Systematic Error on Weak Phase $γ$ from $B \to π^+ π^-$ and $B \to K π$

Abstract

When CP asymmetries in $B^0(t)\to π^+ π^-$ are combined using broken flavor SU(3) with decay rates for $B^+\to K^0π^+$ and/or $B^0\to K^+π^-$, one can obtain stringent limits on the weak phase $γ$ which are consistent with those obtained from other CKM constraints. Experimental data in the past few years have improved to the extent that systematic errors associated with uncertainty in SU(3) symmetry breaking dominate the determination of $γ$. We obtain a value $γ=(73 \pm 4^{+10}_{-8})^\circ$, where the first error is statistical while the second one is systematic.