the isovector components of the penguin operators $O_3^q$ and $O_4^q$ can be related to the usual current–current operators by a Fierz transformation [@Ne97; @Fl96]. For the numerical analysis we choose the renormalization scale $\mu=m_b$ and take $\kappa=\alpha_s(m_b)/\alpha_s(m_W)=1.83$ and $\chi=1.18$, yielding $$\label{abformula}
   |\lambda_u|\,(a+ib) \approx
   - (\bar c_3^{\rm EW} + \bar c_4^{\rm EW})
   + 0.26 (\bar c_1^{\rm EW} + \bar c_5^{\rm EW})
   - 1.40 (\bar c_2^{\rm EW} + \bar c_6^{\rm EW}) \,.$$

Next we consider the New Physics contributions to the parameter $\rho$. In the factorization approximation, we find $$\label{rhobound}
   \frac{\rho}{\sqrt{1+\rho^2}}
   \approx \frac{3\bar\varepsilon_{3/2}}{4|\lambda_u|}\,
   \mbox{Im}\Big[ 
   (\bar c_5^d - \bar c_4^d - \chi\,\bar c_2^d)
   + \frac13\,(\bar c_6^d - \bar c_3^d - \chi\,\bar c_1^d)
   - a_{8g}\,C_{8g} \Big] \,,$$ where $\bar c_i^d\equiv c_i^d(m_b)-\widetilde c_i^d(m_b)$. Because the QCD evolution of the Wilson coefficients $c_i^d$ and $\widetilde c_i^d$ is complicated, we prefer to present the result in terms of coefficients renormalized at the scale $m_b$. Note that by pulling out a factor of $\bar\varepsilon_{3/2}$ on the right-hand side we avoid the difficulty of calculating the overall penguin amplitude $P$ in (\[ampls\]). The contribution of the chromomagnetic dipole operator is formally of next-to-leading order in $\alpha_s$ and thus could be dropped; however, we keep it because in some New 