Understanding IR Divergences in Hadron Colliders

[Jodahr]

Hi @ all,

I have a question about IR divergences at hadron colliders. I can see that there are also IR divergences in loop diagrams such as the vertex correction and so on...

I also see the IR ones in the real gluon/quark/ or photon emission...
so that for example the gluon is soft or collinear to the emitter parton..there I can see it with the amplitudes and the propagators...

but in hadron colliders I saw an additional collinear divergence...if the emitted real gluon is collinear to the unknown part X of the hadron.. p + p -> f + f +g + X..

how can I "see" or understand that divergence...I know that it is absorbed into the PDFs...not as the soft and coll. ones to the emitter parton...they are canceled with the virtual IR divergences...

pls..can someone help me to understand that last divergences?..

thanks

 

[AndyW]

Thank you for your question about IR divergences at hadron colliders. It is a complex topic, but I will try my best to explain it to you.

Firstly, IR (infrared) divergences occur when the momentum of a particle in a loop or emitted from a collision is very small, close to zero. This leads to a singularity in the calculations, which means that the result becomes infinite. This is obviously a problem, as it does not reflect the physical reality of the process.

In loop diagrams, IR divergences can occur when a particle is emitted and then reabsorbed by the same particle. This can happen in the vertex correction you mentioned. In this case, the IR divergence is cancelled out by the virtual IR divergences, as you correctly pointed out.

In real emission processes, such as gluon, quark, or photon emission, IR divergences can occur when the emitted particle is soft or collinear to one of the emitter partons. This is because the particle's momentum is very small in these cases, leading to an IR divergence. These divergences are also cancelled out by the virtual IR divergences.

However, as you mentioned, there is an additional collinear divergence at hadron colliders when the emitted particle is collinear to the unknown part of the hadron. This is because the unknown parton's momentum is not known, and therefore cannot be integrated over in the calculations. This leads to an IR divergence that cannot be cancelled out by the virtual IR divergences.

To understand this divergence, it is important to remember that the hadrons colliding at a collider are made up of partons (quarks and gluons), which have their own momentum distributions within the hadron. These distributions are described by the Parton Distribution Functions (PDFs). When a real particle is emitted at a hadron collider, it can be emitted from any of the partons within the hadron. This creates an uncertainty in the momentum of the emitted particle, which leads to the collinear divergence.

This divergence is absorbed into the PDFs, as you mentioned. The PDFs take into account the uncertainty in the momentum of the emitted particle and include it in the calculations. This allows for the cancellation of the collinear divergence and ensures that the final result is finite.

I hope this helps you understand the last divergences at hadron colliders. If you have any