Photon vs. Z-boson - one massive, one massless, mix of same things?

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The discussion centers on the relationship between massless bosons, specifically the photon and the Z boson, and their expression through the Higgs mechanism. It is established that the photon and Z boson can be represented as mixtures of massless states, with the equations γ = Bcos(θ_w) + W_3sin(θ_w) and Z^0 = -Bsin(θ_w) + W_3cos(θ_w) illustrating this concept. The production of the massive Z^0 boson arises from electroweak symmetry breaking, a fundamental process in particle physics that endows certain particles with mass.

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Apparently before we apply the Higgs mechanism we have a set of massless bosons, the photon, the B, and the W1, W2 & W3 bosons.

I'm reading that the photon and Z boson that we are familiar with can be expressed as a combination of a mixture of some of these massless states:

\gamma = Bcos(\theta_w) + W_3sin(\theta_w)
Z^0 = -Bsin(\theta_w) + W_3cos(\theta_w)

In both cases, we have mixtures of two states that have no mass associated with them. Why is it that we produce a massive Z^0 out of this?
 
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