Time-integrated method for measurement of CP asymmetries $A_{mix}$ and $A_{dir}$ in $B_{d \to \pi^{+}\pi^{-}}$ decay

The time-integrated method proposed here may be useful for current experiments at e^{+}e^{-} colliders and at Fermilab and for future experiments at LHC-LHCb since it is less sensitive to the precision of tau measurements. The method also gives a way to measure CP asymmetries A/sub mix/ and A/sub dir/ in B/sub d/ to pi /sup +/ pi /sup -/ decay experiments without particle identification at hadron colliders.