Electroweak theory: difference between photon and Z-boson

[Petr.Plachy]

The electroweak theory describes the photon and vector bosons (Z⁰, W⁺, W^-) as mixtures of bosons from the electroweak interactions (weak hypercharge and weak isospin). In addition, the vector bosons mix also with the Higgs bosons and thus gain mass. Photon does not mix with the Higgs, so it remains massless.

My question is what causes the difference between the photon and Z⁰. Both photon and Z⁰ rise as a mixture of the same particles (W3 and the hypercharge boson), the only difference is that Z⁰ also gets the Higgs. So what makes the Z⁰ mix additionally with the Higgs? And what prevents the photon from mixing with the Higgs too and become massive?

The problem might be that I don't perfectly understand the details of particle mixing...

 

[Bill_K]

We make choices in the definition of the Higgs field that result in this. Quoting myself from a recent thread:

We choose the Higgs field φ to be an isospin doublet with weak hypercharge Y = 1. Also we choose the vacuum expectation value φ₀ to be (0 v). That is, the only nonzero component is the T³ = -1/2 component. For this component, Q = T³ + Y/2 = 0. Which not only says the Higgs field is neutral, Qφ₀ = 0 also means that the U(1)_em with generator Q remains unbroken: φ₀ → φ'₀ = e^iα(x)φ₀ = φ₀ for any value of α(x). Thus the vacuum remains invariant under U(1)_em transformations, and the photon remains massless.