Institute for Theoretical Particle Physics (TTP)


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preprints:2002:ttp02-16 [2016/03/17 11:03] (current)
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 +====== 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}} {{|PostScript}} [[|arXiv]]   | 
 +| |