Penguin diagrams, charmlessBdecays, and the “missing charm puzzle”

We calculate the contributions of penguin diagrams with internal $u$ or $c$ quarks to various inclusive charmless $B$-decay rates. Further we analyze the influence of the chromomagnetic dipole operator $Q_8$ on these rates. We find that the rates corresponding to $\overline{B}\to X_{uūs},$ $\overline{B}\to X_{d\overline{d}s},$ $\overline{B}\to X_{s\overline{s}s},$ $\overline{B}\to X_{s\overline{s}d},$ and $\overline{B}\to X_{d\overline{d}d}$ are dominated by the new penguin contributions. The contributions of $Q_8$ sizably diminish these rates. Despite an increase of the total charmless decay rate by 36%, the new contributions are not large enough to explain the charm deficit observed by ARGUS and CLEO. We predict $n_c=1.33\mathrm{}\pm 0.06$ for the average number of charmed particles per $B$ decay in the standard model. Then the hypothesis of an enhancement of the chromomagnetic dipole coefficient $C_8$ by new physics contributions is analyzed. We perform a model-independent fit of $C_8$ to the experimental data. If the CKM structure of the new physics contribution is the same as in the standard model, $|C_8{(M}_W)|$ must be enhanced by a factor of 9 to 16 in order to explain the observed charm deficit.