Is observed direct CP violation in $B_d \to K^+ π^-$ due to new physics? Check standard model prediction of equal violation in $B_s \to K^- π^+$

Abstract

The recently observed direct CP violation in $B_d \to K^+ π^-$ has raised suggestions of possible new physics. A robust test of the standard model vs. new physics is its prediction of equal direct CP violation in $B_s \to K^- π^+$ decay. CPT invariance requires the observed CP violation to arise from the interference between the dominant penguin amplitude and another amplitude with a different weak phase and a different strong phase. The penguin contribution to $B_d \to K^+ π^-$ is known to be reduced by a CKM factor in $B_s \to K^- π^+$. Thus the two branching ratios are very different and a different CP violation is expected. But in the standard model a miracle occurs and the interfering tree diagram is enhanced by the same CKM factor that reduces the penguin to give the predicted equality. This miracle is not expected in new physics; thus a search for and measurement of the predicted CP violation in $B_s \to K^- π^+$ decay is a sensitive test for a new physics contribution. A detailed analysis shows this prediction to be robust and insensitive to symmetry breaking effects and possible additional contributions.