Calculation of g-factor correction in Peskin p. 196

• niss
In summary, the conversation discusses the calculation of the correction to the g-factor in QFT, using the formula for F2(q^2=0) and the integration of variables x, y, and z. The conversion from the first line to the second is confirmed, but there is confusion about how to convert the second to the third. The conversation then focuses on the correct method for integrating z, which is ultimately confirmed to be α/π. It is determined that there was a mistake in the integration, but the textbook is correct.
niss
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?

Last edited:
I think the book is correct. After doing the ##y## integration, what does the ##z##-integral look like?

TSny said:
I think the book is correct. After doing the ##y## integration, what does the ##z##-integral look like?
From the second line,

$$\frac{\alpha}{\pi}\int ^1_0 dz \int^{1-z}_0 dy \frac{z}{1-z}=\frac{\alpha}{\pi}\int ^1_0 dz z=\frac{\alpha}{\pi}$$

I agree with the form of your ##z## integral. But it looks like you're not doing the ##z##-integration correctly.

niss
TSny said:
I agree with the form of your ##z## integral. But it looks like you're not doing the ##z##-integration correctly.
What do you mean by "correctly"?

niss said:
What do you mean by "correctly"?
##\int zdz = z^2/2##.

niss
MathematicalPhysicist said:
##\int zdz = z^2/2##.
OMG I seriously missed it. Sorry for posting such a stpd question...

1. What is the g-factor correction in Peskin p. 196?

The g-factor correction in Peskin p. 196 refers to a term that is added to the calculation of the g-factor, which is a measure of the strength of the interaction between a charged particle and a magnetic field.

2. Why is the g-factor correction important?

The g-factor correction is important because it takes into account the effects of quantum mechanics on the measurement of the g-factor. Without this correction, the calculated value of the g-factor would not accurately reflect the true strength of the interaction.

3. How is the g-factor correction calculated?

The g-factor correction is calculated using a combination of theoretical calculations and experimental data. The theoretical calculations involve using quantum field theory to account for the effects of virtual particles on the measurement, while the experimental data is used to fine-tune the value of the correction.

4. What is the significance of the g-factor correction in particle physics?

The g-factor correction is significant in particle physics because it allows for more precise measurements of the g-factor, which is an important parameter in understanding the behavior of particles in magnetic fields. It also serves as a test of the predictions of quantum field theory.

5. Are there any limitations to the g-factor correction?

Yes, there are limitations to the g-factor correction. It is based on theoretical assumptions and experimental data, so there is always a margin of error in the calculated value. Additionally, the g-factor correction may not be applicable to all particles, as it is dependent on the specific properties and interactions of the particle being measured.

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