U-spin breaking in CP asymmetries in B decays

U-spin symmetry predicts equal CP rate asymmetries with opposite signs in pairs of $ΔS=0$ and $ΔS=1$ $B$ meson decays in which initial and final states are related by U-spin reflection. Of particular interest are six decay modes to final states with pairs of charged pions or kaons, including $B_s \to π^+K^-$ and $B_s\to K^+K^-$ for which asymmetries have been reported recently by the LHCb collaboration. After reviewing the current status of these predictions, highlighted by the precision of a relation between asymmetries in $B_s \to π^+K^-$ and $B^0\to K^+π^-$, we perform a perturbative study of U-spin breaking corrections, searching for relations for combined asymmetries which hold to first order. No such relation is found in these six decays, in two-body decays involving a neutral kaon, and in three-body $B^+$ decays to charged pions and kaons.

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