Does anyone know the highest loop order (certain) processes in QED and/or the standard model have been calculated?

 

I suspect it is not very high (~4 maybe?), but does anyone know what is "claimed" and what is in the literature?

 

Of course, one would not expect to see any "new phenomena" past one loop unless one were to sum over all loops. So my question, is really about the technical exercise and what people have put themselves through!

 

Cheers.

That depends. I know things have been calculated to seven loops, e.g. http://arxiv.org/abs/cond-mat/0309060, but that is not SM. If you are talking practical useful SM particle physics calculations, then four is probably as much as there is, e.g. http://arxiv.org/abs/hep-ph/0610206.

 

But then, if you look at it from a different perspective, there are resummations of large logs which are effectively resumming (parts of) all the loops all the way to infinite order.

Seven loops sounds quite impressive!

 

Like the paper you point out 4-loops in QED is the highest I have come across. Apart from 2-PI methods which sum an infinite set of diagrams.

 

Strange to think that one of the best tested and accepted theories is "only" tested to something like 3-4 loops.

This one looks impressive too: http://arxiv.org/abs/0806.3390

Yes the [math]g-2[/math] calculation in QED. People talk about the 10th order correction, but that is not to 10th loop order it is to 5 loops. Also, I am not sure if all order 5 loops have been used in these calculations. Something like 2958 of them!

 

Still, going beyond 2 loops is very impressive to me! I have only ever gone as far as one loop and will probably never do that again. (I have looked at the "triangle diagrams" for anomalies).