   Q_2^q = (\bar b_\alpha q_\alpha)_{V-A}\,
    (\bar q_\beta s_\beta)_{V-A} \,,$$ summed over color indices $\alpha$ and $\beta$, are the usual current–current operators induced by $W$-boson exchange, $$\begin{aligned}
\label{QCDp}
   Q_3 &=& (\bar b_\alpha s_\alpha)_{V-A}\,\sum_q\,
   (\bar q_\beta q_\beta)_{V-A} \,, \nonumber\\
   Q_4 &=& (\bar b_\alpha s_\beta)_{V-A}\,\sum_q\,
    (\bar q_\beta q_\alpha)_{V-A} \,, \nonumber\\
   Q_5 &=& (\bar b_\alpha s_\alpha)_{V-A}\,\sum_q\,
    (\bar q_\beta q_\beta)_{V+A} \,, \nonumber\\
   Q_6 &=& (\bar b_\alpha s_\beta)_{V-A}\,\sum_q\,
    (\bar q_\beta q_\alpha)_{V+A} \,,\end{aligned}$$ summed over the light flavors 