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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Seesaw formula convensions

Tags:

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**