What are infrared and collinear safety? I'm studying particle jets for the first time and I do not understand what "collinear" and "infrared" safety (which are two requirements that a method for counting jets in an event should fulfill, as I understand) are.
Wikipedia says:

A jet algorithm is infrared safe if it yields the same set of jets after modifying an event to add a soft radiation. Similarly, a jet algorithm is collinear safe if the final set of jets is not changed after introducing a collinear splitting of one of the inputs.


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*What does soft radiation, i.e. the detection of photons in the lower energy part of the X-ray spectrum, have to do with jets counting?

*What does it mean to "introduce a collinear splitting" of the particles detected?

 A: *

*"Soft radiation" in particle physics refers to particles or photons with very low energy, typically much lower than the energy scale of the process being studied. These soft particles can arise from a variety of sources, including quantum fluctuations and the decay of heavier particles. The requirement for an infrared safe jet algorithm means that the presence of these soft particles should not affect the algorithm's ability to identify and count the jets in an event.


*"Collinear splitting" refers to the phenomenon where two particles move in very similar directions and can be difficult to distinguish as separate entities. In such cases, it is possible for a jet algorithm to misinterpret these collinear particles as a single jet, or conversely, to mistakenly split a single jet into two separate jets. The requirement for a collinear safe jet algorithm means that the algorithm should not be sensitive to such collinear splittings and should be able to correctly identify the number of jets in an event regardless of the collinearity of the particles.
