Unitarity of CKM matrix

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  • #1
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Main Question or Discussion Point

This is a known fact that CKM matrix, a matrix that is used to connect the weak interaction eigenstates to mass eigenstates is unitary. I have studied that this is due to the conservation of probability. i.e. an up type quark will decay into exactly three type of d quarks, nothing more.
 

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  • #2
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I'm not sure what exactly you're trying to say --- it's all correct and true, but why did you decide to post that as a message?
 
  • #3
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I just want to express the fact that an up quark can only decay to three down types of quarks only and thus the unitarity of ckm matrix mathematically.
 
  • #4
malawi_glenn
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What kind of respons do you want plasmon?
 
  • #5
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Hello, I dont understand the aim of the post too..
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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There is a lepton analogue called the MNS matrix, for Maki, Nakagawa and Sakata.

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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Dear All

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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Thanks Vanadium for your enriching contribution.
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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Vanadium 50,

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.
 
  • #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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