CP asymmetry in $B^{+}\to K^+\pi^{0}$ and New Physics

Abstract

The CP asymmetry in $B^0\to K^+\pi^-$ is expected to be similar to that in $B^+\to K^+\pi^0$. The experimental data however show $\sim 5\sigma$ difference between the two, leading to the so called $\Delta {A}_{K\pi}$ puzzle. Employing sum rule(s) following from (approximate) flavour symmetry, we show that it is possible to accommodate the observed experimental values within the standard model (SM) for a narrow range of parameters. Sub-leading terms can bring the theoretical predictions in better agreement with the data. Resolution via modified electroweak penguin contributions is possible for a large CP violating phase generated by the new physics. However, the data on polarization in $B\to VV(T)$, $B_s$-$\bar{B}_s$ mixing (and large CP phase) and $B^+\to\tau^+\nu_{\tau}$ rate can not be simultaneously accommodated within SM or new physics with only enhanced electroweak penguins. A plausible resolution to these, and not spoiling the $B\to K\pi$ rates and asymmetries, could be a general two Higgs doublet model.