Stupid question on anomalous magnetic moment of the electron

[paolorossi]

I don't understand one think: when we calculated the correction of the magnetic moment of the electron, we consider only the finite terms of the vertex correction that non depend on the parameter μ. Using Ryder notation , we consider only

$\bar{u}$(p')(γ_μ+$\Lambda$_μ⁽²⁾)u(p)

but there is also another finite contribution in $\Lambda$_μ⁽¹⁾
$\Lambda$_μ⁽¹⁾ = divergent + finite

, why we don't consider that? some book to view this?

 

[strangerep]

, why we don't consider that? some book to view this?

Try Peskin & Schroeder. If I remember correctly, they show how only the $\Lambda^{(2)}$ term you mentioned is relevant to the anomalous magnetic moment, because the $\Lambda^{(1)}$ term goes to 1 as $q\to 0$. (I'm guessing here that Ryder's $\Lambda$ corresponds to P&S's $F$.)

 

[andrien]

yes,there are two form factors .The first of which becomes 1 in zero momentum transfer case.However I have not read ryder,so may be it is something different.I will reply after taking a look somewhere else.

 

[paolorossi]

yes,there are two form factors .The first of which becomes 1 in zero momentum transfer case.However I have not read ryder,so may be it is something different.I will reply after taking a look somewhere else.

thanks . however the $\Lambda$_μ is the vertex correction... when the ryder regularize it, whit the dimensional method, he writes it as the sum of two terms: $\Lambda$⁽²⁾_μ that is convergent, and $\Lambda$⁽¹⁾_μ that contains the divergent term plus a finite term. Then he calculates the quantity
$\bar{u}$(p')($\gamma$_μ+$\Lambda$_μ⁽²⁾)u(p)
whit q=p'-p (q is the momentum associated to the external photon ) different fo zero. He find the correction:
g/2=1+α/2π

but why he doesn't consider the finite term in $\Lambda$⁽¹⁾_μ ?

 

[paolorossi]

Try Peskin & Schroeder. If I remember correctly, they show how only the $\Lambda^{(2)}$ term you mentioned is relevant to the anomalous magnetic moment, because the $\Lambda^{(1)}$ term goes to 1 as $q\to 0$. (I'm guessing here that Ryder's $\Lambda$ corresponds to P&S's $F$.)

thanks now I try to read something

 

[paolorossi]

ok now I understand. I calculate Λ⁽¹⁾_μ : the finite term in it is proportional to the matrix γ_μ, so it doesn't give any contribution to the magentic moment of the electron ( it contributes only to the form factor F₁ )

certain that the ryder could write instead of "finite" in the expression of Λ⁽¹⁾_μ the term itself, or say something about ...

 

[andrien]

they are just the form factors.By taking the non relativistic limit you can interpret F₁(0) as the unit of charge(zero momentum transfer case it is 1) and other factor F₂(0) which using gordon identity can be interpreted as electron having a magnetic moment (1+F₂(0)) which interacts with magnetic field .

 

[paolorossi]

they are just the form factors

... I think it's more correct to say that they are connected to form factors, in fact, using the identity of gordon we find that only a part of the finite term $\Lambda$⁽²⁾_μ contributes to the form factor F₂ , and so to the magnetic moment of the electron... anyway thanks to all for your answers, bye