# E+e- -> quark+antiquark

e+e- --> quark+antiquark

Hi!
If I compute the cross section for the annihilation of e+e- in a photon which decays in a quark+antiquark, I find a well-behaved cross-section. However, if I add a QCD correction where the two quarks exchange a virtual gluon, then I find that for the cross-section to be finite in the IR region I have to consider also the emission of a real soft gluon.
Now, is it right to say that this soft real gluon is the responsible of the hadronization of the quarks?

No,

The IR divergence that cancels when the soft gluon is included has nothing to do with the subsequqent hadronization of the quarks.

For example, this divergence happens also in the process $e^{+}e^{-}->\mu^{+}\mu^{+}$ when corrections with virtual photons are included and the emission of soft real photons have to considered in order for the cross section to be finite.

When a quark is created there is a certain probability of emitting a gluon and this probability is greater when the gluon is softer. This soft gluon can create a pair quark-antiquark and they can emit another gluon and so on. This should be the mechanism that leads to hadronization, although we are able to describe what happens just in the first part of the process. When a quark emits a gluon, in fact, it loses energy and going on further emissions the system lose its perturbative quality and so we lose our predictive power.

However, I think that the fact that the soft gluon is also fundamental to solve IR divergences is just a case. In fact, you have an equal situation for QED IR divergence (for example when you apply radiative corrections to coulumbian scattering) but in this case there is no such phenomenon as hadronization.

So the fact that we can't see free quarks, despite the cross section for producing a pair $q\bar q$ is so good, is that we can only describe what happens just in the first part of the process?

P.s. I'm reading http://moby.mib.infn.it/~oleari/public/QCD/appunti_corso/QCD_lectures_Nason.pdf [Broken] page 19 top and 21 bottom

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The fact that we can't observe free quarks is due to the process of hadronization that I mentioned previously. Our ability to describe or not this physical process obviously doesn't affect the process itself. I just wanted to say that, however, we don't know exactly how hadronization works because we can't describe strong interactions in the low energy limit.

Hadronization is associated with a lower energy scale (few 100 MeV) than the collision in which the quarks are produced (few GeV at least) and therefore a longer timescale. Therefore, one can think of hadronization as a slower process which happens after the initial process and thus doesn't affect it properties (cross section, etc). Hope that gives some intuition.

Thank you!