Quark mixing factor in CKM matrix

In summary, the quark mixing factor, also known as ##V_{ub}##, is the same for u ##\Leftrightarrow## b, ##u\Leftrightarrow\bar{b}##, ##\bar{u}\Leftrightarrow## b, and ##\bar{u}\Leftrightarrow\bar{b}##. This is due to the Hermitian property of the Lagrangian density. However, in the decay of charged Kaon, the hadronic part of the current has a different coupling, ##V_{c\bar{s}}##, which is equal to ##V_{cs}##. This is because the decay does not involve a transition between these qu
  • #1
Amith2006
427
2
I find that the quark mixing factor say for example ##V_{ub}## is the same for:
u ##\Leftrightarrow## b
##u\Leftrightarrow\bar{b}##
##\bar{u}\Leftrightarrow## b
##\bar{u}\Leftrightarrow\bar{b}##
Does this have something to do with weak interaction being unable to distinguish these from one another?
Thanks in advance.
 
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  • #2
There is no (known) interaction which turns a quark into an anti-quark as that would violate baryon number.

For the coupling between ##u## and ##b## being equal (in magnitude) to the coupling between ##\bar u## and ##\bar b##, this is a simple consequence of the Lagrangian density being Hermitian.
 
  • #3
Orodruin said:
There is no (known) interaction which turns a quark into an anti-quark as that would violate baryon number.

For the coupling between ##u## and ##b## being equal (in magnitude) to the coupling between ##\bar u## and ##\bar b##, this is a simple consequence of the Lagrangian density being Hermitian.
I can understand that the coupling between u and b is equal (in magnitude) to the coupling between ##\bar{u}## and ##\bar{b}## due to the Hermitian property but in the decay of charged Kaon,
##K^+ \rightarrow \mu^+ + \nu_\mu##
the hadronic part of the current has ##V_{c\bar{s}}## which is the same coupling as ##V_{cs}##.
 
Last edited:
  • #4
It is not a transition between them, that is the point.
You can rotate the diagram to get u -> s+W+, for example (no c involved in a kaon decay). The vertex stays the same, so you need Vus.
 
  • #5
Sorry ##V_{us}##. Ah, now I get it. Thanks.
 

FAQ: Quark mixing factor in CKM matrix

1. What is the CKM matrix and why is it important?

The Cabibbo-Kobayashi-Maskawa (CKM) matrix is a unitary matrix used in the Standard Model of particle physics to describe the mixing of quarks. It is important because it explains the observed phenomenon of flavor-changing weak interactions, which are interactions that change the flavor of quarks (i.e. changing from up-type to down-type or vice versa).

2. What is the quark mixing factor in the CKM matrix?

The quark mixing factor in the CKM matrix refers to the elements of the matrix that describe the probability of a quark of one flavor transforming into a quark of another flavor through a weak interaction. These factors are complex numbers and are denoted by Vud, Vus, Vub, Vcd, Vcs, Vcb, Vtd, Vts, and Vtb.

3. How is the quark mixing factor determined?

The quark mixing factor is determined through experimental measurements of weak interactions involving quarks. Specifically, it is determined through measurements of processes such as beta decay, kaon decays, and B meson decays. These measurements are then used to calculate the values of the elements in the CKM matrix.

4. How does the quark mixing factor affect particle interactions?

The quark mixing factor has a direct impact on the strength of weak interactions between quarks. It determines the probability of a quark of one flavor transforming into a quark of another flavor during a weak interaction. This, in turn, affects the rates of various particle interactions and can explain the observed differences in decay rates of particles containing different types of quarks.

5. Are there any ongoing studies or developments regarding the quark mixing factor in the CKM matrix?

Yes, there are ongoing studies and developments in this area. The precise values of the quark mixing factors are still not fully understood and there is ongoing research to improve our understanding of them. Additionally, there are theoretical models that attempt to explain the structure of the CKM matrix and the origin of the quark mixing factors, which are also being actively studied and developed.

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