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This question is inspired from Why should the Standard Model be renormalizable? Ron Maimon says that standard model is renormalizable, and though there seems to be conflicting (?) answers. Is this because each answer differs in what "renormalizability" means? Furthermore, what paper Ron Maimon is referencing to by saying "'t Hooft proved it"?

Also, in Renormalizability of standard model it says standard model is renormalizable. So standard model is renormalizable?

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As far as I know, there is no rigorous proof that the standard model with spontaneous symmetry breaking is perturbatively renormalizable to all orders. I think the best available result in this direction is "Renormalization of Spontaneaously Broken SU(2) Yang-Mills Theory with Flow Equations" by Christoph Kopper and Volkhard F. Müller. There is also the older article "Renormalization of the electroweak standard model to all orders" by Elisabeth Kraus.

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The paper you asked for is

G. t'Hooft, Renormalizable lagrangians for massive Yang-Mills fields, Nuclear Physics B 35 (1971), 167-188. https://dspace.library.uu.nl/bitstream/handle/1874/4733/14004.pdf

It contains what most physicist regard as a proof for Yang-Mills theories with spontaneously broken symmetry. The paper earned t'Hooft the Nobel prize. It didn't matter that the proof was not rigorous according to the standards of mathematical physics.

The argument also convinced most physicists that the standard model is renormalizable, since no other technical obstacle is known (at the level of rigor of theoretical physics) and it is just a matter of working through messy details. Whether this counts as a proof is up to you.

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