Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A Box diagram calculation (Kaon mixing)

  1. Apr 22, 2016 #1
    I am trying to calculate box diagram of Kaon mixing by follow the "CP Violation" book.

    Now, I arrived at equation (B.8) and I have problem with getting equation (B.12).

    [tex]F(x_\alpha,x_\beta)=\dfrac{1}{(1-x_\alpha)(1-x_\beta)}(\dfrac{7x_\alpha x_\beta}{4}-1)+\dfrac{x_\alpha^2lnx_\alpha}{(x_\beta-x_\alpha)(1-x_\alpha)^2}(1-2x_\beta+\dfrac{x_\alpha x_\beta}{4})+\dfrac{x_\beta^2lnx_\beta}{(x_\alpha-x_\beta)(1-x_\beta)^2}(1-2x_\alpha+\dfrac{x_\alpha x_\beta}{4})[/tex]

    I got a lot of terms with high order of mW (mW2, mW4, mW6, ...) while there is no mW term in the book.

    I checked the integral over Feynman parameter twice.
  2. jcsd
  3. Apr 22, 2016 #2


    User Avatar
    Science Advisor
    Gold Member

    Did you make sure to do the substitution in (B.10)?

    ## x_\alpha \equiv \dfrac{m_\alpha^2}{m_W^2} ##
    Last edited: Apr 22, 2016
  4. Apr 22, 2016 #3
    In the book is [tex]x_\alpha\equiv\dfrac{m_\alpha^2}{m_W^2}[/tex] I used this one. The book is wrong?
  5. Apr 22, 2016 #4


    User Avatar
    Science Advisor
    Gold Member

    No, my bad. The powers of 2 are indeed there.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted