Running Coupling for Weak Interaction

[nigelscott]

How can I derive the running coupling for the weak interaction. I have found derivations for QED and QCD that involve the β function http://www.physics.umd.edu/courses/Phys741/xji/chapter1.pdf but I can't find anything specific for the WI. Thanks.

 

[Orodruin]

How can I derive the running coupling for the weak interaction. I have found derivations for QED and QCD that involve the β function http://www.physics.umd.edu/courses/Phys741/xji/chapter1.pdf but I can't find anything specific for the WI. Thanks.

You would not really compute this for the weak interaction on its own. The weak interactions with Ws and Zs are residuals from the breaking of the electroweak gauge symmetry U(1)xSU(2). Above the scale of electroweak symmetry breaking, the running of the hypercharge U(1) and the SU(2)_L are separate and you can compute the beta functions of these based on the number of fermions and scalars transforming under different representations of the gauge symmetries. This should be described in any intermediate text on quantum field theory such as Peskin-Schröder.

 

[nigelscott]

Thank you for your response. Yes that makes sense. The thing that confused was the single value quoted in http://hyperphysics.phy-astr.gsu.edu/hbase/forces/couple.html#c4. I assume this must refer to some experimentally determined value. I found this post https://www.physicsforums.com/threads/running-coupling-of-the-weak-interactions.457359/ which says exactly what you said. I am still a little confused what n_f and n_s would be for both SU(2) and SU(3) for that matter.