The discussion focuses on deriving the running coupling for weak interactions, specifically addressing the complexities associated with electroweak gauge symmetry breaking. It emphasizes that the weak interactions, mediated by W and Z bosons, are not computed in isolation but rather as residuals from the U(1)xSU(2) symmetry. The beta functions for hypercharge U(1) and SU(2)_L can be calculated based on the number of fermions and scalars in various representations, as detailed in intermediate quantum field theory texts like Peskin-Schröder. The confusion regarding specific values for nf and ns in SU(2) and SU(3) is acknowledged, indicating a need for further clarification.
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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 said: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.