# Electron/Proton Electric Charge Equality Expected?

## Main Question or Discussion Point

Do the SM and Lambda-CDM lepton-era models predict that the electron’s isolated electric charge be equal in magnitude (to 12 significant figures) to that of the proton which is a composite particle?

What makes that this identity in electric charge magnitude is so exquisitely ‘fine-tuned’?

What would be the implications if this fine-tuning were off by a couple of orders of magnitude for the physics of the atom?

IH

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mfb
Mentor
It is necessary for anomaly cancellation. The SM wouldn't make sense without it.
What would be the implications if this fine-tuning were off by a couple of orders of magnitude for the physics of the atom?
It is not fine tuning as it is not accidental. Apart from that: The universe would look completely different, but how depends on the physics that you have to rewrite from scratch. Will the electron to proton number ratio change accordingly? You might get huge atoms, or no atoms at all.

Thanks, I’m trying to understand the concept of anomaly cancellation from wiki and other sources...

One simple question though...what would be the ‘least bad’ lay analogy of what anomaly cancellation consists of?...or is this, like so many other phenomena, not susceptible to analogy?...

Another question of interpretation...from this wiki page, I understand that the gauge couplings for the electromagnetic-weak interaction figure among the 19 values that must be manually set in the SM.

https://en.m.wikipedia.org/wiki/Standard_Model#Construction_of_the_Standard_Model_Lagrangian

Does this mean that anomaly cancellation determines identity of charge between electron and proton but does not determine the strength of the related EM charge?

IH

mfb
Mentor
Without anomaly cancellation you get all sorts of nonsense in calculations, which means your theory doesn’t work - but I‘m not an expert, I work on the experimental side.

Anomaly cancellation just requires them to be the same in magnitude, right. The absolute value of it (or, equivalently, the coupling constant of the electromagnetic interaction - the fine structure constant) is a free parameter.