Renormalization-Group Evolution for the Three-Particle B-Meson Soft Function.

We determine for the first time the renormalization-group equation for the three-particle B-meson soft function dictating the nonperturbative strong interaction dynamics of the long-distance penguin contributions to the double radiative B-meson decays. The distinctive feature of the ultraviolet renormalization of this fundamental soft function consists in the pattern of mixing positive into negative support for an arbitrary initial condition. The exact solution to this integrodifferential evolution equation is then derived with the Laplace transform technique, allowing for the model-independent extraction of the asymptotic behavior at large and small partonic momenta.

Deciphering the Long-Distance Penguin Contribution to B[over ¯]_{d,s}→γγ Decays.

We compute for the first time the long-distance penguin contribution to the double radiative B-meson decays by applying the perturbative factorization theorem. The numerically dominant penguin amplitude arises from the soft-gluon radiation off the light up-quark loop rather than the counterpart charm-loop effect. Importantly, the long-distance up-quark penguin contribution brings about the substantial cancellation of the known factorizable power correction, thus enabling B_{d,s}→γγ to become new benchmark probes of physics beyond the standard model.