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

Abstract

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 known next-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 standard dviation; (b) for $Br(B^0\to {\pi }^0{\pi }^0)$, however, although the NLO contributions can provide a $\sim 100\%$ enhancement to the leading order (LO) result, it is still not large enough to interpret the data; (c) for the CP-violating asymmetries of $B^0\to {\pi }^{+}{\pi }^{-}$ decay, the central values of the NLO PQCD predictions agree with the data; and (d) we also examined the relative strength of the LO and NLO contributions from different sources.

Comments: 11 pages, 1 figure