The $B\to \ddot{I}€K$ Puzzle Revisited

Abstract

For a number of years, there has been a certain inconsistency among the measurements of the branching ratios and CP asymmetries of the four $B\to \ddot{I}€K$ decays ($B^{+}\to \ddot{I}{€}^{+}{K}^0$, $B^{+}\to \ddot{I}{€}^0{K}^{+}$, $B^0\to \ddot{I}{€}^{-}{K}^{+}$, $B^0\to \ddot{I}{€}^0{K}^0$). In this paper, we re-examine this $B\to \ddot{I}€K$ puzzle. We find that the key unknown parameter is $|C^{\prime }/T^{\prime }|$, the ratio of color-suppressed and color-allowed tree amplitudes. If this ratio is large, $|C^{\prime }/T^{\prime }|=0.5$, the SM can explain the data. But if it is small, $|C^{\prime }/T^{\prime }|=0.2$, the SM cannot explain the $B\to \ddot{I}€K$ puzzle -- new physics (NP) is needed. The two types of NP that can contribute to $B\to \ddot{I}€K$ at tree level are $Z^{\prime }$ bosons and diquarks. $Z^{\prime }$ models can explain the puzzle if the $Z^{\prime }$ couples to right-handed $u\bar{u}$ and/or $d\bar{d}$, with $g_R^{dd}\ne g_R^{uu}$. Interestingly, half of the many $Z^{\prime }$ models proposed to explain the present anomalies in $b\to s\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ decays have the required $Z^{\prime }$ couplings to $u\bar{u}$ and/or $d\bar{d}$. Such models could potentially explain both the $b\to s\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ anomalies and the $B\to \ddot{I}€K$ puzzle. The addition of a color sextet diquark that couples to $ud$ can also explain the puzzle.

29 pages, no figures. Details added regarding the masses and couplings of the Z' and diquark required to explain the B -> pi K puzzle