Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,853 answers , 20,624 comments
1,470 users with positive rep
501 active unimported users
More ...

S-Matrix Interpretation and Predictions

+ 6 like - 0 dislike
57 views

How does one distinguish between the second-loop contribution of a known particle, and the first-loop contribution of a more massive-and as yet undiscovered-particle in the S-matrix and/or differential cross section?

Imagine: I calculate a one-loop correction to some scattering process in QED. My photon propagator needs to be corrected for all three lepton generations. I then calculate the differential cross section. The experimentalist then shows me a plot of his precise measurements and tells me that my calculations need further corrections.

Question: How do I know that the necessary correction is from two-loop diagrams, and not from a fourth lepton in the first-loop diagram that I haven't considered?


This post imported from StackExchange Physics at 2016-11-08 14:00 (UTC), posted by SE-user Optimus Prime

asked Nov 1, 2016 in Theoretical Physics by Optimus Prime (80 points) [ revision history ]
edited Nov 8, 2016 by Optimus Prime
Huh, because they are quite different beasts?

This post imported from StackExchange Physics at 2016-11-08 14:00 (UTC), posted by SE-user OON
Please elaborate in what context. If experimentally - you calculate for both models and look what fit observations better.

This post imported from StackExchange Physics at 2016-11-08 14:00 (UTC), posted by SE-user OON
I modified my question. Does it help?

This post imported from StackExchange Physics at 2016-11-08 14:00 (UTC), posted by SE-user Optimus Prime

2 Answers

+ 4 like - 0 dislike

Made up example:

enter image description here

where the solid line represents the one-loop calculation, and the dashed one the two-loop one.

On the other hand,

enter image description here

where the solid line represents the one-loop calculation with three generations, and the dashed one represents the one-loop calculation with four generations (the new particle has a mass close to $s=4$ in this scale).

In other words: more loops slightly change the overall look of the cross section. More particles change its behaviour close to the mass of such particles.

This post imported from StackExchange Physics at 2016-11-08 14:00 (UTC), posted by SE-user AccidentalFourierTransform
answered Nov 1, 2016 by AccidentalFourierTransform (375 points) [ no revision ]
Interesting. So what these plots say is that higher order loops change the diagram as a whole, whereas a new particle would merely show up as a bump. The only question I have is how come the three original leptons didn't show up as bumps near their respective masses?

This post imported from StackExchange Physics at 2016-11-08 14:00 (UTC), posted by SE-user Optimus Prime
They actually do show up in their respective masses! My diagram only shows the fourth bump for simplicity.

This post imported from StackExchange Physics at 2016-11-08 14:00 (UTC), posted by SE-user AccidentalFourierTransform
What are their masses in this scale?

This post imported from StackExchange Physics at 2016-11-08 14:00 (UTC), posted by SE-user Optimus Prime
This is a made up diagram, it doesn't correspond to anything physical. It's only meant to illustrate the general trend of loop corrections and resonances. In this case, you can take the three first masses to be, say, very close to the origin (so that they can be treated as massless).

This post imported from StackExchange Physics at 2016-11-08 14:00 (UTC), posted by SE-user AccidentalFourierTransform
Great. Thanks for the effort.

This post imported from StackExchange Physics at 2016-11-08 14:00 (UTC), posted by SE-user Optimus Prime
@OptimusPrime no problem. If you have any more questions, feel free to ask.

This post imported from StackExchange Physics at 2016-11-08 14:00 (UTC), posted by SE-user AccidentalFourierTransform
+ 0 like - 0 dislike

The question is rather strange. If you can, you make one- and two-loop calculations within an old model, and if possible, estimate contributions of higher order corrections. Then you compare your results and estimations with the experimental data. If the old model fails, you need a new model, for example, with a new and heavier particle, why not?

If you cannot make a two loop calculation and you have a significant uncertainty in your estimations of the old model, you stay with this uncertainty and you cannot decide.

answered Nov 9, 2016 by Vladimir Kalitvianski (22 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOv$\varnothing$rflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...