Lessons from the LHCb measurement of CP violation in $B_s\to K^+K^-$

Abstract

The LHCb experiment measured the time-dependent CP asymmetries $C_{KK}$ and $S_{KK}$ in $B_s\to K^+K^-$ decay. Combining with the corresponding CP asymmetries $C_{\pi\pi}$ and $S_{\pi\pi}$ in $B\to \pi^+\pi^-$ decay, we find that the size of $U$-spin breaking in this system is of order $20\%$. Moreover, the data suggest that these effects are dominated by factorizable contributions. We further study the constraints on new physics contributions to $b\to u\bar uq$ ($q=s,d$). New physics that is minimally flavor violating (MFV) cannot be distinguished from the Standard Model (SM) in these decays. However, new physics that is not MFV can mimic large $U$-spin breaking. Requiring that the $U$-spin breaking parameters remain below the size implied by the data leads to a lower bound of $5-10$ TeV on the scale of generic new physics. If the new physics is subject to the selection rules that follow from the Froggatt-Nielsen (FN) mechanism or from General Minimal Flavor Violation (GMFV), the bound is relaxed to 2 TeV.