Why is the electron EDM so small in the SM?

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Discussion Overview

The discussion centers on the smallness of the electron electric dipole moment (EDM) within the Standard Model (SM) of particle physics, particularly focusing on the cancellation of contributions from loop diagrams at various orders. Participants explore the implications of these cancellations and whether there are underlying symmetry arguments that could explain them.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that the EDM of the electron is small because non-zero contributions require calculations at 4 loops or higher, with 1 and 2 loops canceling due to symmetry arguments.
  • Others question the significance of the lowest non-zero order being 4, suggesting that perfect cancellations in physics are not common and may indicate deeper underlying principles.
  • A participant mentions that extensive calculations have shown that 3-loop diagrams also cancel out, raising the question of whether there are symmetry arguments that could have predicted this cancellation.
  • Some express skepticism about the existence of straightforward symmetry arguments to explain the cancellations, indicating that the need for extensive calculations suggests complexity.
  • There is a discussion about the nature of cancellations in physics, with references to other phenomena like the magnetic moment and the hierarchy problem, suggesting that cancellations may not be purely coincidental.
  • A participant clarifies that they are not claiming significance but are inquiring about the possibility of it, highlighting their limited background in advanced physics topics.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether there are significant reasons for the cancellations observed at 3 loops or whether such cancellations are common in higher-order diagrams. The discussion remains unresolved regarding the implications of these cancellations.

Contextual Notes

Some participants express uncertainty about the mathematical and physical implications of the cancellations, indicating a lack of straightforward symmetry arguments and the complexity of the calculations involved.

Malamala
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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 canceled 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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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?
 
Vanadium 50 said:
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?
 
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?
 
Malamala said:
Well perfect cancelations in physics don't usually happen by chance.

But it's not a perfect cancellation.
 
ChrisVer said:
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.
 
Vanadium 50 said:
But it's not a perfect cancellation.
I meant to 2 and 3 order loop.
 
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?)
 
Vanadium 50 said:
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?
 

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