Short and Long Distance Interplay in Inclusive $ B \to X_d \gamma $ Decays

Abstract

We analyze the short and long distance contributions to inclusive $B \rightarrow X_d \gamma$ decay, paying particular attention to the dependence on the Cabibbo-Kobayashi-Maskawa parameter $V_{td}$. We discuss penguin diagrams with internal $u$ and $c$ quarks in the framework of the effective field theory. We also estimate the size of possible long range contributions by using vector meson dominance.