# Differences

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+ | ====== TTP02-16 Gluonic Penguins in $B\to \pi\pi$ from QCD Light-Cone Sum Rules ====== | ||

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+ | <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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