====== 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 $\bar{B}^0_d\to \pi^0\pi^0$.
 </hidden>
|**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]]   |
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