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- Thread starter plasmon
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- #4

malawi_glenn

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What kind of respons do you want plasmon?

- #5

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but this has raised a question in my mind..

(thanks Plasmon !)

in the leptonic sector, the neutrino also have a CKM-analogue matrix right?

but we dont know yet if it is unitary or not..

if it is just related to probabilites.. where's the problem ?

- #6

Vanadium 50

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The CKM (and MNS) matrices are unitary by construction. Essentially they are a change in basis - a rotation, if you will - so must be unitary. A separate question is experimental: is the 3x3 matrix that we can measure unitary? If the answer is "no", that's proof for new physics: e.g. a 4th family.

For quarks, the answer is that we cannot tell. Partly this is because the effect of new physics can be made arbitrarily small, but there's a little more to it than that. For example, given only the upper 2x2 CKM matrix, one cannot infer the existence of a 3rd family. Additionally, the numbers don't work out nicely: Vtb is so close to 1 that one needs a measurement of single top production good to better than 0.1% to see the effect of other quarks.

- #7

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I guess we can express it as

W-|u>=Vud |d>+Vus |s>+Vub |b>

W-|c>=Vcd |d>+Vcs |s>+Vcb |b>

W-|t>=Vtd |d>+Vts |s>+Vtb |b>

and |d> , |s>, |b> are orthogonal states (not neccessary due to GIM mechanism)

<u|W-(adj) W-|u>=1, <c,t|W-(adj) W-|u>=0

=> V as a unitary matrix

Am i right in making above assumptions.

- #8

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another question, I may be off topic but it's in my mind, so I hope this wont bother you too much :)

Is the eventual non-unitarity of the MNS matrix related to the CP violation ?

- #9

Vanadium 50

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Is the eventual non-unitarity of the MNS matrix related to the CP violation ?

There is no "eventual non-unitarity of the MNS matrix". If there are only three families of neutrinos and no new physics, you will get a unitary matrix.

- #10

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the eventuality is as you stated it : "If there are only three families of neutrinos and no new physics"

..

- #11

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Atakor

The word "if" does not imply an eventuality.

The word "if" does not imply an eventuality.

- #12

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Atakor

The word "if" does not imply an eventuality.

Really ?

==There is no "eventual non-unitarity of the MNS matrix". If there are only three families of neutrinos and no new physics, you will get a unitary matrix.

if we say 'there are only 3 families' THEN MNS is unitary,

otherwise (if you dont like the word 'eventuality') MNS doesnt have to be Unitary.

quiet clear for me...

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