# In what sense $Z_\mu^0$ is orthogonal to $A_\mu$?

I am reading Standard model. Please explain in what sense the $$Z$$-boson $$Z_\mu^0=(g^2+g^{\prime 2})^{-1/2}(g A^3_\mu-g^\prime B_\mu)$$ is an orthogonal linear combination of the photon $$A_\mu=(g^2+g^{\prime 2})^{-1/2}(g A^3_\mu+g^\prime B_\mu)?$$ It doesn't match with my understanding of orthogonality i.e. vanishing scalar product.

• I think, it should read $g$ rather than $g'$ in front of $A^3$, then they would be orthogonal. – Photon Jun 8 at 10:12
• What "scalar product" are you trying to take here? – ACuriousMind Jun 8 at 10:23
• yes. i corrected it – mithusengupta123 Jun 8 at 10:23
• I have no idea. If not, in what sense are they orthogonal? – mithusengupta123 Jun 8 at 10:24
• Orthogonal eigenvectors of the mass matrix? – Cosmas Zachos Jun 8 at 10:51