B → π π decay in QCD

A new method is suggested to calculate the B --> pi pi hadronic matrix elements from QCD light-cone Sum rules. To leading order in alpha (s) and 1/m(b), the sum rule reproduces a factorizable matrix element. in accordance with the prediction of the QCD factorization approach. Whereas the QCD factorization can only take into account the nonfactorizable corrections induced by hard-gluon exchanges, the method suggested here also allows a systematic inclusion of soft-gluon effects. In this paper, I concentrate on the latter aspect and present a calculation of the nonfactorizable soft-gluon exchange contributions to B --> pi pi. The result, including twist 3 and 4 terms, is suppressed by one power of 1/m(b) with respect to the factorizable amplitude. Despite its numerical smallness, the soft effect is at the same level as the O(alpha (s)) correction to the QCD factorization formula for B --> pi pi. The method suggested here can be applied to matrix elements of different topologies and operators and to various other B-decay channels. I also comment on the earlier applications of QCD sum rules to nonleptonic decays of heavy mesons. (C) 2001 Published by Elsevier Science B.V.