Effects of enhanced $Z$ penguin diagrams on lepton polarizations in $B\to X_s{\ell }^{+}{\ell }^{-}$

The sensitivity of the $B\to \pi K$ mode to electroweak penguin diagrams and the recent experimental data for the $B\to \pi \pi ,\pi K$ modes has given rise to what is known as the “$B\to \pi K$ puzzle.” Recently it has been observed that this puzzle can be resolved by considering the new physics which can enter via $Z^0$ penguin diagrams. In this note we analyze the effect of these enhanced $Z^0$ penguin diagrams on the lepton polarization asymmetries of $b\to s{\ell }^{+}{\ell }^{-}$.

Figure 1

Longitudinal polarization asymmetry ($P_L^{-}$) with dilepton invariant mass ($\widehat{s}$).

Figure 2

Normal polarization asymmetry ($P_N^{-}$) with dilepton invariant mass ($\widehat{s}$).

Figure 3

Transverse polarization asymmetry ($P_T^{-}$) with dilepton invariant mass ($\widehat{s}$).