Box diagram calculation (Kaon mixing)

[Natthawin Cho]

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).

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

I got a lot of terms with high order of m_W (m_W², m_W⁴, m_W⁶, ...) while there is no m_W term in the book.

I checked the integral over Feynman parameter twice.

 

[dukwon]

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

$x_\alpha \equiv \dfrac{m_\alpha^2}{m_W^2}$

 

[Natthawin Cho]

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

$x_\alpha \equiv \dfrac{m_\alpha}{m_W}$

In the book is $$x_\alpha\equiv\dfrac{m_\alpha^2}{m_W^2}$$ I used this one. The book is wrong?

 

[dukwon]

No, my bad. The powers of 2 are indeed there.