# A Box diagram calculation (Kaon mixing)

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1. Apr 22, 2016

### 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 mW (mW2, mW4, mW6, ...) while there is no mW term in the book.

I checked the integral over Feynman parameter twice.

2. Apr 22, 2016

### dukwon

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
3. Apr 22, 2016

### Natthawin Cho

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

4. Apr 22, 2016

### dukwon

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