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.

  • $\begingroup$ I think, it should read $g$ rather than $g'$ in front of $A^3$, then they would be orthogonal. $\endgroup$ – Photon Jun 8 at 10:12
  • $\begingroup$ What "scalar product" are you trying to take here? $\endgroup$ – ACuriousMind Jun 8 at 10:23
  • $\begingroup$ yes. i corrected it $\endgroup$ – mithusengupta123 Jun 8 at 10:23
  • $\begingroup$ I have no idea. If not, in what sense are they orthogonal? $\endgroup$ – mithusengupta123 Jun 8 at 10:24
  • 1
    $\begingroup$ Orthogonal eigenvectors of the mass matrix? $\endgroup$ – Cosmas Zachos Jun 8 at 10:51

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