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this is the first time I post here, so if this is not in the correct section please let me know...

I'm working on solving the first final project in peskin - Radiation of gluon jets.

In this project we assume a simplified model for the gluon - it is a massive vector boson (with a small mass [tex]\mu[/tex] to regulate IR singularities) which couples universally to quarks.

The first task is to compute the diagram contributing to [tex]e^+e^-\rightarrow \bar{q}q[/tex] with one virtual gluon. This gives a contribution to [tex]F_1(q^2)[/tex] of the gluon. After quite a lengthy calculation I reached the following correction (omitting constants):

[tex]

\delta F_1(q^2) = \int_0^1 dxdydz\delta(x+y+z-1)\int\frac{d^4 w}{(2\pi)^4}\frac{4q^2-2w^2}{[w^2-z\mu^2+xyq^2+i\epsilon]^3}

[/tex]

where I have defined q to be the sum of the electron and positron incoming momenta ([tex]q = p+p'[/tex]).

In the instructions provided in the text it is said to regulate this integral by doing the substitution [tex]\delta F_1(q^2) \rightarrow \delta F_1(q^2)-\delta F_1(q^2=0)[/tex].

My problem is that it seems to me that there is a branch-cut singularity in this expression, since [tex]q^2 = E_{CM}^2 > 0[/tex].

So my questions are as follows:

- Am I correct in stating that there is a branch-cut singularity here?
- Does it make sense to have such a singularity here?
- What would you suggest to do in order to continue this calculation?

Thanks in advance to any help and insights, and again if this is the wrong place to post I apologize and hope you can point me out to the right direction...

Omri

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# Radiation of gluon jets - Peskin final project question

Can you offer guidance or do you also need help?

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