Improved measurements of the branching fractions for B^{0}→π^{+}π^{-} and B^{0}→K^{+}π^{-}, and a search for B^{0}→K^{+}K^{-}

We present measurements of the branching fractions for the charmless two-body decays B-0 ->pi(+)pi(-) and B-0 -> K+pi(-), and a search for the decay B-0 -> K+K-. We include the effects of final-state radiation from the daughter mesons for the first time, and quote branching fractions for the inclusive processes B-0 -> h(+)h('-)n gamma, where h and h(') are pions or kaons. The maximum value of the sum of the energies of the n undetected photons, E-gamma(max), is mode-dependent. Using a data sample of approximately 227x10(6) Upsilon(4S)-> B (B) over bar decays collected with the BABAR detector at the PEP-II asymmetric-energy e(+)e(-) collider at SLAC, we measure: B(B-0 ->pi(+)pi(-)n gamma;E-gamma(max)=150 MeV)=(5.1 +/- 0.4 +/- 0.2)x10(-6), B(B-0 -> K+pi(-)n gamma;E-gamma(max)=105 MeV)=(18.1 +/- 0.6 +/- 0.6)x10(-6), B(B-0 -> K(+)K(-)n gamma;E-gamma(max)=59 MeV)< 0.5x10(-6)(90% confidence level), where the first uncertainty is statistical and the second is systematic. Theoretical calculations can be used to extrapolate from the above measurements the nonradiative branching fractions, B-0. Using one such calculation, we find: B-0(B-0 ->pi(+)pi(-))=(5.5 +/- 0.4 +/- 0.3)x10(-6), B-0(B-0 -> K+pi(-))=(19.1 +/- 0.6 +/- 0.6)x10(-6), B-0(B-0 -> K+K-)< 0.5x10(-6)(90% confidence level). Meaningful comparison between theory and experiment, as well as combination of measurements from different experiments, can be performed only in terms of these nonradiative quantities.