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

We analyze the short and long distance contributions to inclusive $B \rightarrow X_d γ$ 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.

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