Long Distance Contributions to Penguin Processes $b\rightarrow sγ$ and $b\rightarrow d γ$

Details Long Distance Contributions to Penguin Processes $b\rightarrow sγ$ and $b\rightarrow d γ$ Long Distance Contributions to Penguin Processes $b\rightarrow sγ$ and $b\rightarrow d γ$

1994-12-02

arxiv.org/abs/hep-ph/9412222v3

Phys.Lett. B367 (1996) 362-368

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages, Revtex. Some numerical errors in the calculation of $b\rightarrow d \gamma$ are corrected. The long distance contrib

Scientific paper

10.1016/0370-2693(95)01364-4

We consider the long distance contributions to inclusive penguin processes through processes like $b\rightarrow s V$ and $b\rightarrow d V$ where $V$ are $^3S_1(c\bar c)$ states $\psi_i$ in the former case and include $\rho$, $\omega$ for the latter case. We carefully examine vector dominance for $\bar c c$ states, and conclude that there is a large suppression of $\psi\sim \gamma$ transition when $\psi$ is at $q^2 = 0$. The long distance effects can be at most 10\% in both the amplitudes for $b\rightarrow s\gamma$ and $b\rightarrow d \gamma$. Although the long distance contributions are small, the ratio $BR(b\rightarrow d\gamma)/BR(b \rightarrow s \gamma) = |V_{td}/V_{ts}|^2$ does not hold due to significant $u$ and $c$ loop contributions to the short distance $b\rightarrow d\gamma$ amplitudes .

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