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

Abstract

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 $\overline{B}\ensuremath{\rightarrow}{X}_{u\ifmmode \bar{u}\else \={u}\fi{}s},$ $\overline{B}\ensuremath{\rightarrow}{X}_{d\overline{d}s},$ $\overline{B}\ensuremath{\rightarrow}{X}_{s\overline{s}s},$ $\overline{B}\ensuremath{\rightarrow}{X}_{s\overline{s}d},$ and $\overline{B}\ensuremath{\rightarrow}{X}_{d\overline{d}d}$ 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 ${n}_{c}=1.33\ifmmode\pm\else\textpm\fi{}0.06$ 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.