ok so this is a bit of a boring question, so sorry in advance, but for some reason im struggling with this.(adsbygoogle = window.adsbygoogle || []).push({});

I am deriving the seesaw formula.

Now I have gone through the derivivate and I get A : ## m_{\nu} = - m_D^T M^{-1} m_D ##

Now I have seen other derivations where they get B : ## m_{\nu} = - m_D M^{-1} m_D^T ##

Note( transpose on LH or RH side )

So I think the reason for this is that in the langrangian you always have + h.c.

And so depending on which term you write, and which term you shove in h.c. I think you get these two different versions.

But essentially it must be describing the same physics, obviously.

Now, in a paper I am reading they have version B and they have the diagonalisation

##-Dm = U^{\dagger} m_{\nu} U^* = U^{\dagger} m_D M^{-1} m_D^T U^* ##

They have used B. I need some somehow reconcile A with B and I am a bit confused.

## D_m ## should be the same whatever convension, its real and diagonal, so it is just mass eingenvalues on the diagonal of the mass matrix.

but it doesnt seem obvious that ## U^{\dagger} m_D M^{-1} m_D^T U^* = U^{\dagger} m_D^T M^{-1} m_D U^* ## ??? these dont look equal ..

but it must do, if both give a diagonal matrix of mass values?

is this right? Or have I missed something?

Basically I have written deriviation A in my report. but now I realise some work I did used deriviation B. So I need some smooth transition between the two.

I hope this makes sense, and apologies again for such a boring convension based question, but I guess it means I'm lacking some fundamental understanding if I am struggling with this.

Thanks

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# A Seesaw formula convensions

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