Small questions about weinberg angle

In summary, the conversation discussed the definitions of the photon and Z0 boson, as well as their relationship to the B0 and W0 bosons. The questions asked were about the orthogonality of these particles and how to derive certain equations involving them. The idea of weak-angle rotation was also mentioned as a way to express the W0 and B0 bosons in terms of the A and Z particles. The importance of understanding the relationships between the coupling constants g, g', and e was emphasized.
  • #1
goinginsane
2
0
Hello !

My books defines the photon and Z0 boson as:

16iic6g.png


for the short read :
I have 3 questions

Are B0 and W0 orthogonal or the photon and Z0?
How do you derive that tg(t) = g'/g (with g' corresponding to B0, g to W0)
How do you derive that e = sin(t) ?


The long read:
Also W0 couples with g (same as the "normal" W+ and W-) and B0 couples with g'.
My first question is (rather dumb one but its getting late and can't think clearly anymore haha):
Are W0 and B0 orthogonal or the foton and Z0 eigenfunctions?

Second question is: My book said ==> the photon only interacts with electrical charge
I said "yes, that's very true mister book! You are finally starting to understand it !
Then he said : well, like I was saying " the photon only interacts with electrical charge, this implies that :
tg(t) = g'/g

I said " Mister book, I am sorry if I have offended you but now you are just making stuff up ! "
He answered " HAHA ! I guess YOU are the one that doesn't understand it"
Anyways we kibbeled for a long time more...
How can you derive that ? :eek:

I shut my book (up) and i tried to understand it like this :

for example define weak interaction operator A

<f|A|f> = 0 (cause doesn't interact) = cos(t) <B0|A|B0> + sin(t) <Z0|A|Z0> (With assuming B0 and Z0 were orthogonal.)
so you get 0 = g' cos(t) + g sin(t)
But then ofcourse i get a minus. I had the feeling i was doing a good job.

So i opened the book again and showed him my progress. But alas, he laughed again.
Cause under that formula there was e = sin(t) g and now I am really confused !
I threw the sadistic book in the closest as punishment. And I fear I won't be able to open it again without understanding it first.
so please help !

Kind regards,

an idiot :)
 
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  • #2
goinginsane, I'm thinking this may be an assignment, is it? So I'll just sketch the idea. Write out the neutral current interaction, Lint ~ g JμW0μ + g' JμY Bμ. (I'm deliberately leaving out some factors.) Use the weak-angle rotation to express W0μ and Bμ in terms of Aμ and Zμ: Lint = (...)Aμ + (...)Zμ. The coefficient in front of Aμ must be the electric current, e(Jμ + JμY). (Factors omitted.) Equating this to the expression you just derived should give the relationships between e, g and g'.
 
  • #3
Bill_K said:
goinginsane, I'm thinking this may be an assignment, is it? So I'll just sketch the idea. Write out the neutral current interaction, Lint ~ g JμW0μ + g' JμY Bμ. (I'm deliberately leaving out some factors.) Use the weak-angle rotation to express W0μ and Bμ in terms of Aμ and Zμ: Lint = (...)Aμ + (...)Zμ. The coefficient in front of Aμ must be the electric current, e(Jμ + JμY). (Factors omitted.) Equating this to the expression you just derived should give the relationships between e, g and g'.

No it is not, we don't get assigments just an exam :)
I could just read it and assume its correct. but I always try to derive all equations by myself when I am learning something.
thanks for the help anyways

aha, well this is just introduction to particle physics so I might be asking questions i can't understand yet. sorry :P
 
  • #4
Ok, good. The interesting point is that all three coupling constants g, g' and e are all about the same size. So anybody who tells you that the "weak" force is weak... well, it's not!
 

1. What is the Weinberg angle?

The Weinberg angle, also known as the weak mixing angle, is a fundamental parameter in the Standard Model of particle physics that describes the strength of the electroweak force, which is responsible for interactions between particles such as electrons and quarks.

2. How is the Weinberg angle measured?

The Weinberg angle can be measured through experiments that involve scattering of particles, such as electron-positron collisions or electron-proton collisions. By measuring the angle at which particles are deflected, the value of the Weinberg angle can be determined.

3. What is the significance of the Weinberg angle?

The Weinberg angle is important because it helps to explain the behavior of particles and their interactions. It also plays a crucial role in the unification of the electromagnetic and weak forces into the electroweak force.

4. How does the Weinberg angle relate to the Higgs boson?

The Higgs boson is responsible for giving particles their mass through the Higgs mechanism. The Weinberg angle is a key factor in this mechanism as it determines the strength of the interaction between the Higgs field and particles, thus influencing their mass.

5. Are there any open questions or controversies surrounding the Weinberg angle?

While the Standard Model accurately predicts the value of the Weinberg angle, there are still unanswered questions and areas of research surrounding its value and possible variations. Additionally, the unification of the electroweak and strong forces, which would require a single unified value for the Weinberg angle, is still an ongoing area of study and debate.

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