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 — preprints:2002:ttp02-16 [2016/03/17 11:03] (current) Line 1: Line 1: + ====== TTP02-16 Gluonic Penguins in $B\to \pi\pi$ from QCD Light-Cone Sum Rules ====== + + + <​hidden TTP02-16 ​ Gluonic Penguins in $B\to \pi\pi$ from QCD Light-Cone Sum Rules > The $B\to \pi\pi$ hadronic matrix element + of the chromomagnetic dipole operator $O_{8g}$ + ​(gluonic penguin) is calculated using the QCD + ​light-cone sum rule approach. The resulting sum rule for + ​$\langle \pi\pi |O_{8g}|B\rangle$ contains, in addition + to the $O(\alpha_s)$ part induced by hard gluon exchanges,​ + a contribution due to  soft gluons. We find that in the + limit $m_b\to \infty$ the soft-gluon contribution + is suppressed as a second power of $1/m_b$ with respect + to the leading-order factorizable $B\to \pi\pi$ amplitude,​ + ​whereas the hard-gluon contribution has only an $\alpha_s$ + ​suppression. Nevertheless,​ at  finite $m_b$, soft + and hard effects of the gluonic penguin in $B\to \pi\pi$ + are of the same order. Our result indicates that soft + ​contributions are indispensable for an accurate counting + of nonfactorizable effects in charmless $B$ decays. + On the phenomenological side we predict that the + ​impact of gluonic penguins on $\bar{B}^0_d\to \pi^+\pi^-$ + is very small, but is noticeable for $\bar{B}^0_d\to \pi^0\pi^0$. + ​ + |**Alexander Khodjamirian,​ Thomas Mannel and Piotr Urban** ​ | + |**  Phys.Rev. ​ D67 054027 2003  **  | + | {{preprints:​2002:​ttp02-16.pdf|PDF}} {{preprints:​2002:​ttp02-16.ps|PostScript}} [[http://​arxiv.org/​abs/​hep-ph/​0210378|arXiv]] ​  | + | |