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Within SM you can prove that despite we have baryon number conservation respect to Noether theorem, at quantum level baryon (and lepton) number is violated as

$$ \Delta B = 3·\Delta n_{CS}, \quad n_{CS} \in \mathbb{Z}\ ({\rm Chern-Simons\ index\ for\ vacuum}) \tag1$$

So, I've been thinking: if $B$ is violated, is this implying that electric charge isn't conserved? And I have a technical question on this $B$: is it defined as

$$ B = \frac{N_q - N_{\bar{q}}}{3}, \quad {\rm or}\quad B = N_q - N_{\bar{q}}\ ? $$

At tree level, Feynman diagrams grant conservation but I can imagine a triangle diagram with a loop made with a fermion, $f$, that produces a $Z^0$, goes on the loop and destroys with its antipaticle given as a result another $Z^0$ boson (see image below). Since this vertices contain left and right projectors, then they give an anomaly such as the chiral anomaly.

In the picture,

$$ \sum_f = \sum_{all\ quarks\\within\ SM} $$


Triangle diagramas

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  • $\begingroup$ I'm not sure how your triangle diagram is relevant to your question, since neither of $\gamma, Z^0$ are electrically charged. $\endgroup$ – ACuriousMind May 1 at 23:41
  • $\begingroup$ @ACuriousMind What should I use? $\endgroup$ – Vicky May 2 at 0:07

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