# B violation and electric charge

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,

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

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