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Small questions about weinberg angle !

  1. Aug 26, 2012 #1
    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 cant 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, thats 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 doesnt 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 doesnt 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 realy confused !
    I threw the sadistic book in the closest as punishment. And I fear I wont be able to open it again without understanding it first.
    so please help !




    Kind regards,

    an idiot :)
     
    Last edited: Aug 26, 2012
  2. jcsd
  3. Aug 26, 2012 #2

    Bill_K

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    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'.
     
  4. Aug 26, 2012 #3
    No it is not, we dont 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 im learning something.
    thanks for the help anyways

    aha, well this is just introduction to particle physics so I might be asking questions i cant understand yet. sorry :P
     
  5. Aug 26, 2012 #4

    Bill_K

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    Science Advisor

    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!
     
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