# Why is the electron EDM so small in the SM?

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## Main Question or Discussion Point

Hello! I read in several (more accessible) papers (e.g. https://www.sciencedirect.com/science/article/pii/S1049250X0860110X) that the EDM of the electron is so small, because one needs to go to 4 loops or higher to get a non-zero effect. It seems like at 1 and 2 loops there are some symmetry arguments as to why those terms cancel, but for 3 loops there were extensive calculations made and in the end it turned out that all the diagrams cancelled and one gets zero contributions at 3 loops, too. I was wondering if there is any physical reason for all these 3 loops diagrams to perfectly cancel i.e. are there some symmetry arguments from which one could have at least got a hint that these diagram would cancel, without explicitly doing the math (usually there are some deeper meanings when some terms are perfectly equal)?

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Staff Emeritus
2019 Award
It's in Dugan, Grinstein and Hall, Nucl. Phys. B 255, 413-438 (1985).

But why do you think that there is significance that the lowest non-zero order is 4 and not 3 or 5?

It's in Dugan, Grinstein and Hall, Nucl. Phys. B 255, 413-438 (1985).

But why do you think that there is significance that the lowest non-zero order is 4 and not 3 or 5?
Well perfect cancelations in physics don't usually happen by chance. For example in the case of the magnetic moment, the g factor is not exactly 2. Or the whole hierarchy problem comes from the fact that we might have lots of cancelations (not perfect, tho) and that lead to the idea of supersymmetry. I was wondering if there are any theories/significance as to why we get perfect cancelations up to order 4. Is this something that happens often at higher order diagrams in general?

ChrisVer
Gold Member
Not an expert to these calculations, but I will only say something that starts from the end to go to the start. If people needed to make excessive calculations to prove that the 3-loop diagrams exactly cancel out, there is not a straightforward symmetry argument to explain it.
Obviously since then some symmetry arguments might have been introduced?

Staff Emeritus
2019 Award
Well perfect cancelations in physics don't usually happen by chance.
But it's not a perfect cancellation.

Not an expert to these calculations, but I will only say something that starts from the end to go to the start. If people needed to make excessive calculations to prove that the 3-loop diagrams exactly cancel out, there is not a straightforward symmetry argument to explain it.
Obviously since then some symmetry arguments might have been introduced?
I mean definitely it wasn't obvious beforehand. I was wondering if they found some explanations to it after they did the calculations.

But it's not a perfect cancellation.
I meant to 2 and 3 order loop.

Staff Emeritus
2019 Award
Yes, and that gets me back to my original question: why do you think that there is significance that the lowest non-zero order is 4 and not 3 or 5?

(And you didn't read the reference I posted, did you?)

Yes, and that gets me back to my original question: why do you think that there is significance that the lowest non-zero order is 4 and not 3 or 5?

(And you didn't read the reference I posted, did you?)
I don't think so. As I said in the original post: "I was wondering if there is any physical reason for all these 3 loops diagrams to perfectly cancel". I never claimed there is a significance. I just asked if there is one or not.

I haven't read your reference. I am an undergrad. The most advanced classes I took are probably quantum mechanics and particle physics (not QFT). Do you really think a paper about supergravity will enlighten me?