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I know that a question about why the photon is massless already exists, however it did not answer this question.

First off, I do understand why the photon does neither have a bare mass term due to gauge invariance of the standard model lagrangian nor does it get mass from the Higgs mechanism.

However as far as I understood it particles generally can get loop corrections to their mass (e.g. possibly generating neutrino masses). Since I am not really familiar with this mechanism I would like to know why there seem to be no loop corrections to the photon mass. Do they cancel out or am I just missing something obvious.

I'd also appreciate a link to a review-paper or book chapter dealing with this.

Qmechanic
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Katermickie
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    There's an interesting paper from 2004 you can look at online titled The mass of the photon. There are detailed explanations of experiments to find the upper limit for photon mass and some data on upper limits from various experiments. Perhaps of interest. Another similar paper would be Photon and Graviton mass limit on Arxiv. The point is that the mass of the photon could be non-zero, albeit very small based on experiment. – StephenG - Help Ukraine Sep 03 '18 at 01:03
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    It’s a consequence of gauge invariance, i.e. the Ward identities. I think just about any QFT textbook would cover this, though QFT-lite particle physics books might gloss over it. – knzhou Sep 03 '18 at 01:26
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    @knzhou gauge-invariance requires that the photon doesn't acquire a mass. It doesn't prove it does not. Proving that, indeed, there are no loop-corrections to the photon mass is non-trivial: one has to (diagrammatically/combinatorially) prove $\xi$-independence to all orders in perturbation theory. That being said, adding an explicit mass term for the photon does not break gauge invariance, despite what it is usually said. Doing so for non-abelian theories does break gauge invariance, so you need good ol' Higgs. – AccidentalFourierTransform Sep 03 '18 at 02:02

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