- #1

niss

- 7

- 2

- Homework Statement
- calculation of the correction for g-factor

- Relevant Equations
- F_2(0)=(g-2)/2

I'm reading peskin QFT textbook. In page 196 eq. (6.58) it says

$$F_2(q^2=0)=\frac{\alpha}{2\pi}\int ^1_0 dx dy dz \delta (x+y+z-1) \frac{2m^2z(1-z)}{m^2(1-z)^2}\\=\frac{\alpha}{\pi}\int ^1_0 dz\int ^{1-z}_0 dy \frac{z}{1-z}=\frac{\alpha}{2\pi}$$

I confirmed the conversion from the first line to the second but can't figure out how to convert the second to the third. I think the last line should be α/π.

This is used to calculate the correction to g-factor

$$a_e=\frac{g-2}{2}=F_2(0)=\frac{\alpha}{2\pi}=0.0011614...$$

Is there something I'm missing or is it an error in the textbook?

$$F_2(q^2=0)=\frac{\alpha}{2\pi}\int ^1_0 dx dy dz \delta (x+y+z-1) \frac{2m^2z(1-z)}{m^2(1-z)^2}\\=\frac{\alpha}{\pi}\int ^1_0 dz\int ^{1-z}_0 dy \frac{z}{1-z}=\frac{\alpha}{2\pi}$$

I confirmed the conversion from the first line to the second but can't figure out how to convert the second to the third. I think the last line should be α/π.

This is used to calculate the correction to g-factor

$$a_e=\frac{g-2}{2}=F_2(0)=\frac{\alpha}{2\pi}=0.0011614...$$

Is there something I'm missing or is it an error in the textbook?

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