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In this paper we perform a systematic study for the three $B \to(\pi^+\pi^-,\pi^+\pi^0,\pi^0\pi^0)$ decays in the perturbative QCD (pQCD)factorization approach with the inclusion of all currently knownnext-to-leading order (NLO) contributions from various sources. We found that(a) for the CP-averaged decay rates $Br(B^0\to \pi^+\pi^-)$ and $Br(B^+\to\pi^+\pi^0)$, the NLO pQCD predictions agree with the data within one standarddviation; (b) for $Br(B^0\to \pi^0\pi^0)$, however, although the NLOcontributions can provide a $\sim 100\%$ enhancement to the leading order (LO)result, it is still not large enough to interpret the data; (c) for theCP-violating asymmetries of $B^0\to \pi^+\pi^-$ decay, the central values ofthe NLO PQCD predictions agree with the data; and (d) we also examined therelative strength of the LO and NLO contributions from different sources.

$B\to \pi\pi$ decays and effects of the next-to-leading order contributions