Long-Distance Dominance of the $CP$ Asymmetry in $\overline{B}\to X_{s,d}\gamma$ Decays

We show that in the standard model the parametrically leading (by a factor $1/{\alpha }_s$) contribution to the inclusive $CP$ asymmetry in $\overline{B}\to X_{s,d}\gamma$ decays arises from a long-distance effect in the interference of the electromagnetic dipole amplitude with the amplitude for an up-quark penguin transition accompanied by soft gluon emission. Using model estimates for the associated hadronic parameter ${\tilde{\Lambda }}_{17}^u$, we predict a value in the range $-0.6\%<{\mathcal{A}}_{X_s\gamma }^{\mathrm{SM}}<2.8\%$. In view of current experimental data, a future precision measurement of the flavor-averaged $CP$ asymmetry would signal the presence of new physics only if a value below $-2\%$ was found. A cleaner probe of new physics is offered by the difference of the $CP$ asymmetries in charged versus neutral $\overline{B}\to X_s\gamma$ decays.

Figure 1

Penguin diagrams with virtual and real gluon emissions. The gluons in the first two graphs are highly energetic.