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I'm trying question 1 in this past paper:

http://www.maths.cam.ac.uk/postgrad/mathiii/pastpapers/2009/Paper48.pdf [Broken]

I'm on the bit "Show that the divergent part of this diagram can be written in the form [itex]Ap^2+B[/itex] where [itex]p=p_1=-p_2[/itex] and A and B are momentum independent.

Now, as far as I can tell, this calculation is going to be exactly the same as the one on p48 of these notes:

http://www.damtp.cam.ac.uk/user/ho/Notes.pdf [Broken]

(the final result being given at the top of p49) with the only difference being that when we use dimensional regularisation to analytically continue to [itex]d \in \mathbb{C}[/itex], we should set [itex]d=6-\epsilon[/itex] instead of [itex]d=4-\epsilon[/itex]. However, this will change the powers of some factors in the final answer, it won't change the pole structure, will it? I certainly don't see how we're going to need an [itex]Ap^2[/itex] counter term as there is no divergent piece multiplying a [itex]p^2[/itex] that I can see...

Can anyone offer some help please...

http://www.maths.cam.ac.uk/postgrad/mathiii/pastpapers/2009/Paper48.pdf [Broken]

I'm on the bit "Show that the divergent part of this diagram can be written in the form [itex]Ap^2+B[/itex] where [itex]p=p_1=-p_2[/itex] and A and B are momentum independent.

Now, as far as I can tell, this calculation is going to be exactly the same as the one on p48 of these notes:

http://www.damtp.cam.ac.uk/user/ho/Notes.pdf [Broken]

(the final result being given at the top of p49) with the only difference being that when we use dimensional regularisation to analytically continue to [itex]d \in \mathbb{C}[/itex], we should set [itex]d=6-\epsilon[/itex] instead of [itex]d=4-\epsilon[/itex]. However, this will change the powers of some factors in the final answer, it won't change the pole structure, will it? I certainly don't see how we're going to need an [itex]Ap^2[/itex] counter term as there is no divergent piece multiplying a [itex]p^2[/itex] that I can see...

Can anyone offer some help please...

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