How Does Minimal Flavour Violation Apply in Extensions of the Standard Model?

[Luca_Mantani]

Hi,
i've got a doubt about the application of the principle of minimal flavour violation (MFV) in order to build extension of the standard model.
https://arxiv.org/pdf/1603.08002v2.pdf

In this paper at page 18 defines the MFV: "One very convenient approach to deal with this is to impose that new physics either respect the SM flavor symmetry or the breaking of it is associated with the quark Yukawa matrices."

Then, at page 20 he applies it and it says that it imposes the couplings to be proportional tu the yukawas couplings.

On the other hand at page 27 he uses the same principle, but this time the couplings needs to be all equal.

Why is that?

 

[AndyW]

Hello,

Thank you for your question. The principle of minimal flavour violation (MFV) is a theoretical framework used in particle physics to guide the construction of extensions to the standard model. It is based on the idea that any new physics beyond the standard model should not introduce new sources of flavour violation, which refers to the interactions between different types of quarks and leptons.

In the paper you mentioned, the author defines MFV as either respecting the existing flavour symmetry in the standard model or having the breaking of this symmetry be associated with the quark Yukawa matrices. This means that any new interactions introduced in an extension of the standard model should be proportional to the existing Yukawa couplings, which describe the strength of the interactions between the quarks and the Higgs boson.

At page 20, the author applies this principle by showing that in a certain scenario, the couplings of the new interaction are indeed proportional to the Yukawa couplings. However, at page 27, the author considers a different scenario where the new interactions are not proportional to the Yukawa couplings, but instead they are all equal. This is still in line with the MFV principle, as the new interactions are still respecting the flavour symmetry of the standard model.

In summary, the reason for the two different scenarios is that the MFV principle allows for different possibilities, as long as they do not introduce new sources of flavour violation. The choice between proportional or equal couplings depends on the specific extension of the standard model being considered and the assumptions made about the new interactions. I hope this helps clarify your doubt.