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I was analyzing the effective theory of the process $b \rightarrow s \gamma$ and and I was in doubt about the emergence of the effective operator of photon dipole

$$O_7 = e m_b \bar{s}_L \sigma_{\mu\nu}F^{\mu\nu} b_R.$$

I saw that it emerge of the electroweak penguin diagram in that we have a top quark in the loop and a photon in the vertex. My attempt was integrate out the $W$ boson and the top quark, but I didn't get this operator.

Can anyone help me?

Appreciate.

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    $\begingroup$ That operator is generated at loop level, so getting it from integrating out $t$ and $W$ will be hard. The easiest way is probably to compute it by matching it with the SM loop in the limit $E \ll m_W, m_t$. $\endgroup$
    – FrodCube
    Commented Sep 16, 2021 at 13:31
  • $\begingroup$ ⚫. $\endgroup$
    – Cosmas Zachos
    Commented Sep 16, 2021 at 13:34
  • $\begingroup$ I tried that and I couldn't do it either. Maybe there's some kind of algebraic manipulation I'm missing. $\endgroup$
    – Joao Vitor
    Commented Sep 16, 2021 at 18:28

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