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Because there is a single Yukawa matrix for the SM leptons, the lepton mass and flavour states can be aligned, by diagonalization, even if the Yukawa matrix had off-diagonal elements.

SUSY breaking, however, introduces soft-breaking masses for the sleptons, which could be off-diagonal and introduce flavour-changing currents, e.g. $e\to \mu \gamma$. What, in general, is the connection between the soft-breaking mass and the Yukawa coupling?

I know that in mSUGRA they can be connected by the Kahler potential, but is there any symmetry principle that can connect the two? I understand that the connection in mSUGRA arises only from minimality and nothing deeper? Surely this alignment cannot be an accident?

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Generally, in the MSSM one works with the "minimal flavor violation" paradigm that states that all flavor violation originates in the SM Yukawa sector. This paradigm is ad hoc, but explains why no huge SUSY contributions to FCNC observables are seen.

There are models that go beyond minimal flavor violation and some that give an explanation for the alignment. Those are not the MSSM though.

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OK, I think I see now. In, for example, gauge mediated models, the soft-breaking masses will be flavour diagonal, and, because breaking is mediated by ordinary SM gauge interactions, these interactions can be diagonalised simultaneously with the SM Yukawas. So in general, if the breaking is flavour diagonal, there's no issue with alignment with Yukawas, that can take care of itself. –  innisfree May 15 '13 at 15:48
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