Enhanced effects on extracting γ from untagged B0 and Bs decays

The weak phase γ can be determined using untagged B0→DKS or Bs→Dϕ,Dη(′) decays. In the past, the small lifetime difference y≡ΔΓ/(2Γ) has been neglected in B0, while the CP-violating parameter ϵ≡1−|q/p|2 has been neglected in both B0-B¯0 and Bs-B¯s mixings. We estimate the effect of neglecting y and ϵ. We find that in D decays to flavor states this introduces a systematic error, which is enhanced by a large ratio of Cabibbo-allowed to doubly Cabibbo-suppressed D-decay amplitudes.